TSTP Solution File: SEU120+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU120+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 07:27:33 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SEU120+1 : TPTP v8.1.0. Released v3.3.0.
% 0.05/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 09:30:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(in_type, type, (
% 0.19/0.46 in: ( $i * $i ) > $o)).
% 0.19/0.46 tff(set_intersection2_type, type, (
% 0.19/0.46 set_intersection2: ( $i * $i ) > $i)).
% 0.19/0.46 tff(tptp_fun_B_3_type, type, (
% 0.19/0.46 tptp_fun_B_3: $i)).
% 0.19/0.46 tff(tptp_fun_A_4_type, type, (
% 0.19/0.46 tptp_fun_A_4: $i)).
% 0.19/0.46 tff(tptp_fun_B_0_type, type, (
% 0.19/0.46 tptp_fun_B_0: $i > $i)).
% 0.19/0.46 tff(empty_set_type, type, (
% 0.19/0.46 empty_set: $i)).
% 0.19/0.46 tff(disjoint_type, type, (
% 0.19/0.46 disjoint: ( $i * $i ) > $o)).
% 0.19/0.46 tff(tptp_fun_C_5_type, type, (
% 0.19/0.46 tptp_fun_C_5: $i)).
% 0.19/0.46 tff(1,plain,
% 0.19/0.46 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(2,plain,
% 0.19/0.46 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.46 tff(3,plain,
% 0.19/0.46 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(4,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.19/0.46 tff(5,plain,
% 0.19/0.46 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.46 tff(6,plain,(
% 0.19/0.46 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.46 inference(skolemize,[status(sab)],[5])).
% 0.19/0.46 tff(7,plain,
% 0.19/0.46 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.46 tff(8,plain,
% 0.19/0.46 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!4, B!3) = set_intersection2(B!3, A!4))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(9,plain,
% 0.19/0.46 (set_intersection2(A!4, B!3) = set_intersection2(B!3, A!4)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.46 tff(10,plain,
% 0.19/0.46 (in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(A!4, B!3)) <=> in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[9])).
% 0.19/0.46 tff(11,plain,
% 0.19/0.46 (in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4)) <=> in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(A!4, B!3))),
% 0.19/0.46 inference(symmetry,[status(thm)],[10])).
% 0.19/0.46 tff(12,plain,
% 0.19/0.46 (^[A: $i, B: $i] : refl((~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(13,plain,
% 0.19/0.46 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 (![A: $i] : ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 0.19/0.46 inference(pull_quant,[status(thm)],[])).
% 0.19/0.46 tff(15,plain,
% 0.19/0.46 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(A = empty_set)) | ![B: $i] : (~in(B, A))) <=> ![B: $i] : ((~(A = empty_set)) | (~in(B, A)))), ((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) <=> (~![B: $i] : ((~(A = empty_set)) | (~in(B, A)))))), pull_quant((~![B: $i] : ((~(A = empty_set)) | (~in(B, A)))) <=> ?[B: $i] : (~((~(A = empty_set)) | (~in(B, A))))), ((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) <=> ?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))))), (((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))) <=> (?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), pull_quant((?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))) <=> ?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))), (((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))) <=> ?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), ((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> (~?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))))), pull_quant((~?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), ((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(16,plain,
% 0.19/0.47 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i] : ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.47 tff(17,plain,
% 0.19/0.47 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[16, 14])).
% 0.19/0.47 tff(18,plain,
% 0.19/0.47 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[17, 13])).
% 0.19/0.47 tff(19,plain,
% 0.19/0.47 (^[A: $i] : rewrite((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(20,plain,
% 0.19/0.47 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.47 tff(21,plain,
% 0.19/0.47 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[20, 18])).
% 0.19/0.47 tff(22,plain,
% 0.19/0.47 (^[A: $i] : trans(monotonicity(rewrite(((~(A = empty_set)) | ![B: $i] : (~in(B, A))) <=> ((~(A = empty_set)) | ![B: $i] : (~in(B, A)))), ((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))))), rewrite((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), ((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(23,plain,
% 0.19/0.47 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> ![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.47 tff(24,plain,
% 0.19/0.47 (^[A: $i] : rewrite((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | (~(~in(tptp_fun_B_0(A), A))))) <=> (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(25,plain,
% 0.19/0.47 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | (~(~in(tptp_fun_B_0(A), A))))) <=> ![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.47 tff(26,plain,
% 0.19/0.47 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A))) <=> ![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(27,axiom,(![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_xboole_0')).
% 0.19/0.47 tff(28,plain,
% 0.19/0.47 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.47 tff(29,plain,(
% 0.19/0.47 ![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | (~(~in(tptp_fun_B_0(A), A)))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[28])).
% 0.19/0.47 tff(30,plain,
% 0.19/0.47 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.47 tff(31,plain,
% 0.19/0.47 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.19/0.47 tff(32,plain,
% 0.19/0.47 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.19/0.47 tff(33,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(set_intersection2(B!3, A!4) = empty_set)) | (~in(A!4, set_intersection2(B!3, A!4))))) | (~((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(34,plain,
% 0.19/0.47 (~((~((~(set_intersection2(B!3, A!4) = empty_set)) | (~in(A!4, set_intersection2(B!3, A!4))))) | (~((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.47 tff(35,plain,
% 0.19/0.47 (((~((~(set_intersection2(B!3, A!4) = empty_set)) | (~in(A!4, set_intersection2(B!3, A!4))))) | (~((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))))) | ((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(36,plain,
% 0.19/0.47 ((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.47 tff(37,plain,
% 0.19/0.47 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(38,plain,
% 0.19/0.47 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.47 tff(39,plain,
% 0.19/0.47 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(40,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_xboole_0')).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.47 tff(42,plain,(
% 0.19/0.47 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.19/0.47 inference(skolemize,[status(sab)],[41])).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.47 tff(44,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(B!3, A!4) <=> (set_intersection2(B!3, A!4) = empty_set))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 (disjoint(B!3, A!4) <=> (set_intersection2(B!3, A!4) = empty_set)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.47 tff(46,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(set_intersection2(A!4, B!3) = empty_set)) | (~in(C!5, set_intersection2(A!4, B!3))))) | (~((set_intersection2(A!4, B!3) = empty_set) | in(tptp_fun_B_0(set_intersection2(A!4, B!3)), set_intersection2(A!4, B!3))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(47,plain,
% 0.19/0.47 (~((~((~(set_intersection2(A!4, B!3) = empty_set)) | (~in(C!5, set_intersection2(A!4, B!3))))) | (~((set_intersection2(A!4, B!3) = empty_set) | in(tptp_fun_B_0(set_intersection2(A!4, B!3)), set_intersection2(A!4, B!3)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[46, 32])).
% 0.19/0.47 tff(48,plain,
% 0.19/0.47 (((~((~(set_intersection2(A!4, B!3) = empty_set)) | (~in(C!5, set_intersection2(A!4, B!3))))) | (~((set_intersection2(A!4, B!3) = empty_set) | in(tptp_fun_B_0(set_intersection2(A!4, B!3)), set_intersection2(A!4, B!3))))) | ((~(set_intersection2(A!4, B!3) = empty_set)) | (~in(C!5, set_intersection2(A!4, B!3))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(49,plain,
% 0.19/0.47 ((~(set_intersection2(A!4, B!3) = empty_set)) | (~in(C!5, set_intersection2(A!4, B!3)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.47 tff(50,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(A!4, B!3) <=> (set_intersection2(A!4, B!3) = empty_set))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(51,plain,
% 0.19/0.47 (disjoint(A!4, B!3) <=> (set_intersection2(A!4, B!3) = empty_set)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[50, 43])).
% 0.19/0.47 tff(52,assumption,(~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))), introduced(assumption)).
% 0.19/0.47 tff(53,plain,
% 0.19/0.47 (((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))) | disjoint(A!4, B!3)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(54,plain,
% 0.19/0.47 (disjoint(A!4, B!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.47 tff(55,plain,
% 0.19/0.47 ((~(disjoint(A!4, B!3) <=> (set_intersection2(A!4, B!3) = empty_set))) | (~disjoint(A!4, B!3)) | (set_intersection2(A!4, B!3) = empty_set)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(56,plain,
% 0.19/0.47 ((~(disjoint(A!4, B!3) <=> (set_intersection2(A!4, B!3) = empty_set))) | (set_intersection2(A!4, B!3) = empty_set)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.47 tff(57,plain,
% 0.19/0.47 (set_intersection2(A!4, B!3) = empty_set),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[56, 51])).
% 0.19/0.47 tff(58,plain,
% 0.19/0.47 (((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))) | in(C!5, set_intersection2(A!4, B!3))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(59,plain,
% 0.19/0.47 (in(C!5, set_intersection2(A!4, B!3))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[58, 52])).
% 0.19/0.47 tff(60,plain,
% 0.19/0.47 ((~((~(set_intersection2(A!4, B!3) = empty_set)) | (~in(C!5, set_intersection2(A!4, B!3))))) | (~(set_intersection2(A!4, B!3) = empty_set)) | (~in(C!5, set_intersection2(A!4, B!3)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 ((~((~(set_intersection2(A!4, B!3) = empty_set)) | (~in(C!5, set_intersection2(A!4, B!3))))) | (~(set_intersection2(A!4, B!3) = empty_set))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.47 tff(62,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[61, 57, 49])).
% 0.19/0.47 tff(63,plain,((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 (((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))) <=> ((~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))) | (~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(65,plain,
% 0.19/0.48 ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) <=> (~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(66,plain,
% 0.19/0.48 (((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))) <=> ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[65])).
% 0.19/0.48 tff(67,plain,
% 0.19/0.48 (((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))) <=> ((~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))) | (~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[66, 64])).
% 0.19/0.48 tff(68,plain,
% 0.19/0.48 (((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))) <=> ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(69,plain,
% 0.19/0.48 (((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))) <=> ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(70,plain,
% 0.19/0.48 ((in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3)) <=> (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(71,plain,
% 0.19/0.48 (((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) <=> (~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(72,plain,
% 0.19/0.48 ((((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3))) <=> ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[71, 70])).
% 0.19/0.48 tff(73,plain,
% 0.19/0.48 ((((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3))) <=> ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[72, 69])).
% 0.19/0.48 tff(74,plain,
% 0.19/0.48 ((((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3))) <=> (((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(75,plain,
% 0.19/0.48 (((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) <=> ((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(76,plain,
% 0.19/0.48 ((((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3))) <=> (((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.48 tff(77,plain,
% 0.19/0.48 ((((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3))) <=> (((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[76, 74])).
% 0.19/0.48 tff(78,plain,
% 0.19/0.48 ((~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))) <=> (~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(79,axiom,(~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_xboole_0')).
% 0.19/0.48 tff(80,plain,
% 0.19/0.48 (~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.48 tff(81,plain,
% 0.19/0.48 (~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[80, 78])).
% 0.19/0.48 tff(82,plain,
% 0.19/0.48 (~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.19/0.48 tff(83,plain,
% 0.19/0.48 (~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.19/0.48 tff(84,plain,
% 0.19/0.48 (~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[83, 78])).
% 0.19/0.48 tff(85,plain,
% 0.19/0.48 (~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[84, 78])).
% 0.19/0.48 tff(86,plain,
% 0.19/0.48 (~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.19/0.48 tff(87,plain,
% 0.19/0.48 (((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[86, 77])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[87, 73])).
% 0.19/0.48 tff(89,plain,
% 0.19/0.48 ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[88, 68])).
% 0.19/0.48 tff(90,plain,
% 0.19/0.48 ((~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))) | (~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[89, 67])).
% 0.19/0.48 tff(91,plain,
% 0.19/0.48 (~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[90, 63])).
% 0.19/0.48 tff(92,plain,
% 0.19/0.48 ((disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3))))) | (~disjoint(A!4, B!3))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(93,plain,
% 0.19/0.48 (~disjoint(A!4, B!3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.19/0.48 tff(94,plain,
% 0.19/0.48 (^[A: $i, B: $i] : refl(((~disjoint(A, B)) | disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(95,plain,
% 0.19/0.48 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.48 tff(96,plain,
% 0.19/0.48 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(97,plain,
% 0.19/0.48 (^[A: $i, B: $i] : rewrite((disjoint(A, B) => disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(98,plain,
% 0.19/0.48 (![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[97])).
% 0.19/0.48 tff(99,axiom,(![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.48 tff(101,plain,
% 0.19/0.48 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.19/0.48 tff(102,plain,(
% 0.19/0.48 ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.19/0.48 inference(skolemize,[status(sab)],[101])).
% 0.19/0.48 tff(103,plain,
% 0.19/0.48 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.19/0.48 tff(104,plain,
% 0.19/0.48 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!3, A!4)) | disjoint(A!4, B!3))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!3, A!4)) | disjoint(A!4, B!3))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(105,plain,
% 0.19/0.48 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!3, A!4)) | disjoint(A!4, B!3))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(106,plain,
% 0.19/0.48 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!3, A!4)) | disjoint(A!4, B!3)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 (~disjoint(B!3, A!4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[106, 103, 93])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 ((~(disjoint(B!3, A!4) <=> (set_intersection2(B!3, A!4) = empty_set))) | disjoint(B!3, A!4) | (~(set_intersection2(B!3, A!4) = empty_set))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(109,plain,
% 0.19/0.48 ((~(disjoint(B!3, A!4) <=> (set_intersection2(B!3, A!4) = empty_set))) | (~(set_intersection2(B!3, A!4) = empty_set))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 (~(set_intersection2(B!3, A!4) = empty_set)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[109, 45])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 ((~((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4)))) | (set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(112,plain,
% 0.19/0.48 ((~((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4)))) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.19/0.48 tff(113,plain,
% 0.19/0.48 (in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[112, 36])).
% 0.19/0.48 tff(114,plain,
% 0.19/0.48 (in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(A!4, B!3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[113, 11])).
% 0.19/0.48 tff(115,plain,
% 0.19/0.48 ((disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3))))) | ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(116,plain,
% 0.19/0.48 (![C: $i] : (~in(C, set_intersection2(A!4, B!3)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[115, 91])).
% 0.19/0.48 tff(117,plain,
% 0.19/0.48 ((~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (~in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(A!4, B!3)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(118,plain,
% 0.19/0.48 (~in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(A!4, B!3))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.19/0.48 tff(119,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[118, 114])).
% 0.19/0.48 % SZS output end Proof
%------------------------------------------------------------------------------