TSTP Solution File: SEV425_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEV425_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 08:12:33 EDT 2022
% Result : Theorem 29.48s 19.14s
% Output : Proof 29.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEV425_1 : TPTP v8.1.0. Released v5.0.0.
% 0.08/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.36 % Computer : n024.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Sep 3 18:51:33 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.37 Usage: tptp [options] [-file:]file
% 0.15/0.37 -h, -? prints this message.
% 0.15/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.37 -m, -model generate model.
% 0.15/0.37 -p, -proof generate proof.
% 0.15/0.37 -c, -core generate unsat core of named formulas.
% 0.15/0.37 -st, -statistics display statistics.
% 0.15/0.37 -t:timeout set timeout (in second).
% 0.15/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.37 -<param>:<value> configuration parameter and value.
% 0.15/0.37 -o:<output-file> file to place output in.
% 29.48/19.14 % SZS status Theorem
% 29.48/19.14 % SZS output start Proof
% 29.48/19.14 tff(cardinality_type, type, (
% 29.48/19.14 cardinality: set > $int)).
% 29.48/19.14 tff(singleton_type, type, (
% 29.48/19.14 singleton: element > set)).
% 29.48/19.14 tff(tptp_fun_X_0_type, type, (
% 29.48/19.14 tptp_fun_X_0: set > element)).
% 29.48/19.14 tff(tptp_fun_A1_6_type, type, (
% 29.48/19.14 tptp_fun_A1_6: set)).
% 29.48/19.14 tff(tptp_fun_X1_4_type, type, (
% 29.48/19.14 tptp_fun_X1_4: element)).
% 29.48/19.14 tff(union_type, type, (
% 29.48/19.14 union: ( set * set ) > set)).
% 29.48/19.14 tff(empty_set_type, type, (
% 29.48/19.14 empty_set: set)).
% 29.48/19.14 tff(intersection_type, type, (
% 29.48/19.14 intersection: ( set * set ) > set)).
% 29.48/19.14 tff(member_type, type, (
% 29.48/19.14 member: ( element * set ) > $o)).
% 29.48/19.14 tff(tptp_fun_A0_7_type, type, (
% 29.48/19.14 tptp_fun_A0_7: set)).
% 29.48/19.14 tff(tptp_fun_A2_5_type, type, (
% 29.48/19.14 tptp_fun_A2_5: set)).
% 29.48/19.14 tff(tptp_fun_X3_2_type, type, (
% 29.48/19.14 tptp_fun_X3_2: element)).
% 29.48/19.14 tff(subset_type, type, (
% 29.48/19.14 subset: ( set * set ) > $o)).
% 29.48/19.14 tff(tptp_fun_X2_3_type, type, (
% 29.48/19.14 tptp_fun_X2_3: element)).
% 29.48/19.14 tff(tptp_fun_C_8_type, type, (
% 29.48/19.14 tptp_fun_C_8: set)).
% 29.48/19.14 tff(tptp_fun_X_1_type, type, (
% 29.48/19.14 tptp_fun_X_1: ( set * set ) > element)).
% 29.48/19.14 tff(1,assumption,((~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)))) | (~((~(intersection(singleton(X1!4), empty_set) = empty_set)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(singleton(X1!4), empty_set)))))), introduced(assumption)).
% 29.48/19.14 tff(2,plain,
% 29.48/19.14 (^[S: set, X: element] : rewrite((~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set)))))) <=> (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S))))))),
% 29.48/19.14 inference(bind,[status(th)],[])).
% 29.48/19.14 tff(3,plain,
% 29.48/19.14 (![S: set, X: element] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set)))))) <=> ![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))),
% 29.48/19.14 inference(quant_intro,[status(thm)],[2])).
% 29.48/19.14 tff(4,plain,
% 29.48/19.14 (^[S: set, X: element] : refl((~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set)))))) <=> (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set)))))))),
% 29.48/19.14 inference(bind,[status(th)],[])).
% 29.48/19.14 tff(5,plain,
% 29.48/19.14 (![S: set, X: element] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set)))))) <=> ![S: set, X: element] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set))))))),
% 29.48/19.14 inference(quant_intro,[status(thm)],[4])).
% 29.48/19.14 tff(6,plain,
% 29.48/19.14 (![S: set] : ![X: element] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set)))))) <=> ![S: set, X: element] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set))))))),
% 29.48/19.14 inference(pull_quant,[status(thm)],[])).
% 29.48/19.14 tff(7,plain,
% 29.48/19.14 (^[S: set] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant((![X: element] : (~member(X, S)) | (~(S = empty_set))) <=> ![X: element] : ((~member(X, S)) | (~(S = empty_set)))), ((~(![X: element] : (~member(X, S)) | (~(S = empty_set)))) <=> (~![X: element] : ((~member(X, S)) | (~(S = empty_set)))))), pull_quant((~![X: element] : ((~member(X, S)) | (~(S = empty_set)))) <=> ?[X: element] : (~((~member(X, S)) | (~(S = empty_set))))), ((~(![X: element] : (~member(X, S)) | (~(S = empty_set)))) <=> ?[X: element] : (~((~member(X, S)) | (~(S = empty_set)))))), (((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set))))) <=> ((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | ?[X: element] : (~((~member(X, S)) | (~(S = empty_set))))))), pull_quant(((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | ?[X: element] : (~((~member(X, S)) | (~(S = empty_set))))) <=> ?[X: element] : ((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set)))))), (((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set))))) <=> ?[X: element] : ((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set))))))), ((~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set)))))) <=> (~?[X: element] : ((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set)))))))), pull_quant((~?[X: element] : ((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set)))))) <=> ![X: element] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set))))))), ((~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set)))))) <=> ![X: element] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set))))))))),
% 29.48/19.15 inference(bind,[status(th)],[])).
% 29.48/19.15 tff(8,plain,
% 29.48/19.15 (![S: set] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set)))))) <=> ![S: set] : ![X: element] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set))))))),
% 29.48/19.15 inference(quant_intro,[status(thm)],[7])).
% 29.48/19.15 tff(9,plain,
% 29.48/19.15 (![S: set] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set)))))) <=> ![S: set, X: element] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set))))))),
% 29.48/19.15 inference(transitivity,[status(thm)],[8, 6])).
% 29.48/19.15 tff(10,plain,
% 29.48/19.15 (![S: set] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set)))))) <=> ![S: set, X: element] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set))))))),
% 29.48/19.15 inference(transitivity,[status(thm)],[9, 5])).
% 29.48/19.15 tff(11,plain,
% 29.48/19.15 (^[S: set] : rewrite((~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set)))))) <=> (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set)))))))),
% 29.48/19.15 inference(bind,[status(th)],[])).
% 29.48/19.15 tff(12,plain,
% 29.48/19.15 (![S: set] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set)))))) <=> ![S: set] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set))))))),
% 29.48/19.15 inference(quant_intro,[status(thm)],[11])).
% 29.48/19.15 tff(13,plain,
% 29.48/19.15 (![S: set] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set)))))) <=> ![S: set, X: element] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set))))))),
% 29.48/19.15 inference(transitivity,[status(thm)],[12, 10])).
% 29.48/19.15 tff(14,plain,
% 29.48/19.15 (^[S: set] : trans(monotonicity(rewrite((![X: element] : (~member(X, S)) | (~(S = empty_set))) <=> (![X: element] : (~member(X, S)) | (~(S = empty_set)))), ((((S = empty_set) | member(tptp_fun_X_0(S), S)) & (![X: element] : (~member(X, S)) | (~(S = empty_set)))) <=> (((S = empty_set) | member(tptp_fun_X_0(S), S)) & (![X: element] : (~member(X, S)) | (~(S = empty_set)))))), rewrite((((S = empty_set) | member(tptp_fun_X_0(S), S)) & (![X: element] : (~member(X, S)) | (~(S = empty_set)))) <=> (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set))))))), ((((S = empty_set) | member(tptp_fun_X_0(S), S)) & (![X: element] : (~member(X, S)) | (~(S = empty_set)))) <=> (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set))))))))),
% 29.48/19.15 inference(bind,[status(th)],[])).
% 29.48/19.15 tff(15,plain,
% 29.48/19.15 (![S: set] : (((S = empty_set) | member(tptp_fun_X_0(S), S)) & (![X: element] : (~member(X, S)) | (~(S = empty_set)))) <=> ![S: set] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set))))))),
% 29.48/19.15 inference(quant_intro,[status(thm)],[14])).
% 29.48/19.15 tff(16,plain,
% 29.48/19.15 (^[S: set] : rewrite((((~(~member(tptp_fun_X_0(S), S))) | (S = empty_set)) & (![X: element] : (~member(X, S)) | (~(S = empty_set)))) <=> (((S = empty_set) | member(tptp_fun_X_0(S), S)) & (![X: element] : (~member(X, S)) | (~(S = empty_set)))))),
% 29.48/19.15 inference(bind,[status(th)],[])).
% 29.48/19.15 tff(17,plain,
% 29.48/19.15 (![S: set] : (((~(~member(tptp_fun_X_0(S), S))) | (S = empty_set)) & (![X: element] : (~member(X, S)) | (~(S = empty_set)))) <=> ![S: set] : (((S = empty_set) | member(tptp_fun_X_0(S), S)) & (![X: element] : (~member(X, S)) | (~(S = empty_set))))),
% 29.48/19.15 inference(quant_intro,[status(thm)],[16])).
% 29.48/19.15 tff(18,plain,
% 29.48/19.15 (![S: set] : (![X: element] : (~member(X, S)) <=> (S = empty_set)) <=> ![S: set] : (![X: element] : (~member(X, S)) <=> (S = empty_set))),
% 29.48/19.15 inference(rewrite,[status(thm)],[])).
% 29.48/19.15 tff(19,axiom,(![S: set] : (![X: element] : (~member(X, S)) <=> (S = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','empty_set')).
% 29.48/19.15 tff(20,plain,
% 29.48/19.15 (![S: set] : (![X: element] : (~member(X, S)) <=> (S = empty_set))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[19, 18])).
% 29.48/19.15 tff(21,plain,(
% 29.48/19.15 ![S: set] : (((~(~member(tptp_fun_X_0(S), S))) | (S = empty_set)) & (![X: element] : (~member(X, S)) | (~(S = empty_set))))),
% 29.48/19.15 inference(skolemize,[status(sab)],[20])).
% 29.48/19.15 tff(22,plain,
% 29.48/19.15 (![S: set] : (((S = empty_set) | member(tptp_fun_X_0(S), S)) & (![X: element] : (~member(X, S)) | (~(S = empty_set))))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[21, 17])).
% 29.48/19.15 tff(23,plain,
% 29.48/19.15 (![S: set] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~(![X: element] : (~member(X, S)) | (~(S = empty_set))))))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[22, 15])).
% 29.48/19.15 tff(24,plain,
% 29.48/19.15 (![S: set, X: element] : (~((~((S = empty_set) | member(tptp_fun_X_0(S), S))) | (~((~member(X, S)) | (~(S = empty_set))))))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[23, 13])).
% 29.48/19.15 tff(25,plain,
% 29.48/19.15 (![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[24, 3])).
% 29.48/19.15 tff(26,plain,
% 29.48/19.15 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)))) | (~((~(intersection(singleton(X1!4), empty_set) = empty_set)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(singleton(X1!4), empty_set)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)))) | (~((~(intersection(singleton(X1!4), empty_set) = empty_set)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(singleton(X1!4), empty_set))))))))),
% 29.48/19.15 inference(rewrite,[status(thm)],[])).
% 29.48/19.15 tff(27,plain,
% 29.48/19.15 ((~((~((~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(singleton(X1!4), empty_set))) | (~(intersection(singleton(X1!4), empty_set) = empty_set)))) | (~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)))))) <=> (~((~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)))) | (~((~(intersection(singleton(X1!4), empty_set) = empty_set)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(singleton(X1!4), empty_set)))))))),
% 29.48/19.15 inference(rewrite,[status(thm)],[])).
% 29.48/19.15 tff(28,plain,
% 29.48/19.15 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(singleton(X1!4), empty_set))) | (~(intersection(singleton(X1!4), empty_set) = empty_set)))) | (~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)))) | (~((~(intersection(singleton(X1!4), empty_set) = empty_set)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(singleton(X1!4), empty_set))))))))),
% 29.48/19.15 inference(monotonicity,[status(thm)],[27])).
% 29.48/19.15 tff(29,plain,
% 29.48/19.15 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(singleton(X1!4), empty_set))) | (~(intersection(singleton(X1!4), empty_set) = empty_set)))) | (~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)))) | (~((~(intersection(singleton(X1!4), empty_set) = empty_set)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(singleton(X1!4), empty_set))))))))),
% 29.48/19.15 inference(transitivity,[status(thm)],[28, 26])).
% 29.48/19.15 tff(30,plain,
% 29.48/19.15 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(singleton(X1!4), empty_set))) | (~(intersection(singleton(X1!4), empty_set) = empty_set)))) | (~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set))))))),
% 29.48/19.15 inference(quant_inst,[status(thm)],[])).
% 29.48/19.15 tff(31,plain,
% 29.48/19.15 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)))) | (~((~(intersection(singleton(X1!4), empty_set) = empty_set)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(singleton(X1!4), empty_set)))))))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[30, 29])).
% 29.48/19.15 tff(32,plain,
% 29.48/19.15 ($false),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[31, 25, 1])).
% 29.48/19.15 tff(33,plain,(~((~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)))) | (~((~(intersection(singleton(X1!4), empty_set) = empty_set)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(singleton(X1!4), empty_set))))))), inference(lemma,lemma(discharge,[]))).
% 29.48/19.15 tff(34,plain,
% 29.48/19.15 (((~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)))) | (~((~(intersection(singleton(X1!4), empty_set) = empty_set)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(singleton(X1!4), empty_set)))))) | ((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)))),
% 29.48/19.15 inference(tautology,[status(thm)],[])).
% 29.48/19.15 tff(35,plain,
% 29.48/19.15 ((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set))),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[34, 33])).
% 29.48/19.15 tff(36,assumption,(~(member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), singleton(X1!4))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set)))))), introduced(assumption)).
% 29.48/19.15 tff(37,plain,
% 29.48/19.15 (^[X: element, A: set, B: set] : refl((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 29.48/19.15 inference(bind,[status(th)],[])).
% 29.48/19.15 tff(38,plain,
% 29.48/19.15 (![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> ![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 29.48/19.15 inference(quant_intro,[status(thm)],[37])).
% 29.48/19.15 tff(39,plain,
% 29.48/19.15 (^[X: element, A: set, B: set] : rewrite((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 29.48/19.15 inference(bind,[status(th)],[])).
% 29.48/19.15 tff(40,plain,
% 29.48/19.15 (![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 29.48/19.15 inference(quant_intro,[status(thm)],[39])).
% 29.48/19.15 tff(41,plain,
% 29.48/19.15 (![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 29.48/19.15 inference(rewrite,[status(thm)],[])).
% 29.48/19.15 tff(42,axiom,(![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersection')).
% 29.48/19.15 tff(43,plain,
% 29.48/19.15 (![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[42, 41])).
% 29.48/19.15 tff(44,plain,(
% 29.48/19.15 ![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 29.48/19.15 inference(skolemize,[status(sab)],[43])).
% 29.48/19.15 tff(45,plain,
% 29.48/19.15 (![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[44, 40])).
% 29.48/19.15 tff(46,plain,
% 29.48/19.15 (![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[45, 38])).
% 29.48/19.15 tff(47,plain,
% 29.48/19.15 ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), singleton(X1!4))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set)))))),
% 29.48/19.15 inference(quant_inst,[status(thm)],[])).
% 29.48/19.15 tff(48,plain,
% 29.48/19.15 ($false),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[47, 46, 36])).
% 29.48/19.15 tff(49,plain,(member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), singleton(X1!4))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set))))), inference(lemma,lemma(discharge,[]))).
% 29.48/19.15 tff(50,assumption,(member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set)), introduced(assumption)).
% 29.48/19.15 tff(51,plain,
% 29.48/19.15 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set)))),
% 29.48/19.15 inference(rewrite,[status(thm)],[])).
% 29.48/19.15 tff(52,plain,
% 29.48/19.15 ((~((~((~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set)) | (~(empty_set = empty_set)))) | (~((empty_set = empty_set) | member(tptp_fun_X_0(empty_set), empty_set))))) <=> (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set))),
% 29.48/19.15 inference(rewrite,[status(thm)],[])).
% 29.48/19.15 tff(53,plain,
% 29.48/19.15 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set)) | (~(empty_set = empty_set)))) | (~((empty_set = empty_set) | member(tptp_fun_X_0(empty_set), empty_set)))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set)))),
% 29.48/19.15 inference(monotonicity,[status(thm)],[52])).
% 29.48/19.15 tff(54,plain,
% 29.48/19.15 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set)) | (~(empty_set = empty_set)))) | (~((empty_set = empty_set) | member(tptp_fun_X_0(empty_set), empty_set)))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set)))),
% 29.48/19.15 inference(transitivity,[status(thm)],[53, 51])).
% 29.48/19.15 tff(55,plain,
% 29.48/19.15 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set)) | (~(empty_set = empty_set)))) | (~((empty_set = empty_set) | member(tptp_fun_X_0(empty_set), empty_set)))))),
% 29.48/19.15 inference(quant_inst,[status(thm)],[])).
% 29.48/19.15 tff(56,plain,
% 29.48/19.15 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[55, 54])).
% 29.48/19.15 tff(57,plain,
% 29.48/19.15 ($false),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[56, 25, 50])).
% 29.48/19.15 tff(58,plain,(~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set)), inference(lemma,lemma(discharge,[]))).
% 29.48/19.15 tff(59,plain,
% 29.48/19.15 (((~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), singleton(X1!4))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set))) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set)),
% 29.48/19.15 inference(tautology,[status(thm)],[])).
% 29.48/19.15 tff(60,plain,
% 29.48/19.15 ((~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), singleton(X1!4))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set))),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[59, 58])).
% 29.48/19.15 tff(61,plain,
% 29.48/19.15 ((~(member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), singleton(X1!4))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set)))))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set))) | (~((~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), singleton(X1!4))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set))))),
% 29.48/19.15 inference(tautology,[status(thm)],[])).
% 29.48/19.15 tff(62,plain,
% 29.48/19.15 ((~(member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), singleton(X1!4))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), empty_set)))))) | (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)))),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[61, 60])).
% 29.48/19.15 tff(63,plain,
% 29.48/19.15 (~member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set))),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[62, 49])).
% 29.48/19.15 tff(64,plain,
% 29.48/19.15 ((~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)))) | (intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set))),
% 29.48/19.15 inference(tautology,[status(thm)],[])).
% 29.48/19.15 tff(65,plain,
% 29.48/19.15 ((~((intersection(singleton(X1!4), empty_set) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X1!4), empty_set)), intersection(singleton(X1!4), empty_set)))) | (intersection(singleton(X1!4), empty_set) = empty_set)),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[64, 63])).
% 29.48/19.15 tff(66,plain,
% 29.48/19.15 (intersection(singleton(X1!4), empty_set) = empty_set),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[65, 35])).
% 29.48/19.15 tff(67,plain,
% 29.48/19.15 (^[X: element, S: set] : refl(((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(S), $product(-1, cardinality(union(singleton(X), S)))) = -1)) <=> ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(S), $product(-1, cardinality(union(singleton(X), S)))) = -1)))),
% 29.48/19.15 inference(bind,[status(th)],[])).
% 29.48/19.15 tff(68,plain,
% 29.48/19.15 (![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(S), $product(-1, cardinality(union(singleton(X), S)))) = -1)) <=> ![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(S), $product(-1, cardinality(union(singleton(X), S)))) = -1))),
% 29.48/19.15 inference(quant_intro,[status(thm)],[67])).
% 29.48/19.15 tff(69,plain,
% 29.48/19.15 (^[X: element, S: set] : rewrite(((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(union(singleton(X), S)), $product(-1, cardinality(S))) = 1)) <=> ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(S), $product(-1, cardinality(union(singleton(X), S)))) = -1)))),
% 29.48/19.15 inference(bind,[status(th)],[])).
% 29.48/19.15 tff(70,plain,
% 29.48/19.15 (![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(union(singleton(X), S)), $product(-1, cardinality(S))) = 1)) <=> ![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(S), $product(-1, cardinality(union(singleton(X), S)))) = -1))),
% 29.48/19.15 inference(quant_intro,[status(thm)],[69])).
% 29.48/19.15 tff(71,plain,
% 29.48/19.15 (^[X: element, S: set] : rewrite(((intersection(singleton(X), S) = empty_set) <=> (cardinality(union(singleton(X), S)) = $sum(1, cardinality(S)))) <=> ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(union(singleton(X), S)), $product(-1, cardinality(S))) = 1)))),
% 29.48/19.15 inference(bind,[status(th)],[])).
% 29.48/19.15 tff(72,plain,
% 29.48/19.15 (![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> (cardinality(union(singleton(X), S)) = $sum(1, cardinality(S)))) <=> ![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(union(singleton(X), S)), $product(-1, cardinality(S))) = 1))),
% 29.48/19.15 inference(quant_intro,[status(thm)],[71])).
% 29.48/19.15 tff(73,plain,
% 29.48/19.15 (![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> (cardinality(union(singleton(X), S)) = $sum(1, cardinality(S)))) <=> ![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> (cardinality(union(singleton(X), S)) = $sum(1, cardinality(S))))),
% 29.48/19.15 inference(rewrite,[status(thm)],[])).
% 29.48/19.15 tff(74,plain,
% 29.48/19.15 (^[X: element, S: set] : rewrite(((intersection(singleton(X), S) = empty_set) <=> (cardinality(union(singleton(X), S)) = $sum(cardinality(S), 1))) <=> ((intersection(singleton(X), S) = empty_set) <=> (cardinality(union(singleton(X), S)) = $sum(1, cardinality(S)))))),
% 29.48/19.15 inference(bind,[status(th)],[])).
% 29.48/19.15 tff(75,plain,
% 29.48/19.15 (![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> (cardinality(union(singleton(X), S)) = $sum(cardinality(S), 1))) <=> ![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> (cardinality(union(singleton(X), S)) = $sum(1, cardinality(S))))),
% 29.48/19.15 inference(quant_intro,[status(thm)],[74])).
% 29.48/19.15 tff(76,axiom,(![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> (cardinality(union(singleton(X), S)) = $sum(cardinality(S), 1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cardinality_intersection_2')).
% 29.48/19.15 tff(77,plain,
% 29.48/19.15 (![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> (cardinality(union(singleton(X), S)) = $sum(1, cardinality(S))))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[76, 75])).
% 29.48/19.15 tff(78,plain,
% 29.48/19.15 (![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> (cardinality(union(singleton(X), S)) = $sum(1, cardinality(S))))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[77, 73])).
% 29.48/19.15 tff(79,plain,
% 29.48/19.15 (![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(union(singleton(X), S)), $product(-1, cardinality(S))) = 1))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[78, 72])).
% 29.48/19.15 tff(80,plain,
% 29.48/19.15 (![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(S), $product(-1, cardinality(union(singleton(X), S)))) = -1))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[79, 70])).
% 29.48/19.15 tff(81,plain,(
% 29.48/19.15 ![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(S), $product(-1, cardinality(union(singleton(X), S)))) = -1))),
% 29.48/19.15 inference(skolemize,[status(sab)],[80])).
% 29.48/19.15 tff(82,plain,
% 29.48/19.15 (![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(S), $product(-1, cardinality(union(singleton(X), S)))) = -1))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[81, 68])).
% 29.48/19.15 tff(83,plain,
% 29.48/19.15 ((~![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(S), $product(-1, cardinality(union(singleton(X), S)))) = -1))) | ((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))) = -1))),
% 29.48/19.15 inference(quant_inst,[status(thm)],[])).
% 29.48/19.15 tff(84,plain,
% 29.48/19.15 ((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))) = -1)),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[83, 82])).
% 29.48/19.15 tff(85,plain,
% 29.48/19.15 ((~((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))) = -1))) | (~(intersection(singleton(X1!4), empty_set) = empty_set)) | ($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))) = -1)),
% 29.48/19.15 inference(tautology,[status(thm)],[])).
% 29.48/19.15 tff(86,plain,
% 29.48/19.15 ((~(intersection(singleton(X1!4), empty_set) = empty_set)) | ($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))) = -1)),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[85, 84])).
% 29.48/19.15 tff(87,plain,
% 29.48/19.15 ($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))) = -1),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[86, 66])).
% 29.48/19.15 tff(88,plain,
% 29.48/19.15 ((~($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))) = -1)) | $greatereq($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))), -1)),
% 29.48/19.15 inference(theory_lemma,[status(thm)],[])).
% 29.48/19.15 tff(89,plain,
% 29.48/19.15 ($greatereq($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))), -1)),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[88, 87])).
% 29.48/19.15 tff(90,plain,
% 29.48/19.15 (^[A: set, B: set] : refl(((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0)) <=> ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0)))),
% 29.48/19.15 inference(bind,[status(th)],[])).
% 29.48/19.15 tff(91,plain,
% 29.48/19.15 (![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0)) <=> ![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))),
% 29.48/19.15 inference(quant_intro,[status(thm)],[90])).
% 29.48/19.15 tff(92,plain,
% 29.48/19.15 (^[A: set, B: set] : rewrite(((intersection(A, B) = empty_set) <=> ($sum(cardinality(union(A, B)), $sum($product(-1, cardinality(A)), $product(-1, cardinality(B)))) = 0)) <=> ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0)))),
% 29.48/19.15 inference(bind,[status(th)],[])).
% 29.48/19.15 tff(93,plain,
% 29.48/19.15 (![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(union(A, B)), $sum($product(-1, cardinality(A)), $product(-1, cardinality(B)))) = 0)) <=> ![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))),
% 29.48/19.15 inference(quant_intro,[status(thm)],[92])).
% 29.48/19.15 tff(94,plain,
% 29.48/19.15 (^[A: set, B: set] : rewrite(((intersection(A, B) = empty_set) <=> (cardinality(union(A, B)) = $sum(cardinality(A), cardinality(B)))) <=> ((intersection(A, B) = empty_set) <=> ($sum(cardinality(union(A, B)), $sum($product(-1, cardinality(A)), $product(-1, cardinality(B)))) = 0)))),
% 29.48/19.15 inference(bind,[status(th)],[])).
% 29.48/19.15 tff(95,plain,
% 29.48/19.15 (![A: set, B: set] : ((intersection(A, B) = empty_set) <=> (cardinality(union(A, B)) = $sum(cardinality(A), cardinality(B)))) <=> ![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(union(A, B)), $sum($product(-1, cardinality(A)), $product(-1, cardinality(B)))) = 0))),
% 29.48/19.15 inference(quant_intro,[status(thm)],[94])).
% 29.48/19.15 tff(96,plain,
% 29.48/19.15 (![A: set, B: set] : ((intersection(A, B) = empty_set) <=> (cardinality(union(A, B)) = $sum(cardinality(A), cardinality(B)))) <=> ![A: set, B: set] : ((intersection(A, B) = empty_set) <=> (cardinality(union(A, B)) = $sum(cardinality(A), cardinality(B))))),
% 29.48/19.15 inference(rewrite,[status(thm)],[])).
% 29.48/19.15 tff(97,axiom,(![A: set, B: set] : ((intersection(A, B) = empty_set) <=> (cardinality(union(A, B)) = $sum(cardinality(A), cardinality(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cardinality_union')).
% 29.48/19.15 tff(98,plain,
% 29.48/19.15 (![A: set, B: set] : ((intersection(A, B) = empty_set) <=> (cardinality(union(A, B)) = $sum(cardinality(A), cardinality(B))))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[97, 96])).
% 29.48/19.15 tff(99,plain,
% 29.48/19.15 (![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(union(A, B)), $sum($product(-1, cardinality(A)), $product(-1, cardinality(B)))) = 0))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[98, 95])).
% 29.48/19.15 tff(100,plain,
% 29.48/19.15 (![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[99, 93])).
% 29.48/19.15 tff(101,plain,(
% 29.48/19.15 ![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))),
% 29.48/19.15 inference(skolemize,[status(sab)],[100])).
% 29.48/19.15 tff(102,plain,
% 29.48/19.15 (![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[101, 91])).
% 29.48/19.15 tff(103,plain,
% 29.48/19.15 (((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0))) <=> ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0)))),
% 29.48/19.15 inference(rewrite,[status(thm)],[])).
% 29.48/19.15 tff(104,plain,
% 29.48/19.15 (((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(empty_set), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0)) <=> ((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0))),
% 29.48/19.15 inference(rewrite,[status(thm)],[])).
% 29.48/19.15 tff(105,plain,
% 29.48/19.15 (((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(empty_set), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0))) <=> ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0)))),
% 29.48/19.15 inference(monotonicity,[status(thm)],[104])).
% 29.48/19.15 tff(106,plain,
% 29.48/19.15 (((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(empty_set), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0))) <=> ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0)))),
% 29.48/19.15 inference(transitivity,[status(thm)],[105, 103])).
% 29.48/19.15 tff(107,plain,
% 29.48/19.15 ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(empty_set), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0))),
% 29.48/19.15 inference(quant_inst,[status(thm)],[])).
% 29.48/19.15 tff(108,plain,
% 29.48/19.15 ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0))),
% 29.48/19.15 inference(modus_ponens,[status(thm)],[107, 106])).
% 29.48/19.15 tff(109,plain,
% 29.48/19.15 ((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0)),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[108, 102])).
% 29.48/19.15 tff(110,plain,
% 29.48/19.15 ((~((intersection(singleton(X1!4), empty_set) = empty_set) <=> ($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0))) | (~(intersection(singleton(X1!4), empty_set) = empty_set)) | ($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0)),
% 29.48/19.15 inference(tautology,[status(thm)],[])).
% 29.48/19.15 tff(111,plain,
% 29.48/19.15 ((~(intersection(singleton(X1!4), empty_set) = empty_set)) | ($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0)),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[110, 109])).
% 29.48/19.15 tff(112,plain,
% 29.48/19.15 ($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0),
% 29.48/19.15 inference(unit_resolution,[status(thm)],[111, 66])).
% 29.48/19.15 tff(113,plain,
% 29.48/19.15 ((~($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0)) | $lesseq($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))), 0)),
% 29.48/19.16 inference(theory_lemma,[status(thm)],[])).
% 29.48/19.16 tff(114,plain,
% 29.48/19.16 ($lesseq($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))), 0)),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[113, 112])).
% 29.48/19.16 tff(115,plain,
% 29.48/19.16 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)) | (~member(X1!4, intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) | (~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)) | (~member(X1!4, intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) | (~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))))))),
% 29.48/19.16 inference(rewrite,[status(thm)],[])).
% 29.48/19.16 tff(116,plain,
% 29.48/19.16 ((~((~((~member(X1!4, intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))) | (~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)))) | (~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))))) <=> (~((~((~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)) | (~member(X1!4, intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) | (~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))))),
% 29.48/19.16 inference(rewrite,[status(thm)],[])).
% 29.48/19.16 tff(117,plain,
% 29.48/19.16 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(X1!4, intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))) | (~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)))) | (~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)) | (~member(X1!4, intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) | (~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))))))),
% 29.48/19.16 inference(monotonicity,[status(thm)],[116])).
% 29.48/19.16 tff(118,plain,
% 29.48/19.16 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(X1!4, intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))) | (~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)))) | (~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)) | (~member(X1!4, intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) | (~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))))))),
% 29.48/19.16 inference(transitivity,[status(thm)],[117, 115])).
% 29.48/19.16 tff(119,plain,
% 29.48/19.16 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(X1!4, intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))) | (~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)))) | (~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))))),
% 29.48/19.16 inference(quant_inst,[status(thm)],[])).
% 29.48/19.16 tff(120,plain,
% 29.48/19.16 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)) | (~member(X1!4, intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) | (~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))))),
% 29.48/19.16 inference(modus_ponens,[status(thm)],[119, 118])).
% 29.48/19.16 tff(121,plain,
% 29.48/19.16 (~((~((~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)) | (~member(X1!4, intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) | (~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))))),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[120, 25])).
% 29.48/19.16 tff(122,plain,
% 29.48/19.16 (((~((~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)) | (~member(X1!4, intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) | (~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) | ((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))),
% 29.48/19.16 inference(tautology,[status(thm)],[])).
% 29.48/19.16 tff(123,plain,
% 29.48/19.16 ((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[122, 121])).
% 29.48/19.16 tff(124,assumption,(~(member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4))) <=> (~((~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4))))))), introduced(assumption)).
% 29.48/19.16 tff(125,plain,
% 29.48/19.16 ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4))) <=> (~((~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4))))))),
% 29.48/19.16 inference(quant_inst,[status(thm)],[])).
% 29.48/19.16 tff(126,plain,
% 29.48/19.16 ($false),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[125, 46, 124])).
% 29.48/19.16 tff(127,plain,(member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4))) <=> (~((~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4)))))), inference(lemma,lemma(discharge,[]))).
% 29.48/19.16 tff(128,plain,
% 29.48/19.16 (^[X: element, A: element] : refl((member(X, singleton(A)) <=> (X = A)) <=> (member(X, singleton(A)) <=> (X = A)))),
% 29.48/19.16 inference(bind,[status(th)],[])).
% 29.48/19.16 tff(129,plain,
% 29.48/19.16 (![X: element, A: element] : (member(X, singleton(A)) <=> (X = A)) <=> ![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))),
% 29.48/19.16 inference(quant_intro,[status(thm)],[128])).
% 29.48/19.16 tff(130,plain,
% 29.48/19.16 (![X: element, A: element] : (member(X, singleton(A)) <=> (X = A)) <=> ![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))),
% 29.48/19.16 inference(rewrite,[status(thm)],[])).
% 29.48/19.16 tff(131,axiom,(![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','singleton')).
% 29.48/19.16 tff(132,plain,
% 29.48/19.16 (![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))),
% 29.48/19.16 inference(modus_ponens,[status(thm)],[131, 130])).
% 29.48/19.16 tff(133,plain,(
% 29.48/19.16 ![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))),
% 29.48/19.16 inference(skolemize,[status(sab)],[132])).
% 29.48/19.16 tff(134,plain,
% 29.48/19.16 (![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))),
% 29.48/19.16 inference(modus_ponens,[status(thm)],[133, 129])).
% 29.48/19.16 tff(135,plain,
% 29.48/19.16 ((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4)) <=> (tptp_fun_X_0(intersection(A0!7, singleton(X1!4))) = X1!4))),
% 29.48/19.16 inference(quant_inst,[status(thm)],[])).
% 29.48/19.16 tff(136,plain,
% 29.48/19.16 (member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4)) <=> (tptp_fun_X_0(intersection(A0!7, singleton(X1!4))) = X1!4)),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[135, 134])).
% 29.48/19.16 tff(137,assumption,(~((~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4))))), introduced(assumption)).
% 29.48/19.16 tff(138,plain,
% 29.48/19.16 (((~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4)))) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4))),
% 29.48/19.16 inference(tautology,[status(thm)],[])).
% 29.48/19.16 tff(139,plain,
% 29.48/19.16 (member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4))),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[138, 137])).
% 29.48/19.16 tff(140,plain,
% 29.48/19.16 ((~(member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4)) <=> (tptp_fun_X_0(intersection(A0!7, singleton(X1!4))) = X1!4))) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4))) | (tptp_fun_X_0(intersection(A0!7, singleton(X1!4))) = X1!4)),
% 29.48/19.16 inference(tautology,[status(thm)],[])).
% 29.48/19.16 tff(141,plain,
% 29.48/19.16 ((~(member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4)) <=> (tptp_fun_X_0(intersection(A0!7, singleton(X1!4))) = X1!4))) | (tptp_fun_X_0(intersection(A0!7, singleton(X1!4))) = X1!4)),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[140, 139])).
% 29.48/19.16 tff(142,plain,
% 29.48/19.16 (tptp_fun_X_0(intersection(A0!7, singleton(X1!4))) = X1!4),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[141, 136])).
% 29.48/19.16 tff(143,plain,
% 29.48/19.16 (member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7) <=> member(X1!4, A0!7)),
% 29.48/19.16 inference(monotonicity,[status(thm)],[142])).
% 29.48/19.16 tff(144,plain,
% 29.48/19.16 (member(X1!4, A0!7) <=> member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7)),
% 29.48/19.16 inference(symmetry,[status(thm)],[143])).
% 29.48/19.16 tff(145,plain,
% 29.48/19.16 ((~member(X1!4, A0!7)) <=> (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7))),
% 29.48/19.16 inference(monotonicity,[status(thm)],[144])).
% 29.48/19.16 tff(146,plain,
% 29.48/19.16 ((~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | ($sum(cardinality(C), $product(-1, cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))))) = -3))) <=> (~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | ($sum(cardinality(C), $product(-1, cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))))) = -3)))),
% 29.48/19.16 inference(rewrite,[status(thm)],[])).
% 29.48/19.16 tff(147,plain,
% 29.48/19.16 ((~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | ($sum(cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))), $product(-1, cardinality(C))) = 3))) <=> (~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | ($sum(cardinality(C), $product(-1, cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))))) = -3)))),
% 29.48/19.16 inference(rewrite,[status(thm)],[])).
% 29.48/19.16 tff(148,plain,
% 29.48/19.16 ((~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | (cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))) = $sum(3, cardinality(C))))) <=> (~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | ($sum(cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))), $product(-1, cardinality(C))) = 3)))),
% 29.48/19.16 inference(rewrite,[status(thm)],[])).
% 29.48/19.16 tff(149,plain,
% 29.48/19.16 ((~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | (cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))) = $sum(3, cardinality(C))))) <=> (~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | (cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))) = $sum(3, cardinality(C)))))),
% 29.48/19.16 inference(rewrite,[status(thm)],[])).
% 29.48/19.16 tff(150,plain,
% 29.48/19.16 ((~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((((((subset(C, A0) & (~member(X1, A0))) & subset(union(A0, singleton(X1)), A1)) & (~member(X2, A1))) & subset(union(A1, singleton(X2)), A2)) & (~member(X3, A2))) => (cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))) = $sum(cardinality(C), 3)))) <=> (~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | (cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))) = $sum(3, cardinality(C)))))),
% 29.48/19.16 inference(rewrite,[status(thm)],[])).
% 29.48/19.16 tff(151,axiom,(~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((((((subset(C, A0) & (~member(X1, A0))) & subset(union(A0, singleton(X1)), A1)) & (~member(X2, A1))) & subset(union(A1, singleton(X2)), A2)) & (~member(X3, A2))) => (cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))) = $sum(cardinality(C), 3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','vc5')).
% 29.48/19.16 tff(152,plain,
% 29.48/19.16 (~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | (cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))) = $sum(3, cardinality(C))))),
% 29.48/19.16 inference(modus_ponens,[status(thm)],[151, 150])).
% 29.48/19.16 tff(153,plain,
% 29.48/19.16 (~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | (cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))) = $sum(3, cardinality(C))))),
% 29.48/19.16 inference(modus_ponens,[status(thm)],[152, 149])).
% 29.48/19.16 tff(154,plain,
% 29.48/19.16 (~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | (cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))) = $sum(3, cardinality(C))))),
% 29.48/19.16 inference(modus_ponens,[status(thm)],[153, 149])).
% 29.48/19.16 tff(155,plain,
% 29.48/19.16 (~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | (cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))) = $sum(3, cardinality(C))))),
% 29.48/19.16 inference(modus_ponens,[status(thm)],[154, 149])).
% 29.48/19.16 tff(156,plain,
% 29.48/19.16 (~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | ($sum(cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))), $product(-1, cardinality(C))) = 3))),
% 29.48/19.16 inference(modus_ponens,[status(thm)],[155, 148])).
% 29.48/19.16 tff(157,plain,
% 29.48/19.16 (~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | ($sum(cardinality(C), $product(-1, cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))))) = -3))),
% 29.48/19.16 inference(modus_ponens,[status(thm)],[156, 147])).
% 29.48/19.16 tff(158,plain,
% 29.48/19.16 (~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | ($sum(cardinality(C), $product(-1, cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))))) = -3))),
% 29.48/19.16 inference(modus_ponens,[status(thm)],[157, 146])).
% 29.48/19.16 tff(159,plain,
% 29.48/19.16 (~![C: set, A0: set, A1: set, A2: set, X1: element, X2: element, X3: element] : ((~(subset(C, A0) & (~member(X1, A0)) & subset(union(A0, singleton(X1)), A1) & (~member(X2, A1)) & subset(union(A1, singleton(X2)), A2) & (~member(X3, A2)))) | ($sum(cardinality(C), $product(-1, cardinality(union(union(union(C, singleton(X1)), singleton(X2)), singleton(X3))))) = -3))),
% 29.48/19.16 inference(modus_ponens,[status(thm)],[158, 146])).
% 29.48/19.16 tff(160,plain,(
% 29.48/19.16 ~((~(subset(C!8, A0!7) & (~member(X1!4, A0!7)) & subset(union(A0!7, singleton(X1!4)), A1!6) & (~member(X2!3, A1!6)) & subset(union(A1!6, singleton(X2!3)), A2!5) & (~member(X3!2, A2!5)))) | ($sum(cardinality(C!8), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))) = -3))),
% 29.48/19.16 inference(skolemize,[status(sab)],[159])).
% 29.48/19.16 tff(161,plain,
% 29.48/19.16 (subset(C!8, A0!7) & (~member(X1!4, A0!7)) & subset(union(A0!7, singleton(X1!4)), A1!6) & (~member(X2!3, A1!6)) & subset(union(A1!6, singleton(X2!3)), A2!5) & (~member(X3!2, A2!5))),
% 29.48/19.16 inference(or_elim,[status(thm)],[160])).
% 29.48/19.16 tff(162,plain,
% 29.48/19.16 (~member(X1!4, A0!7)),
% 29.48/19.16 inference(and_elim,[status(thm)],[161])).
% 29.48/19.16 tff(163,plain,
% 29.48/19.16 (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7)),
% 29.48/19.16 inference(modus_ponens,[status(thm)],[162, 145])).
% 29.48/19.16 tff(164,plain,
% 29.48/19.16 (((~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4)))) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7)),
% 29.48/19.16 inference(tautology,[status(thm)],[])).
% 29.48/19.16 tff(165,plain,
% 29.48/19.16 (member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7)),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[164, 137])).
% 29.48/19.16 tff(166,plain,
% 29.48/19.16 ($false),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[165, 163])).
% 29.48/19.16 tff(167,plain,((~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4)))), inference(lemma,lemma(discharge,[]))).
% 29.48/19.16 tff(168,plain,
% 29.48/19.16 ((~(member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4))) <=> (~((~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4))))))) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4)))) | (~((~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4)))))),
% 29.48/19.16 inference(tautology,[status(thm)],[])).
% 29.48/19.16 tff(169,plain,
% 29.48/19.16 ((~(member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4))) <=> (~((~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), A0!7)) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), singleton(X1!4))))))) | (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4))))),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[168, 167])).
% 29.48/19.16 tff(170,plain,
% 29.48/19.16 (~member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4)))),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[169, 127])).
% 29.48/19.16 tff(171,plain,
% 29.48/19.16 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(A0!7, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_0(A1!6), intersection(A0!7, singleton(X1!4)))))) | (~((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(A0!7, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_0(A1!6), intersection(A0!7, singleton(X1!4)))))) | (~((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4))))))))),
% 29.48/19.16 inference(rewrite,[status(thm)],[])).
% 29.48/19.16 tff(172,plain,
% 29.48/19.16 ((~((~((~member(tptp_fun_X_0(A1!6), intersection(A0!7, singleton(X1!4)))) | (~(intersection(A0!7, singleton(X1!4)) = empty_set)))) | (~((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4))))))) <=> (~((~((~(intersection(A0!7, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_0(A1!6), intersection(A0!7, singleton(X1!4)))))) | (~((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4)))))))),
% 29.48/19.16 inference(rewrite,[status(thm)],[])).
% 29.48/19.16 tff(173,plain,
% 29.48/19.16 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(A1!6), intersection(A0!7, singleton(X1!4)))) | (~(intersection(A0!7, singleton(X1!4)) = empty_set)))) | (~((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(A0!7, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_0(A1!6), intersection(A0!7, singleton(X1!4)))))) | (~((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4))))))))),
% 29.48/19.16 inference(monotonicity,[status(thm)],[172])).
% 29.48/19.16 tff(174,plain,
% 29.48/19.16 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(A1!6), intersection(A0!7, singleton(X1!4)))) | (~(intersection(A0!7, singleton(X1!4)) = empty_set)))) | (~((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(A0!7, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_0(A1!6), intersection(A0!7, singleton(X1!4)))))) | (~((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4))))))))),
% 29.48/19.16 inference(transitivity,[status(thm)],[173, 171])).
% 29.48/19.16 tff(175,plain,
% 29.48/19.16 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(A1!6), intersection(A0!7, singleton(X1!4)))) | (~(intersection(A0!7, singleton(X1!4)) = empty_set)))) | (~((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4)))))))),
% 29.48/19.16 inference(quant_inst,[status(thm)],[])).
% 29.48/19.16 tff(176,plain,
% 29.48/19.16 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(A0!7, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_0(A1!6), intersection(A0!7, singleton(X1!4)))))) | (~((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4)))))))),
% 29.48/19.16 inference(modus_ponens,[status(thm)],[175, 174])).
% 29.48/19.16 tff(177,plain,
% 29.48/19.16 (~((~((~(intersection(A0!7, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_0(A1!6), intersection(A0!7, singleton(X1!4)))))) | (~((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4))))))),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[176, 25])).
% 29.48/19.16 tff(178,plain,
% 29.48/19.16 (((~((~(intersection(A0!7, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_0(A1!6), intersection(A0!7, singleton(X1!4)))))) | (~((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4)))))) | ((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4))))),
% 29.48/19.16 inference(tautology,[status(thm)],[])).
% 29.48/19.16 tff(179,plain,
% 29.48/19.16 ((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4)))),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[178, 177])).
% 29.48/19.16 tff(180,plain,
% 29.48/19.16 ((~((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4))))) | (intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4)))),
% 29.48/19.16 inference(tautology,[status(thm)],[])).
% 29.48/19.16 tff(181,plain,
% 29.48/19.16 ((intersection(A0!7, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(A0!7, singleton(X1!4))), intersection(A0!7, singleton(X1!4)))),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[180, 179])).
% 29.48/19.16 tff(182,plain,
% 29.48/19.16 (intersection(A0!7, singleton(X1!4)) = empty_set),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[181, 170])).
% 29.48/19.16 tff(183,plain,
% 29.48/19.16 (empty_set = intersection(A0!7, singleton(X1!4))),
% 29.48/19.16 inference(symmetry,[status(thm)],[182])).
% 29.48/19.16 tff(184,plain,
% 29.48/19.16 (intersection(singleton(tptp_fun_X_0(A1!6)), empty_set) = intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))),
% 29.48/19.16 inference(monotonicity,[status(thm)],[183])).
% 29.48/19.16 tff(185,plain,
% 29.48/19.16 (member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), empty_set)) <=> member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))),
% 29.48/19.16 inference(monotonicity,[status(thm)],[184])).
% 29.48/19.16 tff(186,plain,
% 29.48/19.16 (member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))) <=> member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), empty_set))),
% 29.48/19.16 inference(symmetry,[status(thm)],[185])).
% 29.48/19.16 tff(187,assumption,(member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))), introduced(assumption)).
% 29.48/19.16 tff(188,plain,
% 29.48/19.16 (member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), empty_set))),
% 29.48/19.16 inference(modus_ponens,[status(thm)],[187, 186])).
% 29.48/19.16 tff(189,plain,
% 29.48/19.16 ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), empty_set)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), singleton(tptp_fun_X_0(A1!6)))) | (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set)))))),
% 29.48/19.16 inference(quant_inst,[status(thm)],[])).
% 29.48/19.16 tff(190,plain,
% 29.48/19.16 (member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), empty_set)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), singleton(tptp_fun_X_0(A1!6)))) | (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set))))),
% 29.48/19.16 inference(unit_resolution,[status(thm)],[189, 46])).
% 29.48/19.16 tff(191,assumption,(member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set)), introduced(assumption)).
% 29.48/19.17 tff(192,plain,
% 29.48/19.17 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set)))),
% 29.48/19.17 inference(rewrite,[status(thm)],[])).
% 29.48/19.17 tff(193,plain,
% 29.48/19.17 ((~((~((~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set)) | (~(empty_set = empty_set)))) | (~((empty_set = empty_set) | member(tptp_fun_X_0(empty_set), empty_set))))) <=> (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set))),
% 29.48/19.17 inference(rewrite,[status(thm)],[])).
% 29.48/19.17 tff(194,plain,
% 29.48/19.17 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set)) | (~(empty_set = empty_set)))) | (~((empty_set = empty_set) | member(tptp_fun_X_0(empty_set), empty_set)))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set)))),
% 29.48/19.17 inference(monotonicity,[status(thm)],[193])).
% 29.48/19.17 tff(195,plain,
% 29.48/19.17 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set)) | (~(empty_set = empty_set)))) | (~((empty_set = empty_set) | member(tptp_fun_X_0(empty_set), empty_set)))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set)))),
% 29.48/19.17 inference(transitivity,[status(thm)],[194, 192])).
% 29.48/19.17 tff(196,plain,
% 29.48/19.17 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set)) | (~(empty_set = empty_set)))) | (~((empty_set = empty_set) | member(tptp_fun_X_0(empty_set), empty_set)))))),
% 29.48/19.17 inference(quant_inst,[status(thm)],[])).
% 29.48/19.17 tff(197,plain,
% 29.48/19.17 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set))),
% 29.48/19.17 inference(modus_ponens,[status(thm)],[196, 195])).
% 29.48/19.17 tff(198,plain,
% 29.48/19.17 ($false),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[197, 25, 191])).
% 29.48/19.17 tff(199,plain,(~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set)), inference(lemma,lemma(discharge,[]))).
% 29.48/19.17 tff(200,plain,
% 29.48/19.17 (((~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), singleton(tptp_fun_X_0(A1!6)))) | (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set))) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set)),
% 29.48/19.17 inference(tautology,[status(thm)],[])).
% 29.48/19.17 tff(201,plain,
% 29.48/19.17 ((~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), singleton(tptp_fun_X_0(A1!6)))) | (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set))),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[200, 199])).
% 29.48/19.17 tff(202,plain,
% 29.48/19.17 ((~(member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), empty_set)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), singleton(tptp_fun_X_0(A1!6)))) | (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set)))))) | (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), empty_set))) | (~((~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), singleton(tptp_fun_X_0(A1!6)))) | (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set))))),
% 29.48/19.17 inference(tautology,[status(thm)],[])).
% 29.48/19.17 tff(203,plain,
% 29.48/19.17 ((~(member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), empty_set)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), singleton(tptp_fun_X_0(A1!6)))) | (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), empty_set)))))) | (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), empty_set)))),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[202, 201])).
% 29.48/19.17 tff(204,plain,
% 29.48/19.17 (~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), empty_set))),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[203, 190])).
% 29.48/19.17 tff(205,plain,
% 29.48/19.17 ($false),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[204, 188])).
% 29.48/19.17 tff(206,plain,(~member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))), inference(lemma,lemma(discharge,[]))).
% 29.48/19.17 tff(207,plain,
% 29.48/19.17 ((~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))) | (intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) | member(tptp_fun_X_0(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))),
% 29.48/19.17 inference(tautology,[status(thm)],[])).
% 29.48/19.17 tff(208,plain,
% 29.48/19.17 (intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[207, 206, 123])).
% 29.48/19.17 tff(209,plain,
% 29.48/19.17 ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) <=> ($sum(cardinality(intersection(A0!7, singleton(X1!4))), $sum(cardinality(singleton(tptp_fun_X_0(A1!6))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) = 0))),
% 29.48/19.17 inference(quant_inst,[status(thm)],[])).
% 29.48/19.17 tff(210,plain,
% 29.48/19.17 ((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) <=> ($sum(cardinality(intersection(A0!7, singleton(X1!4))), $sum(cardinality(singleton(tptp_fun_X_0(A1!6))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) = 0)),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[209, 102])).
% 29.48/19.17 tff(211,plain,
% 29.48/19.17 ((~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) <=> ($sum(cardinality(intersection(A0!7, singleton(X1!4))), $sum(cardinality(singleton(tptp_fun_X_0(A1!6))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) = 0))) | (~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)) | ($sum(cardinality(intersection(A0!7, singleton(X1!4))), $sum(cardinality(singleton(tptp_fun_X_0(A1!6))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) = 0)),
% 29.48/19.17 inference(tautology,[status(thm)],[])).
% 29.48/19.17 tff(212,plain,
% 29.48/19.17 ((~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)) | ($sum(cardinality(intersection(A0!7, singleton(X1!4))), $sum(cardinality(singleton(tptp_fun_X_0(A1!6))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) = 0)),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[211, 210])).
% 29.48/19.17 tff(213,plain,
% 29.48/19.17 ($sum(cardinality(intersection(A0!7, singleton(X1!4))), $sum(cardinality(singleton(tptp_fun_X_0(A1!6))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) = 0),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[212, 208])).
% 29.48/19.17 tff(214,plain,
% 29.48/19.17 ((~($sum(cardinality(intersection(A0!7, singleton(X1!4))), $sum(cardinality(singleton(tptp_fun_X_0(A1!6))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) = 0)) | $greatereq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $sum(cardinality(singleton(tptp_fun_X_0(A1!6))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))), 0)),
% 29.48/19.17 inference(theory_lemma,[status(thm)],[])).
% 29.48/19.17 tff(215,plain,
% 29.48/19.17 ($greatereq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $sum(cardinality(singleton(tptp_fun_X_0(A1!6))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))), 0)),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[214, 213])).
% 29.48/19.17 tff(216,plain,
% 29.48/19.17 ((~![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(S), $product(-1, cardinality(union(singleton(X), S)))) = -1))) | ((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) <=> ($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))) = -1))),
% 29.48/19.17 inference(quant_inst,[status(thm)],[])).
% 29.48/19.17 tff(217,plain,
% 29.48/19.17 ((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) <=> ($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))) = -1)),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[216, 82])).
% 29.48/19.17 tff(218,plain,
% 29.48/19.17 ((~((intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set) <=> ($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))) = -1))) | (~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)) | ($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))) = -1)),
% 29.48/19.17 inference(tautology,[status(thm)],[])).
% 29.48/19.17 tff(219,plain,
% 29.48/19.17 ((~(intersection(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))) = empty_set)) | ($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))) = -1)),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[218, 217])).
% 29.48/19.17 tff(220,plain,
% 29.48/19.17 ($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))) = -1),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[219, 208])).
% 29.48/19.17 tff(221,plain,
% 29.48/19.17 ((~($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))) = -1)) | $lesseq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))), -1)),
% 29.48/19.17 inference(theory_lemma,[status(thm)],[])).
% 29.48/19.17 tff(222,plain,
% 29.48/19.17 ($lesseq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))), -1)),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[221, 220])).
% 29.48/19.17 tff(223,plain,
% 29.48/19.17 (^[S: set, T: set] : refl(((cardinality(intersection(S, T)) = 0) <=> (intersection(S, T) = empty_set)) <=> ((cardinality(intersection(S, T)) = 0) <=> (intersection(S, T) = empty_set)))),
% 29.48/19.17 inference(bind,[status(th)],[])).
% 29.48/19.17 tff(224,plain,
% 29.48/19.17 (![S: set, T: set] : ((cardinality(intersection(S, T)) = 0) <=> (intersection(S, T) = empty_set)) <=> ![S: set, T: set] : ((cardinality(intersection(S, T)) = 0) <=> (intersection(S, T) = empty_set))),
% 29.48/19.17 inference(quant_intro,[status(thm)],[223])).
% 29.48/19.17 tff(225,plain,
% 29.48/19.17 (![S: set, T: set] : ((cardinality(intersection(S, T)) = 0) <=> (intersection(S, T) = empty_set)) <=> ![S: set, T: set] : ((cardinality(intersection(S, T)) = 0) <=> (intersection(S, T) = empty_set))),
% 29.48/19.17 inference(rewrite,[status(thm)],[])).
% 29.48/19.17 tff(226,axiom,(![S: set, T: set] : ((cardinality(intersection(S, T)) = 0) <=> (intersection(S, T) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cardinality_intersection_3')).
% 29.48/19.17 tff(227,plain,
% 29.48/19.17 (![S: set, T: set] : ((cardinality(intersection(S, T)) = 0) <=> (intersection(S, T) = empty_set))),
% 29.48/19.17 inference(modus_ponens,[status(thm)],[226, 225])).
% 29.48/19.17 tff(228,plain,(
% 29.48/19.17 ![S: set, T: set] : ((cardinality(intersection(S, T)) = 0) <=> (intersection(S, T) = empty_set))),
% 29.48/19.17 inference(skolemize,[status(sab)],[227])).
% 29.48/19.17 tff(229,plain,
% 29.48/19.17 (![S: set, T: set] : ((cardinality(intersection(S, T)) = 0) <=> (intersection(S, T) = empty_set))),
% 29.48/19.17 inference(modus_ponens,[status(thm)],[228, 224])).
% 29.48/19.17 tff(230,plain,
% 29.48/19.17 ((~![S: set, T: set] : ((cardinality(intersection(S, T)) = 0) <=> (intersection(S, T) = empty_set))) | ((cardinality(intersection(A0!7, singleton(X1!4))) = 0) <=> (intersection(A0!7, singleton(X1!4)) = empty_set))),
% 29.48/19.17 inference(quant_inst,[status(thm)],[])).
% 29.48/19.17 tff(231,plain,
% 29.48/19.17 ((cardinality(intersection(A0!7, singleton(X1!4))) = 0) <=> (intersection(A0!7, singleton(X1!4)) = empty_set)),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[230, 229])).
% 29.48/19.17 tff(232,plain,
% 29.48/19.17 ((~((cardinality(intersection(A0!7, singleton(X1!4))) = 0) <=> (intersection(A0!7, singleton(X1!4)) = empty_set))) | (cardinality(intersection(A0!7, singleton(X1!4))) = 0) | (~(intersection(A0!7, singleton(X1!4)) = empty_set))),
% 29.48/19.17 inference(tautology,[status(thm)],[])).
% 29.48/19.17 tff(233,plain,
% 29.48/19.17 ((cardinality(intersection(A0!7, singleton(X1!4))) = 0) | (~(intersection(A0!7, singleton(X1!4)) = empty_set))),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[232, 231])).
% 29.48/19.17 tff(234,plain,
% 29.48/19.17 (cardinality(intersection(A0!7, singleton(X1!4))) = 0),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[233, 182])).
% 29.48/19.17 tff(235,plain,
% 29.48/19.17 ((~(cardinality(intersection(A0!7, singleton(X1!4))) = 0)) | $greatereq(cardinality(intersection(A0!7, singleton(X1!4))), 0)),
% 29.48/19.17 inference(theory_lemma,[status(thm)],[])).
% 29.48/19.17 tff(236,plain,
% 29.48/19.17 ($greatereq(cardinality(intersection(A0!7, singleton(X1!4))), 0)),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[235, 234])).
% 29.48/19.17 tff(237,plain,
% 29.48/19.17 ((~$lesseq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))), -1)) | (~$greatereq(cardinality(intersection(A0!7, singleton(X1!4))), 0)) | (~$lesseq(cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), 0))),
% 29.48/19.17 inference(theory_lemma,[status(thm)],[])).
% 29.48/19.17 tff(238,plain,
% 29.48/19.17 ((~$lesseq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))), -1)) | (~$lesseq(cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), 0))),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[237, 236])).
% 29.48/19.17 tff(239,plain,
% 29.48/19.17 (~$lesseq(cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), 0)),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[238, 222])).
% 29.48/19.17 tff(240,plain,
% 29.48/19.17 ((~(cardinality(intersection(A0!7, singleton(X1!4))) = 0)) | $lesseq(cardinality(intersection(A0!7, singleton(X1!4))), 0)),
% 29.48/19.17 inference(theory_lemma,[status(thm)],[])).
% 29.48/19.17 tff(241,plain,
% 29.48/19.17 ($lesseq(cardinality(intersection(A0!7, singleton(X1!4))), 0)),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[240, 234])).
% 29.48/19.17 tff(242,plain,
% 29.48/19.17 ((~$lesseq($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))), 0)) | (~$greatereq($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))), -1)) | (~$lesseq(cardinality(intersection(A0!7, singleton(X1!4))), 0)) | (~$greatereq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $sum(cardinality(singleton(tptp_fun_X_0(A1!6))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))), 0)) | $lesseq($sum(cardinality(singleton(X1!4)), $product(-1, cardinality(singleton(tptp_fun_X_0(A1!6))))), 0) | $lesseq(cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))), 0)),
% 29.48/19.17 inference(theory_lemma,[status(thm)],[])).
% 29.48/19.17 tff(243,plain,
% 29.48/19.17 ((~$lesseq($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))), 0)) | (~$greatereq($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))), -1)) | $lesseq($sum(cardinality(singleton(X1!4)), $product(-1, cardinality(singleton(tptp_fun_X_0(A1!6))))), 0)),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[242, 241, 239, 215])).
% 29.48/19.17 tff(244,plain,
% 29.48/19.17 ($lesseq($sum(cardinality(singleton(X1!4)), $product(-1, cardinality(singleton(tptp_fun_X_0(A1!6))))), 0)),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[243, 114, 89])).
% 29.48/19.17 tff(245,plain,
% 29.48/19.17 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set)) | (~member(X3!2, intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))) | (~((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set)) | (~member(X3!2, intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))) | (~((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))))))),
% 29.48/19.17 inference(rewrite,[status(thm)],[])).
% 29.48/19.17 tff(246,plain,
% 29.48/19.17 ((~((~((~member(X3!2, intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))) | (~(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set)))) | (~((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))))) <=> (~((~((~(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set)) | (~member(X3!2, intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))) | (~((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))))),
% 29.48/19.17 inference(rewrite,[status(thm)],[])).
% 29.48/19.17 tff(247,plain,
% 29.48/19.17 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(X3!2, intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))) | (~(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set)))) | (~((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set)) | (~member(X3!2, intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))) | (~((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))))))),
% 29.48/19.17 inference(monotonicity,[status(thm)],[246])).
% 29.48/19.17 tff(248,plain,
% 29.48/19.17 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(X3!2, intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))) | (~(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set)))) | (~((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set)) | (~member(X3!2, intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))) | (~((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))))))),
% 29.48/19.17 inference(transitivity,[status(thm)],[247, 245])).
% 29.48/19.17 tff(249,plain,
% 29.48/19.17 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(X3!2, intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))) | (~(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set)))) | (~((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))))),
% 29.48/19.17 inference(quant_inst,[status(thm)],[])).
% 29.48/19.17 tff(250,plain,
% 29.48/19.17 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set)) | (~member(X3!2, intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))) | (~((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))))),
% 29.48/19.17 inference(modus_ponens,[status(thm)],[249, 248])).
% 29.48/19.17 tff(251,plain,
% 29.48/19.17 (~((~((~(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set)) | (~member(X3!2, intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))) | (~((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))))),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[250, 25])).
% 29.48/19.17 tff(252,plain,
% 29.48/19.17 (((~((~(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set)) | (~member(X3!2, intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))) | (~((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))) | ((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))),
% 29.48/19.17 inference(tautology,[status(thm)],[])).
% 29.48/19.17 tff(253,plain,
% 29.48/19.17 ((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))),
% 29.48/19.17 inference(unit_resolution,[status(thm)],[252, 251])).
% 29.48/19.17 tff(254,assumption,(~(member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) <=> (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3)))))))), introduced(assumption)).
% 29.48/19.17 tff(255,plain,
% 29.48/19.17 (((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) <=> (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3)))))))) <=> ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) <=> (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3))))))))),
% 29.48/19.17 inference(rewrite,[status(thm)],[])).
% 29.48/19.17 tff(256,plain,
% 29.48/19.17 ((member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) <=> (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3)))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2)))))) <=> (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) <=> (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3)))))))),
% 29.48/19.17 inference(rewrite,[status(thm)],[])).
% 29.48/19.17 tff(257,plain,
% 29.48/19.17 (((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) <=> (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3)))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))))))) <=> ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) <=> (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3))))))))),
% 29.48/19.17 inference(monotonicity,[status(thm)],[256])).
% 29.48/19.17 tff(258,plain,
% 29.48/19.17 (((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) <=> (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3)))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))))))) <=> ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) <=> (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3))))))))),
% 29.48/19.17 inference(transitivity,[status(thm)],[257, 255])).
% 29.48/19.17 tff(259,plain,
% 29.48/19.17 ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) <=> (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3)))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))))))),
% 29.48/19.18 inference(quant_inst,[status(thm)],[])).
% 29.48/19.18 tff(260,plain,
% 29.48/19.18 ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) <=> (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3)))))))),
% 29.48/19.18 inference(modus_ponens,[status(thm)],[259, 258])).
% 29.48/19.18 tff(261,plain,
% 29.48/19.18 ($false),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[260, 46, 254])).
% 29.48/19.18 tff(262,plain,(member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) <=> (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3))))))), inference(lemma,lemma(discharge,[]))).
% 29.48/19.18 tff(263,plain,
% 29.48/19.18 ((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2)) <=> (tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) = X3!2))),
% 29.48/19.18 inference(quant_inst,[status(thm)],[])).
% 29.48/19.18 tff(264,plain,
% 29.48/19.18 (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2)) <=> (tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) = X3!2)),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[263, 134])).
% 29.48/19.18 tff(265,assumption,(~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3)))))), introduced(assumption)).
% 29.48/19.18 tff(266,plain,
% 29.48/19.18 (((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3))))) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))),
% 29.48/19.18 inference(tautology,[status(thm)],[])).
% 29.48/19.18 tff(267,plain,
% 29.48/19.18 (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[266, 265])).
% 29.48/19.18 tff(268,plain,
% 29.48/19.18 ((~(member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2)) <=> (tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) = X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) = X3!2)),
% 29.48/19.18 inference(tautology,[status(thm)],[])).
% 29.48/19.18 tff(269,plain,
% 29.48/19.18 ((~(member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2)) <=> (tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) = X3!2))) | (tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) = X3!2)),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[268, 267])).
% 29.48/19.18 tff(270,plain,
% 29.48/19.18 (tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) = X3!2),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[269, 264])).
% 29.48/19.18 tff(271,plain,
% 29.48/19.18 (X3!2 = tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))),
% 29.48/19.18 inference(symmetry,[status(thm)],[270])).
% 29.48/19.18 tff(272,plain,
% 29.48/19.18 (member(X3!2, union(C!8, singleton(X1!4))) <=> member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(C!8, singleton(X1!4)))),
% 29.48/19.18 inference(monotonicity,[status(thm)],[271])).
% 29.48/19.18 tff(273,plain,
% 29.48/19.18 (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(C!8, singleton(X1!4))) <=> member(X3!2, union(C!8, singleton(X1!4)))),
% 29.48/19.18 inference(symmetry,[status(thm)],[272])).
% 29.48/19.18 tff(274,plain,
% 29.48/19.18 (^[X: element, A: set, B: set] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 29.48/19.18 inference(bind,[status(th)],[])).
% 29.48/19.18 tff(275,plain,
% 29.48/19.18 (![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 29.48/19.18 inference(quant_intro,[status(thm)],[274])).
% 29.48/19.18 tff(276,plain,
% 29.48/19.18 (![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 29.48/19.18 inference(rewrite,[status(thm)],[])).
% 29.48/19.18 tff(277,plain,
% 29.48/19.18 (^[X: element, A: set, B: set] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 29.48/19.18 inference(bind,[status(th)],[])).
% 29.48/19.18 tff(278,plain,
% 29.48/19.18 (![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 29.48/19.18 inference(quant_intro,[status(thm)],[277])).
% 29.48/19.18 tff(279,axiom,(![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union')).
% 29.48/19.18 tff(280,plain,
% 29.48/19.18 (![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 29.48/19.18 inference(modus_ponens,[status(thm)],[279, 278])).
% 29.48/19.18 tff(281,plain,
% 29.48/19.18 (![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 29.48/19.18 inference(modus_ponens,[status(thm)],[280, 276])).
% 29.48/19.18 tff(282,plain,(
% 29.48/19.18 ![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 29.48/19.18 inference(skolemize,[status(sab)],[281])).
% 29.48/19.18 tff(283,plain,
% 29.48/19.18 (![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 29.48/19.18 inference(modus_ponens,[status(thm)],[282, 275])).
% 29.48/19.18 tff(284,plain,
% 29.48/19.18 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3))) <=> (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X2!3)) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(C!8, singleton(X1!4)))))),
% 29.48/19.18 inference(quant_inst,[status(thm)],[])).
% 29.48/19.18 tff(285,plain,
% 29.48/19.18 (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3))) <=> (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X2!3)) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(C!8, singleton(X1!4))))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[284, 283])).
% 29.48/19.18 tff(286,plain,
% 29.48/19.18 (((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3))))) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3)))),
% 29.48/19.18 inference(tautology,[status(thm)],[])).
% 29.48/19.18 tff(287,plain,
% 29.48/19.18 (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3)))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[286, 265])).
% 29.48/19.18 tff(288,plain,
% 29.48/19.18 ((~(member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3))) <=> (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X2!3)) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(C!8, singleton(X1!4)))))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3)))) | (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X2!3)) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(C!8, singleton(X1!4))))),
% 29.48/19.18 inference(tautology,[status(thm)],[])).
% 29.48/19.18 tff(289,plain,
% 29.48/19.18 ((~(member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3))) <=> (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X2!3)) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(C!8, singleton(X1!4)))))) | (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X2!3)) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(C!8, singleton(X1!4))))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[288, 287])).
% 29.48/19.18 tff(290,plain,
% 29.48/19.18 (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X2!3)) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(C!8, singleton(X1!4)))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[289, 285])).
% 29.48/19.18 tff(291,plain,
% 29.48/19.18 (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X2!3)) <=> member(X3!2, singleton(X2!3))),
% 29.48/19.18 inference(monotonicity,[status(thm)],[270])).
% 29.48/19.18 tff(292,plain,
% 29.48/19.18 (member(X3!2, singleton(X2!3)) <=> member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X2!3))),
% 29.48/19.18 inference(symmetry,[status(thm)],[291])).
% 29.48/19.18 tff(293,plain,
% 29.48/19.18 ((~member(X3!2, singleton(X2!3))) <=> (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X2!3)))),
% 29.48/19.18 inference(monotonicity,[status(thm)],[292])).
% 29.48/19.18 tff(294,plain,
% 29.48/19.18 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X3!2, union(A1!6, singleton(X2!3))) <=> (member(X3!2, singleton(X2!3)) | member(X3!2, A1!6)))),
% 29.48/19.18 inference(quant_inst,[status(thm)],[])).
% 29.48/19.18 tff(295,plain,
% 29.48/19.18 (member(X3!2, union(A1!6, singleton(X2!3))) <=> (member(X3!2, singleton(X2!3)) | member(X3!2, A1!6))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[294, 283])).
% 29.48/19.18 tff(296,plain,
% 29.48/19.18 (^[A: set, B: set] : refl((~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B))))))))),
% 29.48/19.18 inference(bind,[status(th)],[])).
% 29.48/19.18 tff(297,plain,
% 29.48/19.18 (![A: set, B: set] : (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B))))))) <=> ![A: set, B: set] : (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B)))))))),
% 29.48/19.18 inference(quant_intro,[status(thm)],[296])).
% 29.48/19.18 tff(298,plain,
% 29.48/19.18 (^[A: set, B: set] : rewrite((~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B))))))))),
% 29.48/19.18 inference(bind,[status(th)],[])).
% 29.48/19.18 tff(299,plain,
% 29.48/19.18 (![A: set, B: set] : (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B))))))) <=> ![A: set, B: set] : (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B)))))))),
% 29.48/19.18 inference(quant_intro,[status(thm)],[298])).
% 29.48/19.18 tff(300,plain,
% 29.48/19.18 (![A: set, B: set] : (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B))))))) <=> ![A: set, B: set] : (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B)))))))),
% 29.48/19.18 inference(transitivity,[status(thm)],[299, 297])).
% 29.48/19.18 tff(301,plain,
% 29.48/19.18 (^[A: set, B: set] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B))))), ((((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B))))) <=> (((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B)))))))), ((((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B)))))))))),
% 29.48/19.18 inference(bind,[status(th)],[])).
% 29.48/19.18 tff(302,plain,
% 29.48/19.18 (![A: set, B: set] : (((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B))))) <=> ![A: set, B: set] : (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B)))))))),
% 29.48/19.18 inference(quant_intro,[status(thm)],[301])).
% 29.48/19.18 tff(303,plain,
% 29.48/19.18 (![A: set, B: set] : (subset(A, B) <=> ![X: element] : ((~member(X, A)) | member(X, B))) <=> ![A: set, B: set] : (subset(A, B) <=> ![X: element] : ((~member(X, A)) | member(X, B)))),
% 29.48/19.18 inference(rewrite,[status(thm)],[])).
% 29.48/19.18 tff(304,plain,
% 29.48/19.18 (^[A: set, B: set] : rewrite((subset(A, B) <=> ![X: element] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: element] : ((~member(X, A)) | member(X, B))))),
% 29.48/19.18 inference(bind,[status(th)],[])).
% 29.48/19.18 tff(305,plain,
% 29.48/19.18 (![A: set, B: set] : (subset(A, B) <=> ![X: element] : (member(X, A) => member(X, B))) <=> ![A: set, B: set] : (subset(A, B) <=> ![X: element] : ((~member(X, A)) | member(X, B)))),
% 29.48/19.18 inference(quant_intro,[status(thm)],[304])).
% 29.48/19.18 tff(306,axiom,(![A: set, B: set] : (subset(A, B) <=> ![X: element] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset')).
% 29.48/19.18 tff(307,plain,
% 29.48/19.18 (![A: set, B: set] : (subset(A, B) <=> ![X: element] : ((~member(X, A)) | member(X, B)))),
% 29.48/19.18 inference(modus_ponens,[status(thm)],[306, 305])).
% 29.48/19.18 tff(308,plain,
% 29.48/19.18 (![A: set, B: set] : (subset(A, B) <=> ![X: element] : ((~member(X, A)) | member(X, B)))),
% 29.48/19.18 inference(modus_ponens,[status(thm)],[307, 303])).
% 29.48/19.18 tff(309,plain,(
% 29.48/19.18 ![A: set, B: set] : (((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B)))))),
% 29.48/19.18 inference(skolemize,[status(sab)],[308])).
% 29.48/19.18 tff(310,plain,
% 29.48/19.18 (![A: set, B: set] : (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B)))))))),
% 29.48/19.18 inference(modus_ponens,[status(thm)],[309, 302])).
% 29.48/19.18 tff(311,plain,
% 29.48/19.18 (![A: set, B: set] : (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B)))))))),
% 29.48/19.18 inference(modus_ponens,[status(thm)],[310, 300])).
% 29.48/19.18 tff(312,plain,
% 29.48/19.18 ((~![A: set, B: set] : (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B)))))))) | (~((~((~subset(union(A1!6, singleton(X2!3)), A2!5)) | ![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5)))) | (~(subset(union(A1!6, singleton(X2!3)), A2!5) | (~((~member(tptp_fun_X_1(A2!5, union(A1!6, singleton(X2!3))), union(A1!6, singleton(X2!3)))) | member(tptp_fun_X_1(A2!5, union(A1!6, singleton(X2!3))), A2!5)))))))),
% 29.48/19.18 inference(quant_inst,[status(thm)],[])).
% 29.48/19.18 tff(313,plain,
% 29.48/19.18 (~((~((~subset(union(A1!6, singleton(X2!3)), A2!5)) | ![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5)))) | (~(subset(union(A1!6, singleton(X2!3)), A2!5) | (~((~member(tptp_fun_X_1(A2!5, union(A1!6, singleton(X2!3))), union(A1!6, singleton(X2!3)))) | member(tptp_fun_X_1(A2!5, union(A1!6, singleton(X2!3))), A2!5))))))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[312, 311])).
% 29.48/19.18 tff(314,plain,
% 29.48/19.18 (((~((~subset(union(A1!6, singleton(X2!3)), A2!5)) | ![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5)))) | (~(subset(union(A1!6, singleton(X2!3)), A2!5) | (~((~member(tptp_fun_X_1(A2!5, union(A1!6, singleton(X2!3))), union(A1!6, singleton(X2!3)))) | member(tptp_fun_X_1(A2!5, union(A1!6, singleton(X2!3))), A2!5)))))) | ((~subset(union(A1!6, singleton(X2!3)), A2!5)) | ![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5)))),
% 29.48/19.18 inference(tautology,[status(thm)],[])).
% 29.48/19.18 tff(315,plain,
% 29.48/19.18 ((~subset(union(A1!6, singleton(X2!3)), A2!5)) | ![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[314, 313])).
% 29.48/19.18 tff(316,plain,
% 29.48/19.18 (subset(union(A1!6, singleton(X2!3)), A2!5)),
% 29.48/19.18 inference(and_elim,[status(thm)],[161])).
% 29.48/19.18 tff(317,plain,
% 29.48/19.18 ((~((~subset(union(A1!6, singleton(X2!3)), A2!5)) | ![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5)))) | (~subset(union(A1!6, singleton(X2!3)), A2!5)) | ![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5))),
% 29.48/19.18 inference(tautology,[status(thm)],[])).
% 29.48/19.18 tff(318,plain,
% 29.48/19.18 ((~((~subset(union(A1!6, singleton(X2!3)), A2!5)) | ![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5)))) | ![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[317, 316])).
% 29.48/19.18 tff(319,plain,
% 29.48/19.18 (![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[318, 315])).
% 29.48/19.18 tff(320,plain,
% 29.48/19.18 (~member(X3!2, A2!5)),
% 29.48/19.18 inference(and_elim,[status(thm)],[161])).
% 29.48/19.18 tff(321,plain,
% 29.48/19.18 (((~![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5))) | ((~member(X3!2, union(A1!6, singleton(X2!3)))) | member(X3!2, A2!5))) <=> ((~![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5))) | (~member(X3!2, union(A1!6, singleton(X2!3)))) | member(X3!2, A2!5))),
% 29.48/19.18 inference(rewrite,[status(thm)],[])).
% 29.48/19.18 tff(322,plain,
% 29.48/19.18 ((~![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5))) | ((~member(X3!2, union(A1!6, singleton(X2!3)))) | member(X3!2, A2!5))),
% 29.48/19.18 inference(quant_inst,[status(thm)],[])).
% 29.48/19.18 tff(323,plain,
% 29.48/19.18 ((~![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5))) | (~member(X3!2, union(A1!6, singleton(X2!3)))) | member(X3!2, A2!5)),
% 29.48/19.18 inference(modus_ponens,[status(thm)],[322, 321])).
% 29.48/19.18 tff(324,plain,
% 29.48/19.18 (~member(X3!2, union(A1!6, singleton(X2!3)))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[323, 320, 319])).
% 29.48/19.18 tff(325,plain,
% 29.48/19.18 ((~(member(X3!2, union(A1!6, singleton(X2!3))) <=> (member(X3!2, singleton(X2!3)) | member(X3!2, A1!6)))) | member(X3!2, union(A1!6, singleton(X2!3))) | (~(member(X3!2, singleton(X2!3)) | member(X3!2, A1!6)))),
% 29.48/19.18 inference(tautology,[status(thm)],[])).
% 29.48/19.18 tff(326,plain,
% 29.48/19.18 ((~(member(X3!2, union(A1!6, singleton(X2!3))) <=> (member(X3!2, singleton(X2!3)) | member(X3!2, A1!6)))) | (~(member(X3!2, singleton(X2!3)) | member(X3!2, A1!6)))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[325, 324])).
% 29.48/19.18 tff(327,plain,
% 29.48/19.18 (~(member(X3!2, singleton(X2!3)) | member(X3!2, A1!6))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[326, 295])).
% 29.48/19.18 tff(328,plain,
% 29.48/19.18 ((member(X3!2, singleton(X2!3)) | member(X3!2, A1!6)) | (~member(X3!2, singleton(X2!3)))),
% 29.48/19.18 inference(tautology,[status(thm)],[])).
% 29.48/19.18 tff(329,plain,
% 29.48/19.18 (~member(X3!2, singleton(X2!3))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[328, 327])).
% 29.48/19.18 tff(330,plain,
% 29.48/19.18 (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X2!3))),
% 29.48/19.18 inference(modus_ponens,[status(thm)],[329, 293])).
% 29.48/19.18 tff(331,plain,
% 29.48/19.18 ((~(member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X2!3)) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(C!8, singleton(X1!4))))) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X2!3)) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(C!8, singleton(X1!4)))),
% 29.48/19.18 inference(tautology,[status(thm)],[])).
% 29.48/19.18 tff(332,plain,
% 29.48/19.18 (member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(C!8, singleton(X1!4)))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[331, 330, 290])).
% 29.48/19.18 tff(333,plain,
% 29.48/19.18 (member(X3!2, union(C!8, singleton(X1!4)))),
% 29.48/19.18 inference(modus_ponens,[status(thm)],[332, 273])).
% 29.48/19.18 tff(334,plain,
% 29.48/19.18 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X3!2, union(C!8, singleton(X1!4))) <=> (member(X3!2, singleton(X1!4)) | member(X3!2, C!8)))),
% 29.48/19.18 inference(quant_inst,[status(thm)],[])).
% 29.48/19.18 tff(335,plain,
% 29.48/19.18 (member(X3!2, union(C!8, singleton(X1!4))) <=> (member(X3!2, singleton(X1!4)) | member(X3!2, C!8))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[334, 283])).
% 29.48/19.18 tff(336,plain,
% 29.48/19.18 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X3!2, union(A0!7, singleton(X1!4))) <=> (member(X3!2, singleton(X1!4)) | member(X3!2, A0!7)))),
% 29.48/19.18 inference(quant_inst,[status(thm)],[])).
% 29.48/19.18 tff(337,plain,
% 29.48/19.18 (member(X3!2, union(A0!7, singleton(X1!4))) <=> (member(X3!2, singleton(X1!4)) | member(X3!2, A0!7))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[336, 283])).
% 29.48/19.18 tff(338,plain,
% 29.48/19.18 ((member(X3!2, singleton(X2!3)) | member(X3!2, A1!6)) | (~member(X3!2, A1!6))),
% 29.48/19.18 inference(tautology,[status(thm)],[])).
% 29.48/19.18 tff(339,plain,
% 29.48/19.18 (~member(X3!2, A1!6)),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[338, 327])).
% 29.48/19.18 tff(340,plain,
% 29.48/19.18 ((~![A: set, B: set] : (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B)))))))) | (~((~((~subset(union(A0!7, singleton(X1!4)), A1!6)) | ![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6)))) | (~(subset(union(A0!7, singleton(X1!4)), A1!6) | (~((~member(tptp_fun_X_1(A1!6, union(A0!7, singleton(X1!4))), union(A0!7, singleton(X1!4)))) | member(tptp_fun_X_1(A1!6, union(A0!7, singleton(X1!4))), A1!6)))))))),
% 29.48/19.18 inference(quant_inst,[status(thm)],[])).
% 29.48/19.18 tff(341,plain,
% 29.48/19.18 (~((~((~subset(union(A0!7, singleton(X1!4)), A1!6)) | ![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6)))) | (~(subset(union(A0!7, singleton(X1!4)), A1!6) | (~((~member(tptp_fun_X_1(A1!6, union(A0!7, singleton(X1!4))), union(A0!7, singleton(X1!4)))) | member(tptp_fun_X_1(A1!6, union(A0!7, singleton(X1!4))), A1!6))))))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[340, 311])).
% 29.48/19.18 tff(342,plain,
% 29.48/19.18 (((~((~subset(union(A0!7, singleton(X1!4)), A1!6)) | ![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6)))) | (~(subset(union(A0!7, singleton(X1!4)), A1!6) | (~((~member(tptp_fun_X_1(A1!6, union(A0!7, singleton(X1!4))), union(A0!7, singleton(X1!4)))) | member(tptp_fun_X_1(A1!6, union(A0!7, singleton(X1!4))), A1!6)))))) | ((~subset(union(A0!7, singleton(X1!4)), A1!6)) | ![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6)))),
% 29.48/19.18 inference(tautology,[status(thm)],[])).
% 29.48/19.18 tff(343,plain,
% 29.48/19.18 ((~subset(union(A0!7, singleton(X1!4)), A1!6)) | ![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[342, 341])).
% 29.48/19.18 tff(344,plain,
% 29.48/19.18 (subset(union(A0!7, singleton(X1!4)), A1!6)),
% 29.48/19.18 inference(and_elim,[status(thm)],[161])).
% 29.48/19.18 tff(345,plain,
% 29.48/19.18 ((~((~subset(union(A0!7, singleton(X1!4)), A1!6)) | ![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6)))) | (~subset(union(A0!7, singleton(X1!4)), A1!6)) | ![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6))),
% 29.48/19.18 inference(tautology,[status(thm)],[])).
% 29.48/19.18 tff(346,plain,
% 29.48/19.18 ((~((~subset(union(A0!7, singleton(X1!4)), A1!6)) | ![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6)))) | ![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[345, 344])).
% 29.48/19.18 tff(347,plain,
% 29.48/19.18 (![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6))),
% 29.48/19.18 inference(unit_resolution,[status(thm)],[346, 343])).
% 29.48/19.18 tff(348,plain,
% 29.48/19.18 (((~![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6))) | ((~member(X3!2, union(A0!7, singleton(X1!4)))) | member(X3!2, A1!6))) <=> ((~![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6))) | (~member(X3!2, union(A0!7, singleton(X1!4)))) | member(X3!2, A1!6))),
% 29.48/19.18 inference(rewrite,[status(thm)],[])).
% 29.48/19.18 tff(349,plain,
% 29.48/19.18 ((~![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6))) | ((~member(X3!2, union(A0!7, singleton(X1!4)))) | member(X3!2, A1!6))),
% 29.48/19.18 inference(quant_inst,[status(thm)],[])).
% 29.48/19.18 tff(350,plain,
% 29.48/19.18 ((~![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6))) | (~member(X3!2, union(A0!7, singleton(X1!4)))) | member(X3!2, A1!6)),
% 29.48/19.19 inference(modus_ponens,[status(thm)],[349, 348])).
% 29.48/19.19 tff(351,plain,
% 29.48/19.19 (~member(X3!2, union(A0!7, singleton(X1!4)))),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[350, 347, 339])).
% 29.48/19.19 tff(352,plain,
% 29.48/19.19 ((~(member(X3!2, union(A0!7, singleton(X1!4))) <=> (member(X3!2, singleton(X1!4)) | member(X3!2, A0!7)))) | member(X3!2, union(A0!7, singleton(X1!4))) | (~(member(X3!2, singleton(X1!4)) | member(X3!2, A0!7)))),
% 29.48/19.19 inference(tautology,[status(thm)],[])).
% 29.48/19.19 tff(353,plain,
% 29.48/19.19 ((~(member(X3!2, union(A0!7, singleton(X1!4))) <=> (member(X3!2, singleton(X1!4)) | member(X3!2, A0!7)))) | (~(member(X3!2, singleton(X1!4)) | member(X3!2, A0!7)))),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[352, 351])).
% 29.48/19.19 tff(354,plain,
% 29.48/19.19 (~(member(X3!2, singleton(X1!4)) | member(X3!2, A0!7))),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[353, 337])).
% 29.48/19.19 tff(355,plain,
% 29.48/19.19 ((member(X3!2, singleton(X1!4)) | member(X3!2, A0!7)) | (~member(X3!2, A0!7))),
% 29.48/19.19 inference(tautology,[status(thm)],[])).
% 29.48/19.19 tff(356,plain,
% 29.48/19.19 (~member(X3!2, A0!7)),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[355, 354])).
% 29.48/19.19 tff(357,plain,
% 29.48/19.19 ((~![A: set, B: set] : (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B)))))))) | (~((~((~subset(C!8, A0!7)) | ![X: element] : ((~member(X, C!8)) | member(X, A0!7)))) | (~(subset(C!8, A0!7) | (~((~member(tptp_fun_X_1(A0!7, C!8), C!8)) | member(tptp_fun_X_1(A0!7, C!8), A0!7)))))))),
% 29.48/19.19 inference(quant_inst,[status(thm)],[])).
% 29.48/19.19 tff(358,plain,
% 29.48/19.19 (~((~((~subset(C!8, A0!7)) | ![X: element] : ((~member(X, C!8)) | member(X, A0!7)))) | (~(subset(C!8, A0!7) | (~((~member(tptp_fun_X_1(A0!7, C!8), C!8)) | member(tptp_fun_X_1(A0!7, C!8), A0!7))))))),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[357, 311])).
% 29.48/19.19 tff(359,plain,
% 29.48/19.19 (((~((~subset(C!8, A0!7)) | ![X: element] : ((~member(X, C!8)) | member(X, A0!7)))) | (~(subset(C!8, A0!7) | (~((~member(tptp_fun_X_1(A0!7, C!8), C!8)) | member(tptp_fun_X_1(A0!7, C!8), A0!7)))))) | ((~subset(C!8, A0!7)) | ![X: element] : ((~member(X, C!8)) | member(X, A0!7)))),
% 29.48/19.19 inference(tautology,[status(thm)],[])).
% 29.48/19.19 tff(360,plain,
% 29.48/19.19 ((~subset(C!8, A0!7)) | ![X: element] : ((~member(X, C!8)) | member(X, A0!7))),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[359, 358])).
% 29.48/19.19 tff(361,plain,
% 29.48/19.19 (subset(C!8, A0!7)),
% 29.48/19.19 inference(and_elim,[status(thm)],[161])).
% 29.48/19.19 tff(362,plain,
% 29.48/19.19 ((~((~subset(C!8, A0!7)) | ![X: element] : ((~member(X, C!8)) | member(X, A0!7)))) | (~subset(C!8, A0!7)) | ![X: element] : ((~member(X, C!8)) | member(X, A0!7))),
% 29.48/19.19 inference(tautology,[status(thm)],[])).
% 29.48/19.19 tff(363,plain,
% 29.48/19.19 ((~((~subset(C!8, A0!7)) | ![X: element] : ((~member(X, C!8)) | member(X, A0!7)))) | ![X: element] : ((~member(X, C!8)) | member(X, A0!7))),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[362, 361])).
% 29.48/19.19 tff(364,plain,
% 29.48/19.19 (![X: element] : ((~member(X, C!8)) | member(X, A0!7))),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[363, 360])).
% 29.48/19.19 tff(365,plain,
% 29.48/19.19 (((~![X: element] : ((~member(X, C!8)) | member(X, A0!7))) | ((~member(X3!2, C!8)) | member(X3!2, A0!7))) <=> ((~![X: element] : ((~member(X, C!8)) | member(X, A0!7))) | (~member(X3!2, C!8)) | member(X3!2, A0!7))),
% 29.48/19.19 inference(rewrite,[status(thm)],[])).
% 29.48/19.19 tff(366,plain,
% 29.48/19.19 ((~![X: element] : ((~member(X, C!8)) | member(X, A0!7))) | ((~member(X3!2, C!8)) | member(X3!2, A0!7))),
% 29.48/19.19 inference(quant_inst,[status(thm)],[])).
% 29.48/19.19 tff(367,plain,
% 29.48/19.19 ((~![X: element] : ((~member(X, C!8)) | member(X, A0!7))) | (~member(X3!2, C!8)) | member(X3!2, A0!7)),
% 29.48/19.19 inference(modus_ponens,[status(thm)],[366, 365])).
% 29.48/19.19 tff(368,plain,
% 29.48/19.19 (~member(X3!2, C!8)),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[367, 364, 356])).
% 29.48/19.19 tff(369,plain,
% 29.48/19.19 ((member(X3!2, singleton(X1!4)) | member(X3!2, A0!7)) | (~member(X3!2, singleton(X1!4)))),
% 29.48/19.19 inference(tautology,[status(thm)],[])).
% 29.48/19.19 tff(370,plain,
% 29.48/19.19 (~member(X3!2, singleton(X1!4))),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[369, 354])).
% 29.48/19.19 tff(371,plain,
% 29.48/19.19 ((~(member(X3!2, singleton(X1!4)) | member(X3!2, C!8))) | member(X3!2, singleton(X1!4)) | member(X3!2, C!8)),
% 29.48/19.19 inference(tautology,[status(thm)],[])).
% 29.48/19.19 tff(372,plain,
% 29.48/19.19 (~(member(X3!2, singleton(X1!4)) | member(X3!2, C!8))),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[371, 370, 368])).
% 29.48/19.19 tff(373,plain,
% 29.48/19.19 ((~(member(X3!2, union(C!8, singleton(X1!4))) <=> (member(X3!2, singleton(X1!4)) | member(X3!2, C!8)))) | (~member(X3!2, union(C!8, singleton(X1!4)))) | (member(X3!2, singleton(X1!4)) | member(X3!2, C!8))),
% 29.48/19.19 inference(tautology,[status(thm)],[])).
% 29.48/19.19 tff(374,plain,
% 29.48/19.19 ((~(member(X3!2, union(C!8, singleton(X1!4))) <=> (member(X3!2, singleton(X1!4)) | member(X3!2, C!8)))) | (~member(X3!2, union(C!8, singleton(X1!4))))),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[373, 372])).
% 29.48/19.19 tff(375,plain,
% 29.48/19.19 (~member(X3!2, union(C!8, singleton(X1!4)))),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[374, 335])).
% 29.48/19.19 tff(376,plain,
% 29.48/19.19 ($false),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[375, 333])).
% 29.48/19.19 tff(377,plain,((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3))))), inference(lemma,lemma(discharge,[]))).
% 29.48/19.19 tff(378,plain,
% 29.48/19.19 ((~(member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) <=> (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3)))))))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))) | (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3))))))),
% 29.48/19.19 inference(tautology,[status(thm)],[])).
% 29.48/19.19 tff(379,plain,
% 29.48/19.19 ((~(member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))) <=> (~((~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), union(union(C!8, singleton(X1!4)), singleton(X2!3)))))))) | (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[378, 377])).
% 29.48/19.19 tff(380,plain,
% 29.48/19.19 (~member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[379, 262])).
% 29.48/19.19 tff(381,plain,
% 29.48/19.19 ((~((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))) | (intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) | member(tptp_fun_X_0(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))),
% 29.48/19.19 inference(tautology,[status(thm)],[])).
% 29.48/19.19 tff(382,plain,
% 29.48/19.19 (intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set),
% 29.48/19.19 inference(unit_resolution,[status(thm)],[381, 380, 253])).
% 29.48/19.19 tff(383,plain,
% 29.48/19.19 (((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) <=> ($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))) = 0))) <=> ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) <=> ($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))) = 0)))),
% 29.48/19.19 inference(rewrite,[status(thm)],[])).
% 29.48/19.19 tff(384,plain,
% 29.48/19.19 (((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) <=> ($sum(cardinality(singleton(X3!2)), $sum(cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3))), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))) = 0)) <=> ((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) <=> ($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))) = 0))),
% 29.48/19.19 inference(rewrite,[status(thm)],[])).
% 29.48/19.19 tff(385,plain,
% 29.48/19.19 (((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) <=> ($sum(cardinality(singleton(X3!2)), $sum(cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3))), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))) = 0))) <=> ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) <=> ($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))) = 0)))),
% 29.48/19.19 inference(monotonicity,[status(thm)],[384])).
% 29.48/19.19 tff(386,plain,
% 29.48/19.19 (((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) <=> ($sum(cardinality(singleton(X3!2)), $sum(cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3))), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))) = 0))) <=> ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) <=> ($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))) = 0)))),
% 29.48/19.19 inference(transitivity,[status(thm)],[385, 383])).
% 29.48/19.19 tff(387,plain,
% 29.48/19.19 ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) <=> ($sum(cardinality(singleton(X3!2)), $sum(cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3))), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)))))) = 0))),
% 29.56/19.19 inference(quant_inst,[status(thm)],[])).
% 29.56/19.19 tff(388,plain,
% 29.56/19.19 ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) <=> ($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))) = 0))),
% 29.56/19.19 inference(modus_ponens,[status(thm)],[387, 386])).
% 29.56/19.19 tff(389,plain,
% 29.56/19.19 ((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) <=> ($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))) = 0)),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[388, 102])).
% 29.56/19.19 tff(390,plain,
% 29.56/19.19 ((~((intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set) <=> ($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))) = 0))) | (~(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set)) | ($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))) = 0)),
% 29.56/19.19 inference(tautology,[status(thm)],[])).
% 29.56/19.19 tff(391,plain,
% 29.56/19.19 ((~(intersection(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2)) = empty_set)) | ($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))) = 0)),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[390, 389])).
% 29.56/19.19 tff(392,plain,
% 29.56/19.19 ($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))) = 0),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[391, 382])).
% 29.56/19.19 tff(393,plain,
% 29.56/19.19 ((~($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))) = 0)) | $lesseq($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))), 0)),
% 29.56/19.19 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.19 tff(394,plain,
% 29.56/19.19 ($lesseq($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))), 0)),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[393, 392])).
% 29.56/19.19 tff(395,plain,
% 29.56/19.19 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(X3!2, intersection(singleton(X3!2), A1!6))) | (~(intersection(singleton(X3!2), A1!6) = empty_set)))) | (~((intersection(singleton(X3!2), A1!6) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6))))))),
% 29.56/19.19 inference(quant_inst,[status(thm)],[])).
% 29.56/19.19 tff(396,plain,
% 29.56/19.19 (~((~((~member(X3!2, intersection(singleton(X3!2), A1!6))) | (~(intersection(singleton(X3!2), A1!6) = empty_set)))) | (~((intersection(singleton(X3!2), A1!6) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)))))),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[395, 25])).
% 29.56/19.19 tff(397,plain,
% 29.56/19.19 (((~((~member(X3!2, intersection(singleton(X3!2), A1!6))) | (~(intersection(singleton(X3!2), A1!6) = empty_set)))) | (~((intersection(singleton(X3!2), A1!6) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6))))) | ((intersection(singleton(X3!2), A1!6) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)))),
% 29.56/19.19 inference(tautology,[status(thm)],[])).
% 29.56/19.19 tff(398,plain,
% 29.56/19.19 ((intersection(singleton(X3!2), A1!6) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6))),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[397, 396])).
% 29.56/19.19 tff(399,assumption,(~(member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2))))))), introduced(assumption)).
% 29.56/19.19 tff(400,plain,
% 29.56/19.19 (((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2))))))) <=> ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2)))))))),
% 29.56/19.19 inference(rewrite,[status(thm)],[])).
% 29.56/19.19 tff(401,plain,
% 29.56/19.19 ((member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6))))) <=> (member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2))))))),
% 29.56/19.19 inference(rewrite,[status(thm)],[])).
% 29.56/19.19 tff(402,plain,
% 29.56/19.19 (((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)))))) <=> ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2)))))))),
% 29.56/19.19 inference(monotonicity,[status(thm)],[401])).
% 29.56/19.19 tff(403,plain,
% 29.56/19.19 (((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)))))) <=> ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2)))))))),
% 29.56/19.19 inference(transitivity,[status(thm)],[402, 400])).
% 29.56/19.19 tff(404,plain,
% 29.56/19.19 ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2))) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)))))),
% 29.56/19.19 inference(quant_inst,[status(thm)],[])).
% 29.56/19.19 tff(405,plain,
% 29.56/19.19 ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2))))))),
% 29.56/19.19 inference(modus_ponens,[status(thm)],[404, 403])).
% 29.56/19.19 tff(406,plain,
% 29.56/19.19 ($false),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[405, 46, 399])).
% 29.56/19.19 tff(407,plain,(member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2)))))), inference(lemma,lemma(discharge,[]))).
% 29.56/19.19 tff(408,plain,
% 29.56/19.19 ((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2)) <=> (tptp_fun_X_0(intersection(singleton(X3!2), A1!6)) = X3!2))),
% 29.56/19.19 inference(quant_inst,[status(thm)],[])).
% 29.56/19.19 tff(409,plain,
% 29.56/19.19 (member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2)) <=> (tptp_fun_X_0(intersection(singleton(X3!2), A1!6)) = X3!2)),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[408, 134])).
% 29.56/19.19 tff(410,assumption,(~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2))))), introduced(assumption)).
% 29.56/19.19 tff(411,plain,
% 29.56/19.19 (((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2)))) | member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2))),
% 29.56/19.19 inference(tautology,[status(thm)],[])).
% 29.56/19.19 tff(412,plain,
% 29.56/19.19 (member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2))),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[411, 410])).
% 29.56/19.19 tff(413,plain,
% 29.56/19.19 ((~(member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2)) <=> (tptp_fun_X_0(intersection(singleton(X3!2), A1!6)) = X3!2))) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2))) | (tptp_fun_X_0(intersection(singleton(X3!2), A1!6)) = X3!2)),
% 29.56/19.19 inference(tautology,[status(thm)],[])).
% 29.56/19.19 tff(414,plain,
% 29.56/19.19 ((~(member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2)) <=> (tptp_fun_X_0(intersection(singleton(X3!2), A1!6)) = X3!2))) | (tptp_fun_X_0(intersection(singleton(X3!2), A1!6)) = X3!2)),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[413, 412])).
% 29.56/19.19 tff(415,plain,
% 29.56/19.19 (tptp_fun_X_0(intersection(singleton(X3!2), A1!6)) = X3!2),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[414, 409])).
% 29.56/19.19 tff(416,plain,
% 29.56/19.19 (member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6) <=> member(X3!2, A1!6)),
% 29.56/19.19 inference(monotonicity,[status(thm)],[415])).
% 29.56/19.19 tff(417,plain,
% 29.56/19.19 (member(X3!2, A1!6) <=> member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)),
% 29.56/19.19 inference(symmetry,[status(thm)],[416])).
% 29.56/19.19 tff(418,plain,
% 29.56/19.19 ((~member(X3!2, A1!6)) <=> (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6))),
% 29.56/19.19 inference(monotonicity,[status(thm)],[417])).
% 29.56/19.19 tff(419,plain,
% 29.56/19.19 (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)),
% 29.56/19.19 inference(modus_ponens,[status(thm)],[339, 418])).
% 29.56/19.19 tff(420,plain,
% 29.56/19.19 (((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2)))) | member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)),
% 29.56/19.19 inference(tautology,[status(thm)],[])).
% 29.56/19.19 tff(421,plain,
% 29.56/19.19 (member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[420, 410])).
% 29.56/19.19 tff(422,plain,
% 29.56/19.19 ($false),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[421, 419])).
% 29.56/19.19 tff(423,plain,((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2)))), inference(lemma,lemma(discharge,[]))).
% 29.56/19.19 tff(424,plain,
% 29.56/19.19 ((~(member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2))))))) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6))) | (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2)))))),
% 29.56/19.19 inference(tautology,[status(thm)],[])).
% 29.56/19.19 tff(425,plain,
% 29.56/19.19 ((~(member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), A1!6)) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), singleton(X3!2))))))) | (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)))),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[424, 423])).
% 29.56/19.19 tff(426,plain,
% 29.56/19.19 (~member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6))),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[425, 407])).
% 29.56/19.19 tff(427,plain,
% 29.56/19.19 ((~((intersection(singleton(X3!2), A1!6) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6)))) | (intersection(singleton(X3!2), A1!6) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X3!2), A1!6)), intersection(singleton(X3!2), A1!6))),
% 29.56/19.19 inference(tautology,[status(thm)],[])).
% 29.56/19.19 tff(428,plain,
% 29.56/19.19 (intersection(singleton(X3!2), A1!6) = empty_set),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[427, 426, 398])).
% 29.56/19.19 tff(429,plain,
% 29.56/19.19 ((~![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(S), $product(-1, cardinality(union(singleton(X), S)))) = -1))) | ((intersection(singleton(X3!2), A1!6) = empty_set) <=> ($sum(cardinality(A1!6), $product(-1, cardinality(union(singleton(X3!2), A1!6)))) = -1))),
% 29.56/19.19 inference(quant_inst,[status(thm)],[])).
% 29.56/19.19 tff(430,plain,
% 29.56/19.19 ((intersection(singleton(X3!2), A1!6) = empty_set) <=> ($sum(cardinality(A1!6), $product(-1, cardinality(union(singleton(X3!2), A1!6)))) = -1)),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[429, 82])).
% 29.56/19.19 tff(431,plain,
% 29.56/19.19 ((~((intersection(singleton(X3!2), A1!6) = empty_set) <=> ($sum(cardinality(A1!6), $product(-1, cardinality(union(singleton(X3!2), A1!6)))) = -1))) | (~(intersection(singleton(X3!2), A1!6) = empty_set)) | ($sum(cardinality(A1!6), $product(-1, cardinality(union(singleton(X3!2), A1!6)))) = -1)),
% 29.56/19.19 inference(tautology,[status(thm)],[])).
% 29.56/19.19 tff(432,plain,
% 29.56/19.19 ((~(intersection(singleton(X3!2), A1!6) = empty_set)) | ($sum(cardinality(A1!6), $product(-1, cardinality(union(singleton(X3!2), A1!6)))) = -1)),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[431, 430])).
% 29.56/19.19 tff(433,plain,
% 29.56/19.19 ($sum(cardinality(A1!6), $product(-1, cardinality(union(singleton(X3!2), A1!6)))) = -1),
% 29.56/19.19 inference(unit_resolution,[status(thm)],[432, 428])).
% 29.56/19.19 tff(434,plain,
% 29.56/19.19 ((~($sum(cardinality(A1!6), $product(-1, cardinality(union(singleton(X3!2), A1!6)))) = -1)) | $greatereq($sum(cardinality(A1!6), $product(-1, cardinality(union(singleton(X3!2), A1!6)))), -1)),
% 29.56/19.19 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.19 tff(435,plain,
% 29.56/19.19 ($greatereq($sum(cardinality(A1!6), $product(-1, cardinality(union(singleton(X3!2), A1!6)))), -1)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[434, 433])).
% 29.56/19.20 tff(436,plain,
% 29.56/19.20 ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X3!2), A1!6) = empty_set) <=> ($sum(cardinality(A1!6), $sum(cardinality(singleton(X3!2)), $product(-1, cardinality(union(singleton(X3!2), A1!6))))) = 0))),
% 29.56/19.20 inference(quant_inst,[status(thm)],[])).
% 29.56/19.20 tff(437,plain,
% 29.56/19.20 ((intersection(singleton(X3!2), A1!6) = empty_set) <=> ($sum(cardinality(A1!6), $sum(cardinality(singleton(X3!2)), $product(-1, cardinality(union(singleton(X3!2), A1!6))))) = 0)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[436, 102])).
% 29.56/19.20 tff(438,plain,
% 29.56/19.20 ((~((intersection(singleton(X3!2), A1!6) = empty_set) <=> ($sum(cardinality(A1!6), $sum(cardinality(singleton(X3!2)), $product(-1, cardinality(union(singleton(X3!2), A1!6))))) = 0))) | (~(intersection(singleton(X3!2), A1!6) = empty_set)) | ($sum(cardinality(A1!6), $sum(cardinality(singleton(X3!2)), $product(-1, cardinality(union(singleton(X3!2), A1!6))))) = 0)),
% 29.56/19.20 inference(tautology,[status(thm)],[])).
% 29.56/19.20 tff(439,plain,
% 29.56/19.20 ((~(intersection(singleton(X3!2), A1!6) = empty_set)) | ($sum(cardinality(A1!6), $sum(cardinality(singleton(X3!2)), $product(-1, cardinality(union(singleton(X3!2), A1!6))))) = 0)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[438, 437])).
% 29.56/19.20 tff(440,plain,
% 29.56/19.20 ($sum(cardinality(A1!6), $sum(cardinality(singleton(X3!2)), $product(-1, cardinality(union(singleton(X3!2), A1!6))))) = 0),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[439, 428])).
% 29.56/19.20 tff(441,plain,
% 29.56/19.20 ((~($sum(cardinality(A1!6), $sum(cardinality(singleton(X3!2)), $product(-1, cardinality(union(singleton(X3!2), A1!6))))) = 0)) | $lesseq($sum(cardinality(A1!6), $sum(cardinality(singleton(X3!2)), $product(-1, cardinality(union(singleton(X3!2), A1!6))))), 0)),
% 29.56/19.20 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.20 tff(442,plain,
% 29.56/19.20 ($lesseq($sum(cardinality(A1!6), $sum(cardinality(singleton(X3!2)), $product(-1, cardinality(union(singleton(X3!2), A1!6))))), 0)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[441, 440])).
% 29.56/19.20 tff(443,assumption,((~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))))) | (~((~(intersection(C!8, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_1(intersection(C!8, singleton(X1!4)), singleton(tptp_fun_X_0(A1!6))), intersection(C!8, singleton(X1!4))))))), introduced(assumption)).
% 29.56/19.20 tff(444,plain,
% 29.56/19.20 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))))) | (~((~(intersection(C!8, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_1(intersection(C!8, singleton(X1!4)), singleton(tptp_fun_X_0(A1!6))), intersection(C!8, singleton(X1!4))))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))))) | (~((~(intersection(C!8, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_1(intersection(C!8, singleton(X1!4)), singleton(tptp_fun_X_0(A1!6))), intersection(C!8, singleton(X1!4)))))))))),
% 29.56/19.20 inference(rewrite,[status(thm)],[])).
% 29.56/19.20 tff(445,plain,
% 29.56/19.20 ((~((~((~member(tptp_fun_X_1(intersection(C!8, singleton(X1!4)), singleton(tptp_fun_X_0(A1!6))), intersection(C!8, singleton(X1!4)))) | (~(intersection(C!8, singleton(X1!4)) = empty_set)))) | (~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))))))) <=> (~((~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))))) | (~((~(intersection(C!8, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_1(intersection(C!8, singleton(X1!4)), singleton(tptp_fun_X_0(A1!6))), intersection(C!8, singleton(X1!4))))))))),
% 29.56/19.20 inference(rewrite,[status(thm)],[])).
% 29.56/19.20 tff(446,plain,
% 29.56/19.20 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_1(intersection(C!8, singleton(X1!4)), singleton(tptp_fun_X_0(A1!6))), intersection(C!8, singleton(X1!4)))) | (~(intersection(C!8, singleton(X1!4)) = empty_set)))) | (~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))))) | (~((~(intersection(C!8, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_1(intersection(C!8, singleton(X1!4)), singleton(tptp_fun_X_0(A1!6))), intersection(C!8, singleton(X1!4)))))))))),
% 29.56/19.20 inference(monotonicity,[status(thm)],[445])).
% 29.56/19.20 tff(447,plain,
% 29.56/19.20 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_1(intersection(C!8, singleton(X1!4)), singleton(tptp_fun_X_0(A1!6))), intersection(C!8, singleton(X1!4)))) | (~(intersection(C!8, singleton(X1!4)) = empty_set)))) | (~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))))) | (~((~(intersection(C!8, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_1(intersection(C!8, singleton(X1!4)), singleton(tptp_fun_X_0(A1!6))), intersection(C!8, singleton(X1!4)))))))))),
% 29.56/19.20 inference(transitivity,[status(thm)],[446, 444])).
% 29.56/19.20 tff(448,plain,
% 29.56/19.20 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_1(intersection(C!8, singleton(X1!4)), singleton(tptp_fun_X_0(A1!6))), intersection(C!8, singleton(X1!4)))) | (~(intersection(C!8, singleton(X1!4)) = empty_set)))) | (~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4)))))))),
% 29.56/19.20 inference(quant_inst,[status(thm)],[])).
% 29.56/19.20 tff(449,plain,
% 29.56/19.20 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))))) | (~((~(intersection(C!8, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_1(intersection(C!8, singleton(X1!4)), singleton(tptp_fun_X_0(A1!6))), intersection(C!8, singleton(X1!4))))))))),
% 29.56/19.20 inference(modus_ponens,[status(thm)],[448, 447])).
% 29.56/19.20 tff(450,plain,
% 29.56/19.20 ($false),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[449, 25, 443])).
% 29.56/19.20 tff(451,plain,(~((~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))))) | (~((~(intersection(C!8, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_1(intersection(C!8, singleton(X1!4)), singleton(tptp_fun_X_0(A1!6))), intersection(C!8, singleton(X1!4)))))))), inference(lemma,lemma(discharge,[]))).
% 29.56/19.20 tff(452,plain,
% 29.56/19.20 (((~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))))) | (~((~(intersection(C!8, singleton(X1!4)) = empty_set)) | (~member(tptp_fun_X_1(intersection(C!8, singleton(X1!4)), singleton(tptp_fun_X_0(A1!6))), intersection(C!8, singleton(X1!4))))))) | ((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))))),
% 29.56/19.20 inference(tautology,[status(thm)],[])).
% 29.56/19.20 tff(453,plain,
% 29.56/19.20 ((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4)))),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[452, 451])).
% 29.56/19.20 tff(454,assumption,(~(member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))) <=> (~((~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8)) | (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4))))))), introduced(assumption)).
% 29.56/19.20 tff(455,plain,
% 29.56/19.20 ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))) <=> (~((~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8)) | (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4))))))),
% 29.56/19.20 inference(quant_inst,[status(thm)],[])).
% 29.56/19.20 tff(456,plain,
% 29.56/19.20 ($false),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[455, 46, 454])).
% 29.56/19.20 tff(457,plain,(member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))) <=> (~((~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8)) | (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4)))))), inference(lemma,lemma(discharge,[]))).
% 29.56/19.20 tff(458,plain,
% 29.56/19.20 ((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4)) <=> (tptp_fun_X_0(intersection(C!8, singleton(X1!4))) = X1!4))),
% 29.56/19.20 inference(quant_inst,[status(thm)],[])).
% 29.56/19.20 tff(459,plain,
% 29.56/19.20 (member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4)) <=> (tptp_fun_X_0(intersection(C!8, singleton(X1!4))) = X1!4)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[458, 134])).
% 29.56/19.20 tff(460,assumption,(~((~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8)) | (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4))))), introduced(assumption)).
% 29.56/19.20 tff(461,plain,
% 29.56/19.20 (((~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8)) | (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4)))) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4))),
% 29.56/19.20 inference(tautology,[status(thm)],[])).
% 29.56/19.20 tff(462,plain,
% 29.56/19.20 (member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4))),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[461, 460])).
% 29.56/19.20 tff(463,plain,
% 29.56/19.20 ((~(member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4)) <=> (tptp_fun_X_0(intersection(C!8, singleton(X1!4))) = X1!4))) | (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4))) | (tptp_fun_X_0(intersection(C!8, singleton(X1!4))) = X1!4)),
% 29.56/19.20 inference(tautology,[status(thm)],[])).
% 29.56/19.20 tff(464,plain,
% 29.56/19.20 ((~(member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4)) <=> (tptp_fun_X_0(intersection(C!8, singleton(X1!4))) = X1!4))) | (tptp_fun_X_0(intersection(C!8, singleton(X1!4))) = X1!4)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[463, 462])).
% 29.56/19.20 tff(465,plain,
% 29.56/19.20 (tptp_fun_X_0(intersection(C!8, singleton(X1!4))) = X1!4),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[464, 459])).
% 29.56/19.20 tff(466,plain,
% 29.56/19.20 (member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8) <=> member(X1!4, C!8)),
% 29.56/19.20 inference(monotonicity,[status(thm)],[465])).
% 29.56/19.20 tff(467,plain,
% 29.56/19.20 (member(X1!4, C!8) <=> member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8)),
% 29.56/19.20 inference(symmetry,[status(thm)],[466])).
% 29.56/19.20 tff(468,plain,
% 29.56/19.20 ((~member(X1!4, C!8)) <=> (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8))),
% 29.56/19.20 inference(monotonicity,[status(thm)],[467])).
% 29.56/19.20 tff(469,plain,
% 29.56/19.20 (((~![X: element] : ((~member(X, C!8)) | member(X, A0!7))) | ((~member(X1!4, C!8)) | member(X1!4, A0!7))) <=> ((~![X: element] : ((~member(X, C!8)) | member(X, A0!7))) | (~member(X1!4, C!8)) | member(X1!4, A0!7))),
% 29.56/19.20 inference(rewrite,[status(thm)],[])).
% 29.56/19.20 tff(470,plain,
% 29.56/19.20 ((~![X: element] : ((~member(X, C!8)) | member(X, A0!7))) | ((~member(X1!4, C!8)) | member(X1!4, A0!7))),
% 29.56/19.20 inference(quant_inst,[status(thm)],[])).
% 29.56/19.20 tff(471,plain,
% 29.56/19.20 ((~![X: element] : ((~member(X, C!8)) | member(X, A0!7))) | (~member(X1!4, C!8)) | member(X1!4, A0!7)),
% 29.56/19.20 inference(modus_ponens,[status(thm)],[470, 469])).
% 29.56/19.20 tff(472,plain,
% 29.56/19.20 (~member(X1!4, C!8)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[471, 162, 364])).
% 29.56/19.20 tff(473,plain,
% 29.56/19.20 (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8)),
% 29.56/19.20 inference(modus_ponens,[status(thm)],[472, 468])).
% 29.56/19.20 tff(474,plain,
% 29.56/19.20 (((~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8)) | (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4)))) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8)),
% 29.56/19.20 inference(tautology,[status(thm)],[])).
% 29.56/19.20 tff(475,plain,
% 29.56/19.20 (member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[474, 460])).
% 29.56/19.20 tff(476,plain,
% 29.56/19.20 ($false),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[475, 473])).
% 29.56/19.20 tff(477,plain,((~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8)) | (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4)))), inference(lemma,lemma(discharge,[]))).
% 29.56/19.20 tff(478,plain,
% 29.56/19.20 ((~(member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))) <=> (~((~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8)) | (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4))))))) | (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4)))) | (~((~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8)) | (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4)))))),
% 29.56/19.20 inference(tautology,[status(thm)],[])).
% 29.56/19.20 tff(479,plain,
% 29.56/19.20 ((~(member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))) <=> (~((~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), C!8)) | (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), singleton(X1!4))))))) | (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))))),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[478, 477])).
% 29.56/19.20 tff(480,plain,
% 29.56/19.20 (~member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4)))),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[479, 457])).
% 29.56/19.20 tff(481,plain,
% 29.56/19.20 ((~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))))) | (intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4)))),
% 29.56/19.20 inference(tautology,[status(thm)],[])).
% 29.56/19.20 tff(482,plain,
% 29.56/19.20 ((~((intersection(C!8, singleton(X1!4)) = empty_set) | member(tptp_fun_X_0(intersection(C!8, singleton(X1!4))), intersection(C!8, singleton(X1!4))))) | (intersection(C!8, singleton(X1!4)) = empty_set)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[481, 480])).
% 29.56/19.20 tff(483,plain,
% 29.56/19.20 (intersection(C!8, singleton(X1!4)) = empty_set),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[482, 453])).
% 29.56/19.20 tff(484,plain,
% 29.56/19.20 (((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(C!8, singleton(X1!4)) = empty_set) <=> ($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0))) <=> ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(C!8, singleton(X1!4)) = empty_set) <=> ($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0)))),
% 29.56/19.20 inference(rewrite,[status(thm)],[])).
% 29.56/19.20 tff(485,plain,
% 29.56/19.20 (((intersection(C!8, singleton(X1!4)) = empty_set) <=> ($sum(cardinality(singleton(X1!4)), $sum(cardinality(C!8), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0)) <=> ((intersection(C!8, singleton(X1!4)) = empty_set) <=> ($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0))),
% 29.56/19.20 inference(rewrite,[status(thm)],[])).
% 29.56/19.20 tff(486,plain,
% 29.56/19.20 (((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(C!8, singleton(X1!4)) = empty_set) <=> ($sum(cardinality(singleton(X1!4)), $sum(cardinality(C!8), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0))) <=> ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(C!8, singleton(X1!4)) = empty_set) <=> ($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0)))),
% 29.56/19.20 inference(monotonicity,[status(thm)],[485])).
% 29.56/19.20 tff(487,plain,
% 29.56/19.20 (((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(C!8, singleton(X1!4)) = empty_set) <=> ($sum(cardinality(singleton(X1!4)), $sum(cardinality(C!8), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0))) <=> ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(C!8, singleton(X1!4)) = empty_set) <=> ($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0)))),
% 29.56/19.20 inference(transitivity,[status(thm)],[486, 484])).
% 29.56/19.20 tff(488,plain,
% 29.56/19.20 ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(C!8, singleton(X1!4)) = empty_set) <=> ($sum(cardinality(singleton(X1!4)), $sum(cardinality(C!8), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0))),
% 29.56/19.20 inference(quant_inst,[status(thm)],[])).
% 29.56/19.20 tff(489,plain,
% 29.56/19.20 ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(C!8, singleton(X1!4)) = empty_set) <=> ($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0))),
% 29.56/19.20 inference(modus_ponens,[status(thm)],[488, 487])).
% 29.56/19.20 tff(490,plain,
% 29.56/19.20 ((intersection(C!8, singleton(X1!4)) = empty_set) <=> ($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[489, 102])).
% 29.56/19.20 tff(491,plain,
% 29.56/19.20 ((~((intersection(C!8, singleton(X1!4)) = empty_set) <=> ($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0))) | (~(intersection(C!8, singleton(X1!4)) = empty_set)) | ($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0)),
% 29.56/19.20 inference(tautology,[status(thm)],[])).
% 29.56/19.20 tff(492,plain,
% 29.56/19.20 ((~(intersection(C!8, singleton(X1!4)) = empty_set)) | ($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[491, 490])).
% 29.56/19.20 tff(493,plain,
% 29.56/19.20 ($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[492, 483])).
% 29.56/19.20 tff(494,plain,
% 29.56/19.20 ((~($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0)) | $lesseq($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))), 0)),
% 29.56/19.20 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.20 tff(495,plain,
% 29.56/19.20 ($lesseq($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))), 0)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[494, 493])).
% 29.56/19.20 tff(496,assumption,(~$lesseq($sum(cardinality(C!8), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))), -3)), introduced(assumption)).
% 29.56/19.20 tff(497,plain,
% 29.56/19.20 (cardinality(empty_set) = cardinality(intersection(A0!7, singleton(X1!4)))),
% 29.56/19.20 inference(monotonicity,[status(thm)],[183])).
% 29.56/19.20 tff(498,plain,
% 29.56/19.20 (cardinality(intersection(A0!7, singleton(X1!4))) = cardinality(empty_set)),
% 29.56/19.20 inference(symmetry,[status(thm)],[497])).
% 29.56/19.20 tff(499,plain,
% 29.56/19.20 ((~(cardinality(intersection(A0!7, singleton(X1!4))) = cardinality(empty_set))) | $greatereq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(empty_set))), 0)),
% 29.56/19.20 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.20 tff(500,plain,
% 29.56/19.20 ($greatereq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(empty_set))), 0)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[499, 498])).
% 29.56/19.20 tff(501,plain,
% 29.56/19.20 ((~($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))) = 0)) | $greatereq($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))), 0)),
% 29.56/19.20 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.20 tff(502,plain,
% 29.56/19.20 ($greatereq($sum(cardinality(singleton(X1!4)), $sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set))))), 0)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[501, 112])).
% 29.56/19.20 tff(503,plain,
% 29.56/19.20 ((~($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))) = -1)) | $lesseq($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))), -1)),
% 29.56/19.20 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.20 tff(504,plain,
% 29.56/19.20 ($lesseq($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))), -1)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[503, 87])).
% 29.56/19.20 tff(505,plain,
% 29.56/19.20 ((~(cardinality(intersection(A0!7, singleton(X1!4))) = cardinality(empty_set))) | $lesseq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(empty_set))), 0)),
% 29.56/19.20 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.20 tff(506,plain,
% 29.56/19.20 ($lesseq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(empty_set))), 0)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[505, 498])).
% 29.56/19.20 tff(507,plain,
% 29.56/19.20 ((~$lesseq(cardinality(union(singleton(X1!4), empty_set)), 0)) | (~$lesseq($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))), -1)) | (~$greatereq(cardinality(intersection(A0!7, singleton(X1!4))), 0)) | (~$lesseq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(empty_set))), 0))),
% 29.56/19.20 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.20 tff(508,plain,
% 29.56/19.20 ((~$lesseq(cardinality(union(singleton(X1!4), empty_set)), 0)) | (~$lesseq($sum(cardinality(empty_set), $product(-1, cardinality(union(singleton(X1!4), empty_set)))), -1))),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[507, 506, 236])).
% 29.56/19.20 tff(509,plain,
% 29.56/19.20 (~$lesseq(cardinality(union(singleton(X1!4), empty_set)), 0)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[508, 504])).
% 29.56/19.20 tff(510,plain,
% 29.56/19.20 ((~($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))) = 0)) | $greatereq($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))), 0)),
% 29.56/19.20 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.20 tff(511,plain,
% 29.56/19.20 ($greatereq($sum(cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))), $sum($product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))), $product(-1, cardinality(singleton(X3!2))))), 0)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[510, 392])).
% 29.56/19.20 tff(512,plain,
% 29.56/19.20 ((~($sum(cardinality(A1!6), $product(-1, cardinality(union(singleton(X3!2), A1!6)))) = -1)) | $lesseq($sum(cardinality(A1!6), $product(-1, cardinality(union(singleton(X3!2), A1!6)))), -1)),
% 29.56/19.20 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.20 tff(513,plain,
% 29.56/19.20 ($lesseq($sum(cardinality(A1!6), $product(-1, cardinality(union(singleton(X3!2), A1!6)))), -1)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[512, 433])).
% 29.56/19.20 tff(514,plain,
% 29.56/19.20 ((~($sum(cardinality(A1!6), $sum(cardinality(singleton(X3!2)), $product(-1, cardinality(union(singleton(X3!2), A1!6))))) = 0)) | $greatereq($sum(cardinality(A1!6), $sum(cardinality(singleton(X3!2)), $product(-1, cardinality(union(singleton(X3!2), A1!6))))), 0)),
% 29.56/19.20 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.20 tff(515,plain,
% 29.56/19.20 ($greatereq($sum(cardinality(A1!6), $sum(cardinality(singleton(X3!2)), $product(-1, cardinality(union(singleton(X3!2), A1!6))))), 0)),
% 29.56/19.20 inference(unit_resolution,[status(thm)],[514, 440])).
% 29.56/19.20 tff(516,plain,
% 29.56/19.20 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)) | (~member(tptp_fun_X_0(C!8), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))) | (~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)) | (~member(tptp_fun_X_0(C!8), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))) | (~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3))))))))),
% 29.56/19.20 inference(rewrite,[status(thm)],[])).
% 29.56/19.20 tff(517,plain,
% 29.56/19.20 ((~((~((~member(tptp_fun_X_0(C!8), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))) | (~(intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)))) | (~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3))))))) <=> (~((~((~(intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)) | (~member(tptp_fun_X_0(C!8), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))) | (~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))))),
% 29.56/19.20 inference(rewrite,[status(thm)],[])).
% 29.56/19.20 tff(518,plain,
% 29.56/19.20 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(C!8), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))) | (~(intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)))) | (~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)) | (~member(tptp_fun_X_0(C!8), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))) | (~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3))))))))),
% 29.56/19.20 inference(monotonicity,[status(thm)],[517])).
% 29.56/19.20 tff(519,plain,
% 29.56/19.20 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(C!8), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))) | (~(intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)))) | (~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)) | (~member(tptp_fun_X_0(C!8), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))) | (~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3))))))))),
% 29.56/19.21 inference(transitivity,[status(thm)],[518, 516])).
% 29.56/19.21 tff(520,plain,
% 29.56/19.21 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(C!8), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))) | (~(intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)))) | (~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))))),
% 29.56/19.21 inference(quant_inst,[status(thm)],[])).
% 29.56/19.21 tff(521,plain,
% 29.56/19.21 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)) | (~member(tptp_fun_X_0(C!8), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))) | (~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))))),
% 29.56/19.21 inference(modus_ponens,[status(thm)],[520, 519])).
% 29.56/19.21 tff(522,plain,
% 29.56/19.21 (~((~((~(intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)) | (~member(tptp_fun_X_0(C!8), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))) | (~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3))))))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[521, 25])).
% 29.56/19.21 tff(523,plain,
% 29.56/19.21 (((~((~(intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)) | (~member(tptp_fun_X_0(C!8), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))) | (~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))))) | ((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3))))),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(524,plain,
% 29.56/19.21 ((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[523, 522])).
% 29.56/19.21 tff(525,plain,
% 29.56/19.21 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4))) <=> (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X1!4)) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), C!8)))),
% 29.56/19.21 inference(quant_inst,[status(thm)],[])).
% 29.56/19.21 tff(526,plain,
% 29.56/19.21 (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4))) <=> (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X1!4)) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), C!8))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[525, 283])).
% 29.56/19.21 tff(527,assumption,(~((~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4)))) | (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3))))), introduced(assumption)).
% 29.56/19.21 tff(528,plain,
% 29.56/19.21 (((~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4)))) | (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3)))) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4)))),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(529,plain,
% 29.56/19.21 (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4)))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[528, 527])).
% 29.56/19.21 tff(530,plain,
% 29.56/19.21 ((~(member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4))) <=> (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X1!4)) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), C!8)))) | (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4)))) | (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X1!4)) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), C!8))),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(531,plain,
% 29.56/19.21 ((~(member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4))) <=> (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X1!4)) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), C!8)))) | (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X1!4)) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), C!8))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[530, 529])).
% 29.56/19.21 tff(532,plain,
% 29.56/19.21 (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X1!4)) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), C!8)),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[531, 526])).
% 29.56/19.21 tff(533,plain,
% 29.56/19.21 ((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3)) <=> (tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))) = X2!3))),
% 29.56/19.21 inference(quant_inst,[status(thm)],[])).
% 29.56/19.21 tff(534,plain,
% 29.56/19.21 (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3)) <=> (tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))) = X2!3)),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[533, 134])).
% 29.56/19.21 tff(535,plain,
% 29.56/19.21 (((~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4)))) | (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3)))) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3))),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(536,plain,
% 29.56/19.21 (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[535, 527])).
% 29.56/19.21 tff(537,plain,
% 29.56/19.21 ((~(member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3)) <=> (tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))) = X2!3))) | (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3))) | (tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))) = X2!3)),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(538,plain,
% 29.56/19.21 ((~(member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3)) <=> (tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))) = X2!3))) | (tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))) = X2!3)),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[537, 536])).
% 29.56/19.21 tff(539,plain,
% 29.56/19.21 (tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))) = X2!3),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[538, 534])).
% 29.56/19.21 tff(540,plain,
% 29.56/19.21 (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X1!4)) <=> member(X2!3, singleton(X1!4))),
% 29.56/19.21 inference(monotonicity,[status(thm)],[539])).
% 29.56/19.21 tff(541,plain,
% 29.56/19.21 (member(X2!3, singleton(X1!4)) <=> member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X1!4))),
% 29.56/19.21 inference(symmetry,[status(thm)],[540])).
% 29.56/19.21 tff(542,plain,
% 29.56/19.21 ((~member(X2!3, singleton(X1!4))) <=> (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X1!4)))),
% 29.56/19.21 inference(monotonicity,[status(thm)],[541])).
% 29.56/19.21 tff(543,plain,
% 29.56/19.21 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A0!7, singleton(X1!4))) <=> (member(X2!3, singleton(X1!4)) | member(X2!3, A0!7)))),
% 29.56/19.21 inference(quant_inst,[status(thm)],[])).
% 29.56/19.21 tff(544,plain,
% 29.56/19.21 (member(X2!3, union(A0!7, singleton(X1!4))) <=> (member(X2!3, singleton(X1!4)) | member(X2!3, A0!7))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[543, 283])).
% 29.56/19.21 tff(545,plain,
% 29.56/19.21 (~member(X2!3, A1!6)),
% 29.56/19.21 inference(and_elim,[status(thm)],[161])).
% 29.56/19.21 tff(546,plain,
% 29.56/19.21 (((~![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6))) | ((~member(X2!3, union(A0!7, singleton(X1!4)))) | member(X2!3, A1!6))) <=> ((~![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6))) | (~member(X2!3, union(A0!7, singleton(X1!4)))) | member(X2!3, A1!6))),
% 29.56/19.21 inference(rewrite,[status(thm)],[])).
% 29.56/19.21 tff(547,plain,
% 29.56/19.21 ((~![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6))) | ((~member(X2!3, union(A0!7, singleton(X1!4)))) | member(X2!3, A1!6))),
% 29.56/19.21 inference(quant_inst,[status(thm)],[])).
% 29.56/19.21 tff(548,plain,
% 29.56/19.21 ((~![X: element] : ((~member(X, union(A0!7, singleton(X1!4)))) | member(X, A1!6))) | (~member(X2!3, union(A0!7, singleton(X1!4)))) | member(X2!3, A1!6)),
% 29.56/19.21 inference(modus_ponens,[status(thm)],[547, 546])).
% 29.56/19.21 tff(549,plain,
% 29.56/19.21 (~member(X2!3, union(A0!7, singleton(X1!4)))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[548, 545, 347])).
% 29.56/19.21 tff(550,plain,
% 29.56/19.21 ((~(member(X2!3, union(A0!7, singleton(X1!4))) <=> (member(X2!3, singleton(X1!4)) | member(X2!3, A0!7)))) | member(X2!3, union(A0!7, singleton(X1!4))) | (~(member(X2!3, singleton(X1!4)) | member(X2!3, A0!7)))),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(551,plain,
% 29.56/19.21 ((~(member(X2!3, union(A0!7, singleton(X1!4))) <=> (member(X2!3, singleton(X1!4)) | member(X2!3, A0!7)))) | (~(member(X2!3, singleton(X1!4)) | member(X2!3, A0!7)))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[550, 549])).
% 29.56/19.21 tff(552,plain,
% 29.56/19.21 (~(member(X2!3, singleton(X1!4)) | member(X2!3, A0!7))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[551, 544])).
% 29.56/19.21 tff(553,plain,
% 29.56/19.21 ((member(X2!3, singleton(X1!4)) | member(X2!3, A0!7)) | (~member(X2!3, singleton(X1!4)))),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(554,plain,
% 29.56/19.21 (~member(X2!3, singleton(X1!4))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[553, 552])).
% 29.56/19.21 tff(555,plain,
% 29.56/19.21 (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X1!4))),
% 29.56/19.21 inference(modus_ponens,[status(thm)],[554, 542])).
% 29.56/19.21 tff(556,plain,
% 29.56/19.21 (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), C!8) <=> member(X2!3, C!8)),
% 29.56/19.21 inference(monotonicity,[status(thm)],[539])).
% 29.56/19.21 tff(557,plain,
% 29.56/19.21 (member(X2!3, C!8) <=> member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), C!8)),
% 29.56/19.21 inference(symmetry,[status(thm)],[556])).
% 29.56/19.21 tff(558,plain,
% 29.56/19.21 ((~member(X2!3, C!8)) <=> (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), C!8))),
% 29.56/19.21 inference(monotonicity,[status(thm)],[557])).
% 29.56/19.21 tff(559,plain,
% 29.56/19.21 ((member(X2!3, singleton(X1!4)) | member(X2!3, A0!7)) | (~member(X2!3, A0!7))),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(560,plain,
% 29.56/19.21 (~member(X2!3, A0!7)),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[559, 552])).
% 29.56/19.21 tff(561,plain,
% 29.56/19.21 (((~![X: element] : ((~member(X, C!8)) | member(X, A0!7))) | ((~member(X2!3, C!8)) | member(X2!3, A0!7))) <=> ((~![X: element] : ((~member(X, C!8)) | member(X, A0!7))) | (~member(X2!3, C!8)) | member(X2!3, A0!7))),
% 29.56/19.21 inference(rewrite,[status(thm)],[])).
% 29.56/19.21 tff(562,plain,
% 29.56/19.21 ((~![X: element] : ((~member(X, C!8)) | member(X, A0!7))) | ((~member(X2!3, C!8)) | member(X2!3, A0!7))),
% 29.56/19.21 inference(quant_inst,[status(thm)],[])).
% 29.56/19.21 tff(563,plain,
% 29.56/19.21 ((~![X: element] : ((~member(X, C!8)) | member(X, A0!7))) | (~member(X2!3, C!8)) | member(X2!3, A0!7)),
% 29.56/19.21 inference(modus_ponens,[status(thm)],[562, 561])).
% 29.56/19.21 tff(564,plain,
% 29.56/19.21 (~member(X2!3, C!8)),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[563, 364, 560])).
% 29.56/19.21 tff(565,plain,
% 29.56/19.21 (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), C!8)),
% 29.56/19.21 inference(modus_ponens,[status(thm)],[564, 558])).
% 29.56/19.21 tff(566,plain,
% 29.56/19.21 ((~(member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X1!4)) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), C!8))) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X1!4)) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), C!8)),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(567,plain,
% 29.56/19.21 ($false),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[566, 565, 555, 532])).
% 29.56/19.21 tff(568,plain,((~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4)))) | (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3)))), inference(lemma,lemma(discharge,[]))).
% 29.56/19.21 tff(569,assumption,(~(member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3))) <=> (~((~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4)))) | (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3))))))), introduced(assumption)).
% 29.56/19.21 tff(570,plain,
% 29.56/19.21 ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3))) <=> (~((~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4)))) | (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3))))))),
% 29.56/19.21 inference(quant_inst,[status(thm)],[])).
% 29.56/19.21 tff(571,plain,
% 29.56/19.21 ($false),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[570, 46, 569])).
% 29.56/19.21 tff(572,plain,(member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3))) <=> (~((~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4)))) | (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3)))))), inference(lemma,lemma(discharge,[]))).
% 29.56/19.21 tff(573,plain,
% 29.56/19.21 ((~(member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3))) <=> (~((~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4)))) | (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3))))))) | (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))) | (~((~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4)))) | (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3)))))),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(574,plain,
% 29.56/19.21 ((~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))) | (~((~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), union(C!8, singleton(X1!4)))) | (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), singleton(X2!3)))))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[573, 572])).
% 29.56/19.21 tff(575,plain,
% 29.56/19.21 (~member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[574, 568])).
% 29.56/19.21 tff(576,plain,
% 29.56/19.21 ((~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3))))) | (intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3)))),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(577,plain,
% 29.56/19.21 ((~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) | member(tptp_fun_X_0(intersection(union(C!8, singleton(X1!4)), singleton(X2!3))), intersection(union(C!8, singleton(X1!4)), singleton(X2!3))))) | (intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[576, 575])).
% 29.56/19.21 tff(578,plain,
% 29.56/19.21 (intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[577, 524])).
% 29.56/19.21 tff(579,plain,
% 29.56/19.21 ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) <=> ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(C!8, singleton(X1!4))), $product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))))) = 0))),
% 29.56/19.21 inference(quant_inst,[status(thm)],[])).
% 29.56/19.21 tff(580,plain,
% 29.56/19.21 ((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) <=> ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(C!8, singleton(X1!4))), $product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))))) = 0)),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[579, 102])).
% 29.56/19.21 tff(581,plain,
% 29.56/19.21 ((~((intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set) <=> ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(C!8, singleton(X1!4))), $product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))))) = 0))) | (~(intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)) | ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(C!8, singleton(X1!4))), $product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))))) = 0)),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(582,plain,
% 29.56/19.21 ((~(intersection(union(C!8, singleton(X1!4)), singleton(X2!3)) = empty_set)) | ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(C!8, singleton(X1!4))), $product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))))) = 0)),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[581, 580])).
% 29.56/19.21 tff(583,plain,
% 29.56/19.21 ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(C!8, singleton(X1!4))), $product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))))) = 0),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[582, 578])).
% 29.56/19.21 tff(584,plain,
% 29.56/19.21 ((~($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(C!8, singleton(X1!4))), $product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))))) = 0)) | $lesseq($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(C!8, singleton(X1!4))), $product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))))), 0)),
% 29.56/19.21 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.21 tff(585,plain,
% 29.56/19.21 ($lesseq($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(C!8, singleton(X1!4))), $product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))))), 0)),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[584, 583])).
% 29.56/19.21 tff(586,assumption,(~(member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7))) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3))) | (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7))))))), introduced(assumption)).
% 29.56/19.21 tff(587,plain,
% 29.56/19.21 ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7))) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3))) | (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7))))))),
% 29.56/19.21 inference(quant_inst,[status(thm)],[])).
% 29.56/19.21 tff(588,plain,
% 29.56/19.21 ($false),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[587, 46, 586])).
% 29.56/19.21 tff(589,plain,(member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7))) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3))) | (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7)))))), inference(lemma,lemma(discharge,[]))).
% 29.56/19.21 tff(590,plain,
% 29.56/19.21 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7)) <=> (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), A0!7) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X3!2))))),
% 29.56/19.21 inference(quant_inst,[status(thm)],[])).
% 29.56/19.21 tff(591,plain,
% 29.56/19.21 (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7)) <=> (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), A0!7) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X3!2)))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[590, 283])).
% 29.56/19.21 tff(592,assumption,(~((~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3))) | (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7))))), introduced(assumption)).
% 29.56/19.21 tff(593,plain,
% 29.56/19.21 (((~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3))) | (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7)))) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7))),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(594,plain,
% 29.56/19.21 (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[593, 592])).
% 29.56/19.21 tff(595,plain,
% 29.56/19.21 ((~(member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7)) <=> (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), A0!7) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X3!2))))) | (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7))) | (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), A0!7) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X3!2)))),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(596,plain,
% 29.56/19.21 ((~(member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7)) <=> (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), A0!7) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X3!2))))) | (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), A0!7) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X3!2)))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[595, 594])).
% 29.56/19.21 tff(597,plain,
% 29.56/19.21 (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), A0!7) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X3!2))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[596, 591])).
% 29.56/19.21 tff(598,plain,
% 29.56/19.21 ((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3)) <=> (tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))) = X2!3))),
% 29.56/19.21 inference(quant_inst,[status(thm)],[])).
% 29.56/19.21 tff(599,plain,
% 29.56/19.21 (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3)) <=> (tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))) = X2!3)),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[598, 134])).
% 29.56/19.21 tff(600,plain,
% 29.56/19.21 (((~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3))) | (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7)))) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3))),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(601,plain,
% 29.56/19.21 (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[600, 592])).
% 29.56/19.21 tff(602,plain,
% 29.56/19.21 ((~(member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3)) <=> (tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))) = X2!3))) | (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3))) | (tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))) = X2!3)),
% 29.56/19.21 inference(tautology,[status(thm)],[])).
% 29.56/19.21 tff(603,plain,
% 29.56/19.21 ((~(member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3)) <=> (tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))) = X2!3))) | (tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))) = X2!3)),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[602, 601])).
% 29.56/19.21 tff(604,plain,
% 29.56/19.21 (tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))) = X2!3),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[603, 599])).
% 29.56/19.21 tff(605,plain,
% 29.56/19.21 (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), A0!7) <=> member(X2!3, A0!7)),
% 29.56/19.21 inference(monotonicity,[status(thm)],[604])).
% 29.56/19.21 tff(606,plain,
% 29.56/19.21 (member(X2!3, A0!7) <=> member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), A0!7)),
% 29.56/19.21 inference(symmetry,[status(thm)],[605])).
% 29.56/19.21 tff(607,plain,
% 29.56/19.21 ((~member(X2!3, A0!7)) <=> (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), A0!7))),
% 29.56/19.21 inference(monotonicity,[status(thm)],[606])).
% 29.56/19.21 tff(608,plain,
% 29.56/19.21 (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), A0!7)),
% 29.56/19.21 inference(modus_ponens,[status(thm)],[560, 607])).
% 29.56/19.21 tff(609,plain,
% 29.56/19.21 (member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X3!2)) <=> member(X2!3, singleton(X3!2))),
% 29.56/19.21 inference(monotonicity,[status(thm)],[604])).
% 29.56/19.21 tff(610,plain,
% 29.56/19.21 (member(X2!3, singleton(X3!2)) <=> member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X3!2))),
% 29.56/19.21 inference(symmetry,[status(thm)],[609])).
% 29.56/19.21 tff(611,plain,
% 29.56/19.21 ((~member(X2!3, singleton(X3!2))) <=> (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X3!2)))),
% 29.56/19.21 inference(monotonicity,[status(thm)],[610])).
% 29.56/19.21 tff(612,plain,
% 29.56/19.21 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(singleton(X3!2), A1!6)) <=> (member(X2!3, A1!6) | member(X2!3, singleton(X3!2))))),
% 29.56/19.21 inference(quant_inst,[status(thm)],[])).
% 29.56/19.21 tff(613,plain,
% 29.56/19.21 (member(X2!3, union(singleton(X3!2), A1!6)) <=> (member(X2!3, A1!6) | member(X2!3, singleton(X3!2)))),
% 29.56/19.21 inference(unit_resolution,[status(thm)],[612, 283])).
% 29.56/19.21 tff(614,assumption,(~(member(X2!3, union(A1!6, singleton(X2!3))) <=> (member(X2!3, A1!6) | member(X2!3, singleton(X2!3))))), introduced(assumption)).
% 29.56/19.21 tff(615,plain,
% 29.56/19.21 (((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A1!6, singleton(X2!3))) <=> (member(X2!3, A1!6) | member(X2!3, singleton(X2!3))))) <=> ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A1!6, singleton(X2!3))) <=> (member(X2!3, A1!6) | member(X2!3, singleton(X2!3)))))),
% 29.56/19.21 inference(rewrite,[status(thm)],[])).
% 29.56/19.21 tff(616,plain,
% 29.56/19.21 ((member(X2!3, union(A1!6, singleton(X2!3))) <=> (member(X2!3, singleton(X2!3)) | member(X2!3, A1!6))) <=> (member(X2!3, union(A1!6, singleton(X2!3))) <=> (member(X2!3, A1!6) | member(X2!3, singleton(X2!3))))),
% 29.56/19.21 inference(rewrite,[status(thm)],[])).
% 29.56/19.21 tff(617,plain,
% 29.56/19.21 (((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A1!6, singleton(X2!3))) <=> (member(X2!3, singleton(X2!3)) | member(X2!3, A1!6)))) <=> ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A1!6, singleton(X2!3))) <=> (member(X2!3, A1!6) | member(X2!3, singleton(X2!3)))))),
% 29.56/19.21 inference(monotonicity,[status(thm)],[616])).
% 29.56/19.21 tff(618,plain,
% 29.56/19.22 (((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A1!6, singleton(X2!3))) <=> (member(X2!3, singleton(X2!3)) | member(X2!3, A1!6)))) <=> ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A1!6, singleton(X2!3))) <=> (member(X2!3, A1!6) | member(X2!3, singleton(X2!3)))))),
% 29.56/19.22 inference(transitivity,[status(thm)],[617, 615])).
% 29.56/19.22 tff(619,plain,
% 29.56/19.22 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A1!6, singleton(X2!3))) <=> (member(X2!3, singleton(X2!3)) | member(X2!3, A1!6)))),
% 29.56/19.22 inference(quant_inst,[status(thm)],[])).
% 29.56/19.22 tff(620,plain,
% 29.56/19.22 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A1!6, singleton(X2!3))) <=> (member(X2!3, A1!6) | member(X2!3, singleton(X2!3))))),
% 29.56/19.22 inference(modus_ponens,[status(thm)],[619, 618])).
% 29.56/19.22 tff(621,plain,
% 29.56/19.22 ($false),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[620, 283, 614])).
% 29.56/19.22 tff(622,plain,(member(X2!3, union(A1!6, singleton(X2!3))) <=> (member(X2!3, A1!6) | member(X2!3, singleton(X2!3)))), inference(lemma,lemma(discharge,[]))).
% 29.56/19.22 tff(623,assumption,(~member(X2!3, singleton(X2!3))), introduced(assumption)).
% 29.56/19.22 tff(624,plain,
% 29.56/19.22 (((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | member(X2!3, singleton(X2!3))) <=> ((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | member(X2!3, singleton(X2!3)))),
% 29.56/19.22 inference(rewrite,[status(thm)],[])).
% 29.56/19.22 tff(625,plain,
% 29.56/19.22 ((member(X2!3, singleton(X2!3)) <=> $true) <=> member(X2!3, singleton(X2!3))),
% 29.56/19.22 inference(rewrite,[status(thm)],[])).
% 29.56/19.22 tff(626,plain,
% 29.56/19.22 ((X2!3 = X2!3) <=> $true),
% 29.56/19.22 inference(rewrite,[status(thm)],[])).
% 29.56/19.22 tff(627,plain,
% 29.56/19.22 ((member(X2!3, singleton(X2!3)) <=> (X2!3 = X2!3)) <=> (member(X2!3, singleton(X2!3)) <=> $true)),
% 29.56/19.22 inference(monotonicity,[status(thm)],[626])).
% 29.56/19.22 tff(628,plain,
% 29.56/19.22 ((member(X2!3, singleton(X2!3)) <=> (X2!3 = X2!3)) <=> member(X2!3, singleton(X2!3))),
% 29.56/19.22 inference(transitivity,[status(thm)],[627, 625])).
% 29.56/19.22 tff(629,plain,
% 29.56/19.22 (((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | (member(X2!3, singleton(X2!3)) <=> (X2!3 = X2!3))) <=> ((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | member(X2!3, singleton(X2!3)))),
% 29.56/19.22 inference(monotonicity,[status(thm)],[628])).
% 29.56/19.22 tff(630,plain,
% 29.56/19.22 (((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | (member(X2!3, singleton(X2!3)) <=> (X2!3 = X2!3))) <=> ((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | member(X2!3, singleton(X2!3)))),
% 29.56/19.22 inference(transitivity,[status(thm)],[629, 624])).
% 29.56/19.22 tff(631,plain,
% 29.56/19.22 ((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | (member(X2!3, singleton(X2!3)) <=> (X2!3 = X2!3))),
% 29.56/19.22 inference(quant_inst,[status(thm)],[])).
% 29.56/19.22 tff(632,plain,
% 29.56/19.22 ((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | member(X2!3, singleton(X2!3))),
% 29.56/19.22 inference(modus_ponens,[status(thm)],[631, 630])).
% 29.56/19.22 tff(633,plain,
% 29.56/19.22 ($false),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[632, 134, 623])).
% 29.56/19.22 tff(634,plain,(member(X2!3, singleton(X2!3))), inference(lemma,lemma(discharge,[]))).
% 29.56/19.22 tff(635,plain,
% 29.56/19.22 ((member(X2!3, A1!6) | member(X2!3, singleton(X2!3))) | (~member(X2!3, singleton(X2!3)))),
% 29.56/19.22 inference(tautology,[status(thm)],[])).
% 29.56/19.22 tff(636,plain,
% 29.56/19.22 (member(X2!3, A1!6) | member(X2!3, singleton(X2!3))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[635, 634])).
% 29.56/19.22 tff(637,plain,
% 29.56/19.22 ((~(member(X2!3, union(A1!6, singleton(X2!3))) <=> (member(X2!3, A1!6) | member(X2!3, singleton(X2!3))))) | member(X2!3, union(A1!6, singleton(X2!3))) | (~(member(X2!3, A1!6) | member(X2!3, singleton(X2!3))))),
% 29.56/19.22 inference(tautology,[status(thm)],[])).
% 29.56/19.22 tff(638,plain,
% 29.56/19.22 ((~(member(X2!3, union(A1!6, singleton(X2!3))) <=> (member(X2!3, A1!6) | member(X2!3, singleton(X2!3))))) | member(X2!3, union(A1!6, singleton(X2!3)))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[637, 636])).
% 29.56/19.22 tff(639,plain,
% 29.56/19.22 (member(X2!3, union(A1!6, singleton(X2!3)))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[638, 622])).
% 29.56/19.22 tff(640,assumption,(~member(X2!3, A2!5)), introduced(assumption)).
% 29.56/19.22 tff(641,plain,
% 29.56/19.22 (((~![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5))) | ((~member(X2!3, union(A1!6, singleton(X2!3)))) | member(X2!3, A2!5))) <=> ((~![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5))) | (~member(X2!3, union(A1!6, singleton(X2!3)))) | member(X2!3, A2!5))),
% 29.56/19.22 inference(rewrite,[status(thm)],[])).
% 29.56/19.22 tff(642,plain,
% 29.56/19.22 ((~![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5))) | ((~member(X2!3, union(A1!6, singleton(X2!3)))) | member(X2!3, A2!5))),
% 29.56/19.22 inference(quant_inst,[status(thm)],[])).
% 29.56/19.22 tff(643,plain,
% 29.56/19.22 ((~![X: element] : ((~member(X, union(A1!6, singleton(X2!3)))) | member(X, A2!5))) | (~member(X2!3, union(A1!6, singleton(X2!3)))) | member(X2!3, A2!5)),
% 29.56/19.22 inference(modus_ponens,[status(thm)],[642, 641])).
% 29.56/19.22 tff(644,plain,
% 29.56/19.22 ($false),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[643, 319, 640, 639])).
% 29.56/19.22 tff(645,plain,(member(X2!3, A2!5)), inference(lemma,lemma(discharge,[]))).
% 29.56/19.22 tff(646,assumption,(~(member(X2!3, union(A2!5, A2!5)) <=> member(X2!3, A2!5))), introduced(assumption)).
% 29.56/19.22 tff(647,plain,
% 29.56/19.22 (((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A2!5, A2!5)) <=> member(X2!3, A2!5))) <=> ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A2!5, A2!5)) <=> member(X2!3, A2!5)))),
% 29.56/19.22 inference(rewrite,[status(thm)],[])).
% 29.56/19.22 tff(648,plain,
% 29.56/19.22 ((member(X2!3, union(A2!5, A2!5)) <=> (member(X2!3, A2!5) | member(X2!3, A2!5))) <=> (member(X2!3, union(A2!5, A2!5)) <=> member(X2!3, A2!5))),
% 29.56/19.22 inference(rewrite,[status(thm)],[])).
% 29.56/19.22 tff(649,plain,
% 29.56/19.22 (((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A2!5, A2!5)) <=> (member(X2!3, A2!5) | member(X2!3, A2!5)))) <=> ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A2!5, A2!5)) <=> member(X2!3, A2!5)))),
% 29.56/19.22 inference(monotonicity,[status(thm)],[648])).
% 29.56/19.22 tff(650,plain,
% 29.56/19.22 (((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A2!5, A2!5)) <=> (member(X2!3, A2!5) | member(X2!3, A2!5)))) <=> ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A2!5, A2!5)) <=> member(X2!3, A2!5)))),
% 29.56/19.22 inference(transitivity,[status(thm)],[649, 647])).
% 29.56/19.22 tff(651,plain,
% 29.56/19.22 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A2!5, A2!5)) <=> (member(X2!3, A2!5) | member(X2!3, A2!5)))),
% 29.56/19.22 inference(quant_inst,[status(thm)],[])).
% 29.56/19.22 tff(652,plain,
% 29.56/19.22 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X2!3, union(A2!5, A2!5)) <=> member(X2!3, A2!5))),
% 29.56/19.22 inference(modus_ponens,[status(thm)],[651, 650])).
% 29.56/19.22 tff(653,plain,
% 29.56/19.22 ($false),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[652, 283, 646])).
% 29.56/19.22 tff(654,plain,(member(X2!3, union(A2!5, A2!5)) <=> member(X2!3, A2!5)), inference(lemma,lemma(discharge,[]))).
% 29.56/19.22 tff(655,plain,
% 29.56/19.22 ((~(member(X2!3, union(A2!5, A2!5)) <=> member(X2!3, A2!5))) | member(X2!3, union(A2!5, A2!5)) | (~member(X2!3, A2!5))),
% 29.56/19.22 inference(tautology,[status(thm)],[])).
% 29.56/19.22 tff(656,plain,
% 29.56/19.22 (member(X2!3, union(A2!5, A2!5)) | (~member(X2!3, A2!5))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[655, 654])).
% 29.56/19.22 tff(657,plain,
% 29.56/19.22 (member(X2!3, union(A2!5, A2!5))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[656, 645])).
% 29.56/19.22 tff(658,plain,
% 29.56/19.22 ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(X2!3, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) <=> (~((~member(X2!3, union(A2!5, A2!5))) | (~member(X2!3, union(singleton(X3!2), A1!6))))))),
% 29.56/19.22 inference(quant_inst,[status(thm)],[])).
% 29.56/19.22 tff(659,plain,
% 29.56/19.22 (member(X2!3, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) <=> (~((~member(X2!3, union(A2!5, A2!5))) | (~member(X2!3, union(singleton(X3!2), A1!6)))))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[658, 46])).
% 29.56/19.22 tff(660,plain,
% 29.56/19.22 ((~![X: element, A: element] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2)) <=> (tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) = X3!2))),
% 29.56/19.22 inference(quant_inst,[status(thm)],[])).
% 29.56/19.22 tff(661,plain,
% 29.56/19.22 (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2)) <=> (tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) = X3!2)),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[660, 134])).
% 29.56/19.22 tff(662,plain,
% 29.56/19.22 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6)) <=> (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2))))),
% 29.56/19.22 inference(quant_inst,[status(thm)],[])).
% 29.56/19.22 tff(663,plain,
% 29.56/19.22 (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6)) <=> (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2)))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[662, 283])).
% 29.56/19.22 tff(664,plain,
% 29.56/19.22 ((~![X: element, A: set, B: set] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) <=> (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5))) | (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6))))))),
% 29.56/19.22 inference(quant_inst,[status(thm)],[])).
% 29.56/19.22 tff(665,plain,
% 29.56/19.22 (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) <=> (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5))) | (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6)))))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[664, 46])).
% 29.56/19.22 tff(666,assumption,(~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6))), introduced(assumption)).
% 29.56/19.22 tff(667,plain,
% 29.56/19.22 (((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6)) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))),
% 29.56/19.22 inference(tautology,[status(thm)],[])).
% 29.56/19.22 tff(668,plain,
% 29.56/19.22 (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[667, 666])).
% 29.56/19.22 tff(669,plain,
% 29.56/19.22 ((~(member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) <=> (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5))) | (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6))))))) | (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5))) | (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6)))))),
% 29.56/19.22 inference(tautology,[status(thm)],[])).
% 29.56/19.22 tff(670,plain,
% 29.56/19.22 ((~(member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) <=> (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5))) | (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6))))))) | (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5))) | (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6)))))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[669, 668])).
% 29.56/19.22 tff(671,plain,
% 29.56/19.22 (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5))) | (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6))))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[670, 665])).
% 29.56/19.22 tff(672,plain,
% 29.56/19.22 (((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5))) | (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6))),
% 29.56/19.22 inference(tautology,[status(thm)],[])).
% 29.56/19.22 tff(673,plain,
% 29.56/19.22 (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[672, 671])).
% 29.56/19.22 tff(674,plain,
% 29.56/19.22 ((~(member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6)) <=> (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2))))) | (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6))) | (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2)))),
% 29.56/19.22 inference(tautology,[status(thm)],[])).
% 29.56/19.22 tff(675,plain,
% 29.56/19.22 ((~(member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6)) <=> (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2))))) | (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2)))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[674, 673])).
% 29.56/19.22 tff(676,plain,
% 29.56/19.22 (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[675, 663])).
% 29.56/19.22 tff(677,plain,
% 29.56/19.22 (((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6)) | (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6))),
% 29.56/19.22 inference(tautology,[status(thm)],[])).
% 29.56/19.22 tff(678,plain,
% 29.56/19.22 (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6)),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[677, 666])).
% 29.56/19.22 tff(679,plain,
% 29.56/19.22 ((~(member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2))),
% 29.56/19.22 inference(tautology,[status(thm)],[])).
% 29.56/19.22 tff(680,plain,
% 29.56/19.22 ((~(member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[679, 678])).
% 29.56/19.22 tff(681,plain,
% 29.56/19.22 (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[680, 676])).
% 29.56/19.22 tff(682,plain,
% 29.56/19.22 ((~(member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2)) <=> (tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) = X3!2))) | (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2))) | (tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) = X3!2)),
% 29.56/19.22 inference(tautology,[status(thm)],[])).
% 29.56/19.22 tff(683,plain,
% 29.56/19.22 ((~(member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), singleton(X3!2)) <=> (tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) = X3!2))) | (tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) = X3!2)),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[682, 681])).
% 29.56/19.22 tff(684,plain,
% 29.56/19.22 (tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) = X3!2),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[683, 661])).
% 29.56/19.22 tff(685,plain,
% 29.56/19.22 (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5) <=> member(X3!2, A2!5)),
% 29.56/19.22 inference(monotonicity,[status(thm)],[684])).
% 29.56/19.22 tff(686,plain,
% 29.56/19.22 (member(X3!2, A2!5) <=> member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5)),
% 29.56/19.22 inference(symmetry,[status(thm)],[685])).
% 29.56/19.22 tff(687,plain,
% 29.56/19.22 ((~member(X3!2, A2!5)) <=> (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5))),
% 29.56/19.22 inference(monotonicity,[status(thm)],[686])).
% 29.56/19.22 tff(688,plain,
% 29.56/19.22 (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5)),
% 29.56/19.22 inference(modus_ponens,[status(thm)],[320, 687])).
% 29.56/19.22 tff(689,plain,
% 29.56/19.22 (((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5)) <=> member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5))) <=> ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5)) <=> member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5)))),
% 29.56/19.22 inference(rewrite,[status(thm)],[])).
% 29.56/19.22 tff(690,plain,
% 29.56/19.22 ((member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5)) <=> (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5))) <=> (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5)) <=> member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5))),
% 29.56/19.22 inference(rewrite,[status(thm)],[])).
% 29.56/19.22 tff(691,plain,
% 29.56/19.22 (((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5)) <=> (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5)))) <=> ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5)) <=> member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5)))),
% 29.56/19.22 inference(monotonicity,[status(thm)],[690])).
% 29.56/19.22 tff(692,plain,
% 29.56/19.22 (((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5)) <=> (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5)))) <=> ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5)) <=> member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5)))),
% 29.56/19.22 inference(transitivity,[status(thm)],[691, 689])).
% 29.56/19.22 tff(693,plain,
% 29.56/19.22 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5)) <=> (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5)))),
% 29.56/19.22 inference(quant_inst,[status(thm)],[])).
% 29.56/19.22 tff(694,plain,
% 29.56/19.22 ((~![X: element, A: set, B: set] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5)) <=> member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5))),
% 29.56/19.22 inference(modus_ponens,[status(thm)],[693, 692])).
% 29.56/19.22 tff(695,plain,
% 29.56/19.22 (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5)) <=> member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5)),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[694, 283])).
% 29.56/19.22 tff(696,plain,
% 29.56/19.22 (((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5))) | (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5))),
% 29.56/19.22 inference(tautology,[status(thm)],[])).
% 29.56/19.22 tff(697,plain,
% 29.56/19.22 (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5))),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[696, 671])).
% 29.56/19.22 tff(698,plain,
% 29.56/19.22 ((~(member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5)) <=> member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5))) | (~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5)),
% 29.56/19.22 inference(tautology,[status(thm)],[])).
% 29.56/19.22 tff(699,plain,
% 29.56/19.22 ((~(member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), union(A2!5, A2!5)) <=> member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5)),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[698, 697])).
% 29.56/19.22 tff(700,plain,
% 29.56/19.22 (member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A2!5)),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[699, 695])).
% 29.56/19.22 tff(701,plain,
% 29.56/19.22 ($false),
% 29.56/19.22 inference(unit_resolution,[status(thm)],[700, 688])).
% 29.56/19.22 tff(702,plain,((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6)), inference(lemma,lemma(discharge,[]))).
% 29.56/19.23 tff(703,plain,
% 29.56/19.23 ((~![A: set, B: set] : (~((~((~subset(A, B)) | ![X: element] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_1(B, A), A)) | member(tptp_fun_X_1(B, A), B)))))))) | (~((~((~subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6)) | ![X: element] : ((~member(X, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X, A1!6)))) | (~(subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6) | (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6)))))))),
% 29.56/19.23 inference(quant_inst,[status(thm)],[])).
% 29.56/19.23 tff(704,plain,
% 29.56/19.23 (~((~((~subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6)) | ![X: element] : ((~member(X, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X, A1!6)))) | (~(subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6) | (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6))))))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[703, 311])).
% 29.56/19.23 tff(705,plain,
% 29.56/19.23 (((~((~subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6)) | ![X: element] : ((~member(X, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X, A1!6)))) | (~(subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6) | (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6)))))) | (subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6) | (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6))))),
% 29.56/19.23 inference(tautology,[status(thm)],[])).
% 29.56/19.23 tff(706,plain,
% 29.56/19.23 (subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6) | (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6)))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[705, 704])).
% 29.56/19.23 tff(707,plain,
% 29.56/19.23 ((~(subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6) | (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6))))) | subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6) | (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6)))),
% 29.56/19.23 inference(tautology,[status(thm)],[])).
% 29.56/19.23 tff(708,plain,
% 29.56/19.23 (subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6) | (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6)))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[707, 706])).
% 29.56/19.23 tff(709,plain,
% 29.56/19.23 (subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6)),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[708, 702])).
% 29.56/19.23 tff(710,plain,
% 29.56/19.23 (((~((~subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6)) | ![X: element] : ((~member(X, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X, A1!6)))) | (~(subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6) | (~((~member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(tptp_fun_X_1(A1!6, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))), A1!6)))))) | ((~subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6)) | ![X: element] : ((~member(X, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X, A1!6)))),
% 29.56/19.23 inference(tautology,[status(thm)],[])).
% 29.56/19.23 tff(711,plain,
% 29.56/19.23 ((~subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6)) | ![X: element] : ((~member(X, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X, A1!6))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[710, 704])).
% 29.56/19.23 tff(712,plain,
% 29.56/19.23 ((~((~subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6)) | ![X: element] : ((~member(X, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X, A1!6)))) | (~subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6)) | ![X: element] : ((~member(X, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X, A1!6))),
% 29.56/19.23 inference(tautology,[status(thm)],[])).
% 29.56/19.23 tff(713,plain,
% 29.56/19.23 ((~subset(intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)), A1!6)) | ![X: element] : ((~member(X, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X, A1!6))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[712, 711])).
% 29.56/19.23 tff(714,plain,
% 29.56/19.23 (![X: element] : ((~member(X, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X, A1!6))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[713, 709])).
% 29.56/19.23 tff(715,plain,
% 29.56/19.23 (((~![X: element] : ((~member(X, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X, A1!6))) | ((~member(X2!3, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X2!3, A1!6))) <=> ((~![X: element] : ((~member(X, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X, A1!6))) | (~member(X2!3, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X2!3, A1!6))),
% 29.56/19.23 inference(rewrite,[status(thm)],[])).
% 29.56/19.23 tff(716,plain,
% 29.56/19.23 ((~![X: element] : ((~member(X, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X, A1!6))) | ((~member(X2!3, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X2!3, A1!6))),
% 29.56/19.23 inference(quant_inst,[status(thm)],[])).
% 29.56/19.23 tff(717,plain,
% 29.56/19.23 ((~![X: element] : ((~member(X, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X, A1!6))) | (~member(X2!3, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))) | member(X2!3, A1!6)),
% 29.56/19.23 inference(modus_ponens,[status(thm)],[716, 715])).
% 29.56/19.23 tff(718,plain,
% 29.56/19.23 (~member(X2!3, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6)))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[717, 545, 714])).
% 29.56/19.23 tff(719,plain,
% 29.56/19.23 ((~(member(X2!3, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) <=> (~((~member(X2!3, union(A2!5, A2!5))) | (~member(X2!3, union(singleton(X3!2), A1!6))))))) | member(X2!3, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) | ((~member(X2!3, union(A2!5, A2!5))) | (~member(X2!3, union(singleton(X3!2), A1!6))))),
% 29.56/19.23 inference(tautology,[status(thm)],[])).
% 29.56/19.23 tff(720,plain,
% 29.56/19.23 ((~(member(X2!3, intersection(union(A2!5, A2!5), union(singleton(X3!2), A1!6))) <=> (~((~member(X2!3, union(A2!5, A2!5))) | (~member(X2!3, union(singleton(X3!2), A1!6))))))) | ((~member(X2!3, union(A2!5, A2!5))) | (~member(X2!3, union(singleton(X3!2), A1!6))))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[719, 718])).
% 29.56/19.23 tff(721,plain,
% 29.56/19.23 ((~member(X2!3, union(A2!5, A2!5))) | (~member(X2!3, union(singleton(X3!2), A1!6)))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[720, 659])).
% 29.56/19.23 tff(722,plain,
% 29.56/19.23 ((~((~member(X2!3, union(A2!5, A2!5))) | (~member(X2!3, union(singleton(X3!2), A1!6))))) | (~member(X2!3, union(A2!5, A2!5))) | (~member(X2!3, union(singleton(X3!2), A1!6)))),
% 29.56/19.23 inference(tautology,[status(thm)],[])).
% 29.56/19.23 tff(723,plain,
% 29.56/19.23 ((~member(X2!3, union(A2!5, A2!5))) | (~member(X2!3, union(singleton(X3!2), A1!6)))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[722, 721])).
% 29.56/19.23 tff(724,plain,
% 29.56/19.23 (~member(X2!3, union(singleton(X3!2), A1!6))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[723, 657])).
% 29.56/19.23 tff(725,plain,
% 29.56/19.23 ((~(member(X2!3, union(singleton(X3!2), A1!6)) <=> (member(X2!3, A1!6) | member(X2!3, singleton(X3!2))))) | member(X2!3, union(singleton(X3!2), A1!6)) | (~(member(X2!3, A1!6) | member(X2!3, singleton(X3!2))))),
% 29.56/19.23 inference(tautology,[status(thm)],[])).
% 29.56/19.23 tff(726,plain,
% 29.56/19.23 ((~(member(X2!3, union(singleton(X3!2), A1!6)) <=> (member(X2!3, A1!6) | member(X2!3, singleton(X3!2))))) | (~(member(X2!3, A1!6) | member(X2!3, singleton(X3!2))))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[725, 724])).
% 29.56/19.23 tff(727,plain,
% 29.56/19.23 (~(member(X2!3, A1!6) | member(X2!3, singleton(X3!2)))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[726, 613])).
% 29.56/19.23 tff(728,plain,
% 29.56/19.23 ((member(X2!3, A1!6) | member(X2!3, singleton(X3!2))) | (~member(X2!3, singleton(X3!2)))),
% 29.56/19.23 inference(tautology,[status(thm)],[])).
% 29.56/19.23 tff(729,plain,
% 29.56/19.23 (~member(X2!3, singleton(X3!2))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[728, 727])).
% 29.56/19.23 tff(730,plain,
% 29.56/19.23 (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X3!2))),
% 29.56/19.23 inference(modus_ponens,[status(thm)],[729, 611])).
% 29.56/19.23 tff(731,plain,
% 29.56/19.23 ((~(member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), A0!7) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X3!2)))) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), A0!7) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X3!2))),
% 29.56/19.23 inference(tautology,[status(thm)],[])).
% 29.56/19.23 tff(732,plain,
% 29.56/19.23 ($false),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[731, 730, 608, 597])).
% 29.56/19.23 tff(733,plain,((~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3))) | (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7)))), inference(lemma,lemma(discharge,[]))).
% 29.56/19.23 tff(734,plain,
% 29.56/19.23 ((~(member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7))) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3))) | (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7))))))) | (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))) | (~((~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3))) | (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7)))))),
% 29.56/19.23 inference(tautology,[status(thm)],[])).
% 29.56/19.23 tff(735,plain,
% 29.56/19.23 ((~(member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7))) <=> (~((~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), singleton(X2!3))) | (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), union(singleton(X3!2), A0!7))))))) | (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7))))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[734, 733])).
% 29.56/19.23 tff(736,plain,
% 29.56/19.23 (~member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[735, 589])).
% 29.56/19.23 tff(737,plain,
% 29.56/19.23 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)) | (~member(tptp_fun_X_0(union(singleton(X3!2), A0!7)), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))) | (~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)) | (~member(tptp_fun_X_0(union(singleton(X3!2), A0!7)), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))) | (~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7))))))))),
% 29.56/19.23 inference(rewrite,[status(thm)],[])).
% 29.56/19.23 tff(738,plain,
% 29.56/19.23 ((~((~((~member(tptp_fun_X_0(union(singleton(X3!2), A0!7)), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))) | (~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)))) | (~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7))))))) <=> (~((~((~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)) | (~member(tptp_fun_X_0(union(singleton(X3!2), A0!7)), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))) | (~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))))),
% 29.56/19.23 inference(rewrite,[status(thm)],[])).
% 29.56/19.23 tff(739,plain,
% 29.56/19.23 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(union(singleton(X3!2), A0!7)), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))) | (~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)))) | (~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)) | (~member(tptp_fun_X_0(union(singleton(X3!2), A0!7)), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))) | (~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7))))))))),
% 29.56/19.23 inference(monotonicity,[status(thm)],[738])).
% 29.56/19.23 tff(740,plain,
% 29.56/19.23 (((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(union(singleton(X3!2), A0!7)), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))) | (~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)))) | (~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))))) <=> ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)) | (~member(tptp_fun_X_0(union(singleton(X3!2), A0!7)), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))) | (~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7))))))))),
% 29.56/19.23 inference(transitivity,[status(thm)],[739, 737])).
% 29.56/19.23 tff(741,plain,
% 29.56/19.23 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~member(tptp_fun_X_0(union(singleton(X3!2), A0!7)), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))) | (~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)))) | (~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))))),
% 29.56/19.23 inference(quant_inst,[status(thm)],[])).
% 29.56/19.23 tff(742,plain,
% 29.56/19.23 ((~![S: set, X: element] : (~((~((~member(X, S)) | (~(S = empty_set)))) | (~((S = empty_set) | member(tptp_fun_X_0(S), S)))))) | (~((~((~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)) | (~member(tptp_fun_X_0(union(singleton(X3!2), A0!7)), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))) | (~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))))),
% 29.56/19.23 inference(modus_ponens,[status(thm)],[741, 740])).
% 29.56/19.23 tff(743,plain,
% 29.56/19.23 (~((~((~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)) | (~member(tptp_fun_X_0(union(singleton(X3!2), A0!7)), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))) | (~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7))))))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[742, 25])).
% 29.56/19.23 tff(744,plain,
% 29.56/19.23 (((~((~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)) | (~member(tptp_fun_X_0(union(singleton(X3!2), A0!7)), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))) | (~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))))) | ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7))))),
% 29.56/19.23 inference(tautology,[status(thm)],[])).
% 29.56/19.23 tff(745,plain,
% 29.56/19.23 ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[744, 743])).
% 29.56/19.23 tff(746,plain,
% 29.56/19.23 ((~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7))))) | (intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))),
% 29.56/19.23 inference(tautology,[status(thm)],[])).
% 29.56/19.23 tff(747,plain,
% 29.56/19.23 ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) | member(tptp_fun_X_0(intersection(singleton(X2!3), union(singleton(X3!2), A0!7))), intersection(singleton(X2!3), union(singleton(X3!2), A0!7)))),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[746, 745])).
% 29.56/19.23 tff(748,plain,
% 29.56/19.23 (intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[747, 736])).
% 29.56/19.23 tff(749,plain,
% 29.56/19.23 ((~![X: element, S: set] : ((intersection(singleton(X), S) = empty_set) <=> ($sum(cardinality(S), $product(-1, cardinality(union(singleton(X), S)))) = -1))) | ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7))))) = -1))),
% 29.56/19.23 inference(quant_inst,[status(thm)],[])).
% 29.56/19.23 tff(750,plain,
% 29.56/19.23 ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7))))) = -1)),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[749, 82])).
% 29.56/19.23 tff(751,plain,
% 29.56/19.23 ((~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7))))) = -1))) | (~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)) | ($sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7))))) = -1)),
% 29.56/19.23 inference(tautology,[status(thm)],[])).
% 29.56/19.23 tff(752,plain,
% 29.56/19.23 ((~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)) | ($sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7))))) = -1)),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[751, 750])).
% 29.56/19.23 tff(753,plain,
% 29.56/19.23 ($sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7))))) = -1),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[752, 748])).
% 29.56/19.23 tff(754,plain,
% 29.56/19.23 ((~($sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7))))) = -1)) | $lesseq($sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7))))), -1)),
% 29.56/19.23 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.23 tff(755,plain,
% 29.56/19.23 ($lesseq($sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7))))), -1)),
% 29.56/19.23 inference(unit_resolution,[status(thm)],[754, 753])).
% 29.56/19.23 tff(756,plain,
% 29.56/19.23 (((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0))) <=> ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0)))),
% 29.56/19.23 inference(rewrite,[status(thm)],[])).
% 29.56/19.23 tff(757,plain,
% 29.56/19.23 (((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(union(singleton(X3!2), A0!7)), $sum(cardinality(singleton(X2!3)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0)) <=> ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0))),
% 29.56/19.24 inference(rewrite,[status(thm)],[])).
% 29.56/19.24 tff(758,plain,
% 29.56/19.24 (((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(union(singleton(X3!2), A0!7)), $sum(cardinality(singleton(X2!3)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0))) <=> ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0)))),
% 29.56/19.24 inference(monotonicity,[status(thm)],[757])).
% 29.56/19.24 tff(759,plain,
% 29.56/19.24 (((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(union(singleton(X3!2), A0!7)), $sum(cardinality(singleton(X2!3)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0))) <=> ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0)))),
% 29.56/19.24 inference(transitivity,[status(thm)],[758, 756])).
% 29.56/19.24 tff(760,plain,
% 29.56/19.24 ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(union(singleton(X3!2), A0!7)), $sum(cardinality(singleton(X2!3)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0))),
% 29.56/19.24 inference(quant_inst,[status(thm)],[])).
% 29.56/19.24 tff(761,plain,
% 29.56/19.24 ((~![A: set, B: set] : ((intersection(A, B) = empty_set) <=> ($sum(cardinality(B), $sum(cardinality(A), $product(-1, cardinality(union(A, B))))) = 0))) | ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0))),
% 29.56/19.24 inference(modus_ponens,[status(thm)],[760, 759])).
% 29.56/19.24 tff(762,plain,
% 29.56/19.24 ((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0)),
% 29.56/19.24 inference(unit_resolution,[status(thm)],[761, 102])).
% 29.56/19.24 tff(763,plain,
% 29.56/19.24 ((~((intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set) <=> ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0))) | (~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)) | ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0)),
% 29.56/19.24 inference(tautology,[status(thm)],[])).
% 29.56/19.24 tff(764,plain,
% 29.56/19.24 ((~(intersection(singleton(X2!3), union(singleton(X3!2), A0!7)) = empty_set)) | ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0)),
% 29.56/19.24 inference(unit_resolution,[status(thm)],[763, 762])).
% 29.56/19.24 tff(765,plain,
% 29.56/19.24 ($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0),
% 29.56/19.24 inference(unit_resolution,[status(thm)],[764, 748])).
% 29.56/19.24 tff(766,plain,
% 29.56/19.24 ((~($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0)) | $greatereq($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))), 0)),
% 29.56/19.24 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.24 tff(767,plain,
% 29.56/19.24 ($greatereq($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))), 0)),
% 29.56/19.24 inference(unit_resolution,[status(thm)],[766, 765])).
% 29.56/19.24 tff(768,assumption,($lesseq($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))), 0)), introduced(assumption)).
% 29.56/19.24 tff(769,plain,
% 29.56/19.24 ($false),
% 29.56/19.24 inference(theory_lemma,[status(thm)],[768, 767, 755, 585, 515, 513, 511, 509, 502, 500, 241, 496])).
% 29.56/19.24 tff(770,plain,((~$lesseq($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))), 0)) | $lesseq($sum(cardinality(C!8), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))), -3)), inference(lemma,lemma(discharge,[]))).
% 29.56/19.24 tff(771,plain,
% 29.56/19.24 ($lesseq($sum(cardinality(C!8), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))), -3)),
% 29.56/19.24 inference(unit_resolution,[status(thm)],[770, 495])).
% 29.56/19.24 tff(772,plain,
% 29.56/19.24 (~($sum(cardinality(C!8), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))) = -3)),
% 29.56/19.24 inference(or_elim,[status(thm)],[160])).
% 29.56/19.24 tff(773,plain,
% 29.56/19.24 (($sum(cardinality(C!8), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))) = -3) | (~$lesseq($sum(cardinality(C!8), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))), -3)) | (~$greatereq($sum(cardinality(C!8), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))), -3))),
% 29.56/19.24 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.24 tff(774,plain,
% 29.56/19.24 ((~$lesseq($sum(cardinality(C!8), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))), -3)) | (~$greatereq($sum(cardinality(C!8), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))), -3))),
% 29.56/19.24 inference(unit_resolution,[status(thm)],[773, 772])).
% 29.56/19.24 tff(775,plain,
% 29.56/19.24 (~$greatereq($sum(cardinality(C!8), $product(-1, cardinality(union(union(union(C!8, singleton(X1!4)), singleton(X2!3)), singleton(X3!2))))), -3)),
% 29.56/19.24 inference(unit_resolution,[status(thm)],[774, 771])).
% 29.56/19.24 tff(776,plain,
% 29.56/19.24 ((~($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(C!8, singleton(X1!4))), $product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))))) = 0)) | $greatereq($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(C!8, singleton(X1!4))), $product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))))), 0)),
% 29.56/19.24 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.24 tff(777,plain,
% 29.56/19.24 ($greatereq($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(C!8, singleton(X1!4))), $product(-1, cardinality(union(union(C!8, singleton(X1!4)), singleton(X2!3)))))), 0)),
% 29.56/19.24 inference(unit_resolution,[status(thm)],[776, 583])).
% 29.56/19.24 tff(778,plain,
% 29.56/19.24 ((~($sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7))))) = -1)) | $greatereq($sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7))))), -1)),
% 29.56/19.24 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.24 tff(779,plain,
% 29.56/19.24 ($greatereq($sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7))))), -1)),
% 29.56/19.25 inference(unit_resolution,[status(thm)],[778, 753])).
% 29.56/19.25 tff(780,plain,
% 29.56/19.25 ((~($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))) = 0)) | $lesseq($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))), 0)),
% 29.56/19.25 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.25 tff(781,plain,
% 29.56/19.25 ($lesseq($sum(cardinality(singleton(X2!3)), $sum(cardinality(union(singleton(X3!2), A0!7)), $product(-1, cardinality(union(singleton(X2!3), union(singleton(X3!2), A0!7)))))), 0)),
% 29.56/19.25 inference(unit_resolution,[status(thm)],[780, 765])).
% 29.56/19.25 tff(782,plain,
% 29.56/19.25 ((~($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))) = 0)) | $greatereq($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))), 0)),
% 29.56/19.25 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.25 tff(783,plain,
% 29.56/19.25 ($greatereq($sum(cardinality(C!8), $sum(cardinality(singleton(X1!4)), $product(-1, cardinality(union(C!8, singleton(X1!4)))))), 0)),
% 29.56/19.25 inference(unit_resolution,[status(thm)],[782, 493])).
% 29.56/19.25 tff(784,plain,
% 29.56/19.25 ((~($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))) = -1)) | $greatereq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))), -1)),
% 29.56/19.25 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.25 tff(785,plain,
% 29.56/19.25 ($greatereq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4)))))), -1)),
% 29.56/19.25 inference(unit_resolution,[status(thm)],[784, 220])).
% 29.56/19.25 tff(786,plain,
% 29.56/19.25 ((~($sum(cardinality(intersection(A0!7, singleton(X1!4))), $sum(cardinality(singleton(tptp_fun_X_0(A1!6))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))) = 0)) | $lesseq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $sum(cardinality(singleton(tptp_fun_X_0(A1!6))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))), 0)),
% 29.56/19.25 inference(theory_lemma,[status(thm)],[])).
% 29.56/19.25 tff(787,plain,
% 29.56/19.25 ($lesseq($sum(cardinality(intersection(A0!7, singleton(X1!4))), $sum(cardinality(singleton(tptp_fun_X_0(A1!6))), $product(-1, cardinality(union(singleton(tptp_fun_X_0(A1!6)), intersection(A0!7, singleton(X1!4))))))), 0)),
% 29.56/19.25 inference(unit_resolution,[status(thm)],[786, 213])).
% 29.56/19.25 tff(788,plain,
% 29.56/19.25 ($false),
% 29.56/19.25 inference(theory_lemma,[status(thm)],[787, 785, 783, 781, 779, 777, 775, 442, 435, 394, 244])).
% 29.56/19.25 % SZS output end Proof
%------------------------------------------------------------------------------