TSTP Solution File: SEU142+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU142+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 07:27:44 EDT 2022
% Result : Theorem 65.27s 41.97s
% Output : Proof 65.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU142+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n025.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 09:48:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 65.27/41.97 % SZS status Theorem
% 65.27/41.97 % SZS output start Proof
% 65.27/41.97 tff(set_union2_type, type, (
% 65.27/41.97 set_union2: ( $i * $i ) > $i)).
% 65.27/41.97 tff(tptp_fun_A_12_type, type, (
% 65.27/41.97 tptp_fun_A_12: $i)).
% 65.27/41.97 tff(tptp_fun_A_7_type, type, (
% 65.27/41.97 tptp_fun_A_7: $i)).
% 65.27/41.97 tff(tptp_fun_C_4_type, type, (
% 65.27/41.97 tptp_fun_C_4: ( $i * $i ) > $i)).
% 65.27/41.97 tff(unordered_pair_type, type, (
% 65.27/41.97 unordered_pair: ( $i * $i ) > $i)).
% 65.27/41.97 tff(singleton_type, type, (
% 65.27/41.97 singleton: $i > $i)).
% 65.27/41.97 tff(set_intersection2_type, type, (
% 65.27/41.97 set_intersection2: ( $i * $i ) > $i)).
% 65.27/41.97 tff(set_difference_type, type, (
% 65.27/41.97 set_difference: ( $i * $i ) > $i)).
% 65.27/41.97 tff(in_type, type, (
% 65.27/41.97 in: ( $i * $i ) > $o)).
% 65.27/41.97 tff(tptp_fun_C_0_type, type, (
% 65.27/41.97 tptp_fun_C_0: ( $i * $i ) > $i)).
% 65.27/41.97 tff(empty_set_type, type, (
% 65.27/41.97 empty_set: $i)).
% 65.27/41.97 tff(empty_type, type, (
% 65.27/41.97 empty: $i > $o)).
% 65.27/41.97 tff(subset_type, type, (
% 65.27/41.97 subset: ( $i * $i ) > $o)).
% 65.27/41.97 tff(tptp_fun_D_2_type, type, (
% 65.27/41.97 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 65.27/41.97 tff(1,plain,
% 65.27/41.97 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 65.27/41.97 inference(bind,[status(th)],[])).
% 65.27/41.97 tff(2,plain,
% 65.27/41.97 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 65.27/41.97 inference(quant_intro,[status(thm)],[1])).
% 65.27/41.97 tff(3,plain,
% 65.27/41.97 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 65.27/41.97 inference(pull_quant,[status(thm)],[])).
% 65.27/41.97 tff(4,plain,
% 65.27/41.97 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 65.27/41.97 inference(bind,[status(th)],[])).
% 65.27/41.97 tff(5,plain,
% 65.27/41.97 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 65.27/41.97 inference(quant_intro,[status(thm)],[4])).
% 65.27/41.97 tff(6,plain,
% 65.27/41.97 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 65.27/41.97 inference(transitivity,[status(thm)],[5, 3])).
% 65.27/41.97 tff(7,plain,
% 65.27/41.97 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 65.27/41.97 inference(transitivity,[status(thm)],[6, 2])).
% 65.27/41.97 tff(8,plain,
% 65.27/41.97 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 65.27/41.97 inference(bind,[status(th)],[])).
% 65.27/41.97 tff(9,plain,
% 65.27/41.97 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 65.27/41.97 inference(quant_intro,[status(thm)],[8])).
% 65.27/41.97 tff(10,plain,
% 65.27/41.97 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 65.27/41.97 inference(transitivity,[status(thm)],[9, 7])).
% 65.27/41.97 tff(11,plain,
% 65.27/41.97 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 65.27/41.97 inference(bind,[status(th)],[])).
% 65.27/41.97 tff(12,plain,
% 65.27/41.97 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 65.27/41.97 inference(quant_intro,[status(thm)],[11])).
% 65.27/41.97 tff(13,plain,
% 65.27/41.97 (^[A: $i, B: $i] : rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))),
% 65.27/41.97 inference(bind,[status(th)],[])).
% 65.27/41.97 tff(14,plain,
% 65.27/41.97 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 65.27/41.97 inference(quant_intro,[status(thm)],[13])).
% 65.27/41.97 tff(15,plain,
% 65.27/41.97 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 65.27/41.97 inference(rewrite,[status(thm)],[])).
% 65.27/41.97 tff(16,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 65.27/41.97 tff(17,plain,
% 65.27/41.97 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 65.27/41.97 inference(modus_ponens,[status(thm)],[16, 15])).
% 65.27/41.97 tff(18,plain,(
% 65.27/41.97 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 65.27/41.97 inference(skolemize,[status(sab)],[17])).
% 65.27/41.97 tff(19,plain,
% 65.27/41.97 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 65.27/41.97 inference(modus_ponens,[status(thm)],[18, 14])).
% 65.27/41.97 tff(20,plain,
% 65.27/41.97 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 65.27/41.97 inference(modus_ponens,[status(thm)],[19, 12])).
% 65.27/41.97 tff(21,plain,
% 65.27/41.97 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 65.27/41.97 inference(modus_ponens,[status(thm)],[20, 10])).
% 65.27/41.97 tff(22,plain,
% 65.27/41.97 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))) | (~((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))) | (~((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))))))),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(23,plain,
% 65.27/41.98 ((~((~((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (~((set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))) <=> (~((~((set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))) | (~((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))))))),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(24,plain,
% 65.27/41.98 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (~((set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))) | (~((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))))))),
% 65.27/41.98 inference(monotonicity,[status(thm)],[23])).
% 65.27/41.98 tff(25,plain,
% 65.27/41.98 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (~((set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))) | (~((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))))))),
% 65.27/41.98 inference(transitivity,[status(thm)],[24, 22])).
% 65.27/41.98 tff(26,plain,
% 65.27/41.98 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (~((set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))))),
% 65.27/41.98 inference(quant_inst,[status(thm)],[])).
% 65.27/41.98 tff(27,plain,
% 65.27/41.98 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))) | (~((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))))))),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[26, 25])).
% 65.27/41.98 tff(28,plain,
% 65.27/41.98 (~((~((set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))) | (~((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))))),
% 65.27/41.98 inference(unit_resolution,[status(thm)],[27, 21])).
% 65.27/41.98 tff(29,plain,
% 65.27/41.98 (((~((set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))) | (~((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))))) | ((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))),
% 65.27/41.98 inference(tautology,[status(thm)],[])).
% 65.27/41.98 tff(30,plain,
% 65.27/41.98 ((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))),
% 65.27/41.98 inference(unit_resolution,[status(thm)],[29, 28])).
% 65.27/41.98 tff(31,plain,
% 65.27/41.98 (^[A: $i] : refl((set_union2(A, empty_set) = A) <=> (set_union2(A, empty_set) = A))),
% 65.27/41.98 inference(bind,[status(th)],[])).
% 65.27/41.98 tff(32,plain,
% 65.27/41.98 (![A: $i] : (set_union2(A, empty_set) = A) <=> ![A: $i] : (set_union2(A, empty_set) = A)),
% 65.27/41.98 inference(quant_intro,[status(thm)],[31])).
% 65.27/41.98 tff(33,plain,
% 65.27/41.98 (![A: $i] : (set_union2(A, empty_set) = A) <=> ![A: $i] : (set_union2(A, empty_set) = A)),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(34,axiom,(![A: $i] : (set_union2(A, empty_set) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_boole')).
% 65.27/41.98 tff(35,plain,
% 65.27/41.98 (![A: $i] : (set_union2(A, empty_set) = A)),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[34, 33])).
% 65.27/41.98 tff(36,plain,(
% 65.27/41.98 ![A: $i] : (set_union2(A, empty_set) = A)),
% 65.27/41.98 inference(skolemize,[status(sab)],[35])).
% 65.27/41.98 tff(37,plain,
% 65.27/41.98 (![A: $i] : (set_union2(A, empty_set) = A)),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[36, 32])).
% 65.27/41.98 tff(38,plain,
% 65.27/41.98 ((~![A: $i] : (set_union2(A, empty_set) = A)) | (set_union2(A!12, empty_set) = A!12)),
% 65.27/41.98 inference(quant_inst,[status(thm)],[])).
% 65.27/41.98 tff(39,plain,
% 65.27/41.98 (set_union2(A!12, empty_set) = A!12),
% 65.27/41.98 inference(unit_resolution,[status(thm)],[38, 37])).
% 65.27/41.98 tff(40,plain,
% 65.27/41.98 (^[A: $i, B: $i] : refl(((A = B) | (~empty(A)) | (~empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B))))),
% 65.27/41.98 inference(bind,[status(th)],[])).
% 65.27/41.98 tff(41,plain,
% 65.27/41.98 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 65.27/41.98 inference(quant_intro,[status(thm)],[40])).
% 65.27/41.98 tff(42,plain,
% 65.27/41.98 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((A = B) | (~empty(A)) | (~empty(B))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((A = B) | (~empty(A)) | (~empty(B))))))), rewrite((~(~((A = B) | (~empty(A)) | (~empty(B))))) <=> ((A = B) | (~empty(A)) | (~empty(B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B)))))),
% 65.27/41.98 inference(bind,[status(th)],[])).
% 65.27/41.98 tff(43,plain,
% 65.27/41.98 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 65.27/41.98 inference(quant_intro,[status(thm)],[42])).
% 65.27/41.98 tff(44,plain,
% 65.27/41.98 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(45,plain,
% 65.27/41.98 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 65.27/41.98 inference(bind,[status(th)],[])).
% 65.27/41.98 tff(46,plain,
% 65.27/41.98 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 65.27/41.98 inference(quant_intro,[status(thm)],[45])).
% 65.27/41.98 tff(47,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_boole')).
% 65.27/41.98 tff(48,plain,
% 65.27/41.98 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[47, 46])).
% 65.27/41.98 tff(49,plain,
% 65.27/41.98 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[48, 44])).
% 65.27/41.98 tff(50,plain,(
% 65.27/41.98 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 65.27/41.98 inference(skolemize,[status(sab)],[49])).
% 65.27/41.98 tff(51,plain,
% 65.27/41.98 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[50, 43])).
% 65.27/41.98 tff(52,plain,
% 65.27/41.98 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[51, 41])).
% 65.27/41.98 tff(53,plain,
% 65.27/41.98 (?[A: $i] : empty(A) <=> ?[A: $i] : empty(A)),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(54,axiom,(?[A: $i] : empty(A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rc1_xboole_0')).
% 65.27/41.98 tff(55,plain,
% 65.27/41.98 (?[A: $i] : empty(A)),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[54, 53])).
% 65.27/41.98 tff(56,plain,(
% 65.27/41.98 empty(A!7)),
% 65.27/41.98 inference(skolemize,[status(sab)],[55])).
% 65.27/41.98 tff(57,plain,
% 65.27/41.98 (empty(empty_set) <=> empty(empty_set)),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(58,axiom,(empty(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 65.27/41.98 tff(59,plain,
% 65.27/41.98 (empty(empty_set)),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[58, 57])).
% 65.27/41.98 tff(60,plain,
% 65.27/41.98 (((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((empty_set = A!7) | (~empty(empty_set)) | (~empty(A!7)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (empty_set = A!7) | (~empty(empty_set)) | (~empty(A!7)))),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(61,plain,
% 65.27/41.98 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((empty_set = A!7) | (~empty(empty_set)) | (~empty(A!7)))),
% 65.27/41.98 inference(quant_inst,[status(thm)],[])).
% 65.27/41.98 tff(62,plain,
% 65.27/41.98 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (empty_set = A!7) | (~empty(empty_set)) | (~empty(A!7))),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[61, 60])).
% 65.27/41.98 tff(63,plain,
% 65.27/41.98 (empty_set = A!7),
% 65.27/41.98 inference(unit_resolution,[status(thm)],[62, 59, 56, 52])).
% 65.27/41.98 tff(64,plain,
% 65.27/41.98 (set_union2(A!12, empty_set) = set_union2(A!12, A!7)),
% 65.27/41.98 inference(monotonicity,[status(thm)],[63])).
% 65.27/41.98 tff(65,plain,
% 65.27/41.98 (set_union2(A!12, A!7) = set_union2(A!12, empty_set)),
% 65.27/41.98 inference(symmetry,[status(thm)],[64])).
% 65.27/41.98 tff(66,plain,
% 65.27/41.98 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 65.27/41.98 inference(bind,[status(th)],[])).
% 65.27/41.98 tff(67,plain,
% 65.27/41.98 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 65.27/41.98 inference(quant_intro,[status(thm)],[66])).
% 65.27/41.98 tff(68,plain,
% 65.27/41.98 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(69,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 65.27/41.98 tff(70,plain,
% 65.27/41.98 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[69, 68])).
% 65.27/41.98 tff(71,plain,(
% 65.27/41.98 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 65.27/41.98 inference(skolemize,[status(sab)],[70])).
% 65.27/41.98 tff(72,plain,
% 65.27/41.98 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[71, 67])).
% 65.27/41.98 tff(73,plain,
% 65.27/41.98 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!12, A!7) = set_union2(A!7, A!12))),
% 65.27/41.98 inference(quant_inst,[status(thm)],[])).
% 65.27/41.98 tff(74,plain,
% 65.27/41.98 (set_union2(A!12, A!7) = set_union2(A!7, A!12)),
% 65.27/41.98 inference(unit_resolution,[status(thm)],[73, 72])).
% 65.27/41.98 tff(75,plain,
% 65.27/41.98 (set_union2(A!7, A!12) = set_union2(A!12, A!7)),
% 65.27/41.98 inference(symmetry,[status(thm)],[74])).
% 65.27/41.98 tff(76,plain,
% 65.27/41.98 (set_union2(A!7, A!12) = A!12),
% 65.27/41.98 inference(transitivity,[status(thm)],[75, 65, 39])).
% 65.27/41.98 tff(77,plain,
% 65.27/41.98 (singleton(set_union2(A!7, A!12)) = singleton(A!12)),
% 65.27/41.98 inference(monotonicity,[status(thm)],[76])).
% 65.27/41.98 tff(78,plain,
% 65.27/41.98 (singleton(A!12) = singleton(set_union2(A!7, A!12))),
% 65.27/41.98 inference(symmetry,[status(thm)],[77])).
% 65.27/41.98 tff(79,plain,
% 65.27/41.98 (^[A: $i, B: $i] : refl(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 65.27/41.98 inference(bind,[status(th)],[])).
% 65.27/41.98 tff(80,plain,
% 65.27/41.98 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 65.27/41.98 inference(quant_intro,[status(thm)],[79])).
% 65.27/41.98 tff(81,plain,
% 65.27/41.98 (^[A: $i, B: $i] : rewrite(((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 65.27/41.98 inference(bind,[status(th)],[])).
% 65.27/41.98 tff(82,plain,
% 65.27/41.98 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 65.27/41.98 inference(quant_intro,[status(thm)],[81])).
% 65.27/41.98 tff(83,plain,
% 65.27/41.98 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(84,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_xboole_0')).
% 65.27/41.98 tff(85,plain,
% 65.27/41.98 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[84, 83])).
% 65.27/41.98 tff(86,plain,(
% 65.27/41.98 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 65.27/41.98 inference(skolemize,[status(sab)],[85])).
% 65.27/41.98 tff(87,plain,
% 65.27/41.98 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[86, 82])).
% 65.27/41.98 tff(88,plain,
% 65.27/41.98 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[87, 80])).
% 65.27/41.98 tff(89,plain,
% 65.27/41.98 (((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | subset(singleton(A!12), singleton(A!12))) <=> ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | subset(singleton(A!12), singleton(A!12)))),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(90,plain,
% 65.27/41.98 (($true <=> subset(singleton(A!12), singleton(A!12))) <=> subset(singleton(A!12), singleton(A!12))),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(91,plain,
% 65.27/41.98 ((~(~subset(singleton(A!12), singleton(A!12)))) <=> subset(singleton(A!12), singleton(A!12))),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(92,plain,
% 65.27/41.98 (((~subset(singleton(A!12), singleton(A!12))) | (~subset(singleton(A!12), singleton(A!12)))) <=> (~subset(singleton(A!12), singleton(A!12)))),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(93,plain,
% 65.27/41.98 ((~((~subset(singleton(A!12), singleton(A!12))) | (~subset(singleton(A!12), singleton(A!12))))) <=> (~(~subset(singleton(A!12), singleton(A!12))))),
% 65.27/41.98 inference(monotonicity,[status(thm)],[92])).
% 65.27/41.98 tff(94,plain,
% 65.27/41.98 ((~((~subset(singleton(A!12), singleton(A!12))) | (~subset(singleton(A!12), singleton(A!12))))) <=> subset(singleton(A!12), singleton(A!12))),
% 65.27/41.98 inference(transitivity,[status(thm)],[93, 91])).
% 65.27/41.98 tff(95,plain,
% 65.27/41.98 ((singleton(A!12) = singleton(A!12)) <=> $true),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(96,plain,
% 65.27/41.98 (((singleton(A!12) = singleton(A!12)) <=> (~((~subset(singleton(A!12), singleton(A!12))) | (~subset(singleton(A!12), singleton(A!12)))))) <=> ($true <=> subset(singleton(A!12), singleton(A!12)))),
% 65.27/41.98 inference(monotonicity,[status(thm)],[95, 94])).
% 65.27/41.98 tff(97,plain,
% 65.27/41.98 (((singleton(A!12) = singleton(A!12)) <=> (~((~subset(singleton(A!12), singleton(A!12))) | (~subset(singleton(A!12), singleton(A!12)))))) <=> subset(singleton(A!12), singleton(A!12))),
% 65.27/41.98 inference(transitivity,[status(thm)],[96, 90])).
% 65.27/41.98 tff(98,plain,
% 65.27/41.98 (((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | ((singleton(A!12) = singleton(A!12)) <=> (~((~subset(singleton(A!12), singleton(A!12))) | (~subset(singleton(A!12), singleton(A!12))))))) <=> ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | subset(singleton(A!12), singleton(A!12)))),
% 65.27/41.98 inference(monotonicity,[status(thm)],[97])).
% 65.27/41.98 tff(99,plain,
% 65.27/41.98 (((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | ((singleton(A!12) = singleton(A!12)) <=> (~((~subset(singleton(A!12), singleton(A!12))) | (~subset(singleton(A!12), singleton(A!12))))))) <=> ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | subset(singleton(A!12), singleton(A!12)))),
% 65.27/41.98 inference(transitivity,[status(thm)],[98, 89])).
% 65.27/41.98 tff(100,plain,
% 65.27/41.98 ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | ((singleton(A!12) = singleton(A!12)) <=> (~((~subset(singleton(A!12), singleton(A!12))) | (~subset(singleton(A!12), singleton(A!12))))))),
% 65.27/41.98 inference(quant_inst,[status(thm)],[])).
% 65.27/41.98 tff(101,plain,
% 65.27/41.98 ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | subset(singleton(A!12), singleton(A!12))),
% 65.27/41.98 inference(modus_ponens,[status(thm)],[100, 99])).
% 65.27/41.98 tff(102,plain,
% 65.27/41.98 (subset(singleton(A!12), singleton(A!12))),
% 65.27/41.98 inference(unit_resolution,[status(thm)],[101, 88])).
% 65.27/41.98 tff(103,plain,
% 65.27/41.98 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 65.27/41.98 inference(bind,[status(th)],[])).
% 65.27/41.98 tff(104,plain,
% 65.27/41.98 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 65.27/41.98 inference(quant_intro,[status(thm)],[103])).
% 65.27/41.98 tff(105,plain,
% 65.27/41.98 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 65.27/41.98 inference(rewrite,[status(thm)],[])).
% 65.27/41.98 tff(106,plain,
% 65.27/41.98 (^[A: $i, B: $i] : rewrite((subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 65.27/41.99 inference(bind,[status(th)],[])).
% 65.27/41.99 tff(107,plain,
% 65.27/41.99 (![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 65.27/41.99 inference(quant_intro,[status(thm)],[106])).
% 65.27/41.99 tff(108,axiom,(![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t45_xboole_1')).
% 65.27/41.99 tff(109,plain,
% 65.27/41.99 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 65.27/41.99 inference(modus_ponens,[status(thm)],[108, 107])).
% 65.27/41.99 tff(110,plain,
% 65.27/41.99 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 65.27/41.99 inference(modus_ponens,[status(thm)],[109, 105])).
% 65.27/41.99 tff(111,plain,(
% 65.27/41.99 ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 65.27/41.99 inference(skolemize,[status(sab)],[110])).
% 65.27/41.99 tff(112,plain,
% 65.27/41.99 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 65.27/41.99 inference(modus_ponens,[status(thm)],[111, 104])).
% 65.27/41.99 tff(113,plain,
% 65.27/41.99 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(singleton(A!12), singleton(A!12))) | (singleton(A!12) = set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(singleton(A!12), singleton(A!12))) | (singleton(A!12) = set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))),
% 65.27/41.99 inference(rewrite,[status(thm)],[])).
% 65.27/41.99 tff(114,plain,
% 65.27/41.99 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(singleton(A!12), singleton(A!12))) | (singleton(A!12) = set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))),
% 65.27/41.99 inference(quant_inst,[status(thm)],[])).
% 65.27/41.99 tff(115,plain,
% 65.27/41.99 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(singleton(A!12), singleton(A!12))) | (singleton(A!12) = set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))),
% 65.27/41.99 inference(modus_ponens,[status(thm)],[114, 113])).
% 65.27/41.99 tff(116,plain,
% 65.27/41.99 (singleton(A!12) = set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))),
% 65.27/41.99 inference(unit_resolution,[status(thm)],[115, 112, 102])).
% 65.27/41.99 tff(117,plain,
% 65.27/41.99 (set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = singleton(A!12)),
% 65.27/41.99 inference(symmetry,[status(thm)],[116])).
% 65.27/41.99 tff(118,plain,
% 65.27/41.99 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))) <=> (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))),
% 65.27/41.99 inference(bind,[status(th)],[])).
% 65.27/41.99 tff(119,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))),
% 65.27/41.99 inference(quant_intro,[status(thm)],[118])).
% 65.27/41.99 tff(120,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))),
% 65.27/41.99 inference(pull_quant,[status(thm)],[])).
% 65.27/41.99 tff(121,plain,
% 65.27/41.99 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> (~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), pull_quant((~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A)))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))) <=> (?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))), pull_quant((?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))) <=> (~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))), pull_quant((~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))))),
% 65.27/41.99 inference(bind,[status(th)],[])).
% 65.27/41.99 tff(122,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))),
% 65.27/41.99 inference(quant_intro,[status(thm)],[121])).
% 65.27/41.99 tff(123,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))),
% 65.27/41.99 inference(transitivity,[status(thm)],[122, 120])).
% 65.27/41.99 tff(124,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))),
% 65.27/41.99 inference(transitivity,[status(thm)],[123, 119])).
% 65.27/41.99 tff(125,plain,
% 65.27/41.99 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))),
% 65.27/41.99 inference(bind,[status(th)],[])).
% 65.27/41.99 tff(126,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))),
% 65.27/41.99 inference(quant_intro,[status(thm)],[125])).
% 65.27/41.99 tff(127,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))),
% 65.27/41.99 inference(transitivity,[status(thm)],[126, 124])).
% 65.27/41.99 tff(128,plain,
% 65.27/41.99 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))), rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))))),
% 65.27/41.99 inference(bind,[status(th)],[])).
% 65.27/41.99 tff(129,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))),
% 65.27/41.99 inference(quant_intro,[status(thm)],[128])).
% 65.27/41.99 tff(130,plain,
% 65.27/41.99 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))),
% 65.27/41.99 inference(bind,[status(th)],[])).
% 65.27/41.99 tff(131,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))),
% 65.27/41.99 inference(quant_intro,[status(thm)],[130])).
% 65.27/41.99 tff(132,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 65.27/41.99 inference(rewrite,[status(thm)],[])).
% 65.27/41.99 tff(133,plain,
% 65.27/41.99 (^[A: $i, B: $i, C: $i] : rewrite(((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))))),
% 65.27/41.99 inference(bind,[status(th)],[])).
% 65.27/41.99 tff(134,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 65.27/41.99 inference(quant_intro,[status(thm)],[133])).
% 65.27/41.99 tff(135,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_tarski')).
% 65.27/41.99 tff(136,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 65.27/41.99 inference(modus_ponens,[status(thm)],[135, 134])).
% 65.27/41.99 tff(137,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 65.27/41.99 inference(modus_ponens,[status(thm)],[136, 132])).
% 65.27/41.99 tff(138,plain,(
% 65.27/41.99 ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))),
% 65.27/41.99 inference(skolemize,[status(sab)],[137])).
% 65.27/41.99 tff(139,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))),
% 65.27/41.99 inference(modus_ponens,[status(thm)],[138, 131])).
% 65.27/41.99 tff(140,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))),
% 65.27/41.99 inference(modus_ponens,[status(thm)],[139, 129])).
% 65.27/41.99 tff(141,plain,
% 65.27/41.99 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))),
% 65.27/41.99 inference(modus_ponens,[status(thm)],[140, 127])).
% 65.27/41.99 tff(142,plain,
% 65.27/41.99 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (~((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) <=> (tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (~((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) <=> (tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))))),
% 65.27/41.99 inference(rewrite,[status(thm)],[])).
% 65.27/41.99 tff(143,plain,
% 65.27/41.99 ((~((~((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> ((tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)) | (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))))) | (~((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) <=> ((tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)) | (tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))))) <=> (~((~((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (~((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) <=> (tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))))),
% 65.27/41.99 inference(rewrite,[status(thm)],[])).
% 65.27/41.99 tff(144,plain,
% 65.27/41.99 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> ((tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)) | (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))))) | (~((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) <=> ((tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)) | (tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (~((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) <=> (tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))))),
% 65.27/41.99 inference(monotonicity,[status(thm)],[143])).
% 65.27/41.99 tff(145,plain,
% 65.27/41.99 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> ((tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)) | (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))))) | (~((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) <=> ((tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)) | (tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (~((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) <=> (tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))))),
% 65.27/41.99 inference(transitivity,[status(thm)],[144, 142])).
% 65.27/41.99 tff(146,plain,
% 65.27/41.99 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> ((tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)) | (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))))) | (~((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) <=> ((tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)) | (tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))))),
% 65.27/42.00 inference(quant_inst,[status(thm)],[])).
% 65.27/42.00 tff(147,plain,
% 65.27/42.00 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (~((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) <=> (tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))))),
% 65.27/42.00 inference(modus_ponens,[status(thm)],[146, 145])).
% 65.27/42.00 tff(148,plain,
% 65.27/42.00 (~((~((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (~((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) <=> (tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))),
% 65.27/42.00 inference(unit_resolution,[status(thm)],[147, 141])).
% 65.27/42.00 tff(149,plain,
% 65.27/42.00 (((~((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (~((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) <=> (tptp_fun_D_2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))) | ((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))),
% 65.27/42.00 inference(tautology,[status(thm)],[])).
% 65.27/42.00 tff(150,plain,
% 65.27/42.00 ((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))),
% 65.27/42.00 inference(unit_resolution,[status(thm)],[149, 148])).
% 65.27/42.00 tff(151,plain,
% 65.27/42.00 (unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)) = unordered_pair(A!12, A!12)),
% 65.27/42.00 inference(monotonicity,[status(thm)],[76, 76])).
% 65.27/42.00 tff(152,plain,
% 65.27/42.00 (unordered_pair(A!12, A!12) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))),
% 65.27/42.00 inference(symmetry,[status(thm)],[151])).
% 65.27/42.00 tff(153,plain,
% 65.27/42.00 (^[A: $i, B: $i] : refl(subset(A, set_union2(A, B)) <=> subset(A, set_union2(A, B)))),
% 65.27/42.00 inference(bind,[status(th)],[])).
% 65.27/42.00 tff(154,plain,
% 65.27/42.00 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 65.27/42.00 inference(quant_intro,[status(thm)],[153])).
% 65.27/42.00 tff(155,plain,
% 65.27/42.00 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 65.27/42.00 inference(rewrite,[status(thm)],[])).
% 65.27/42.00 tff(156,axiom,(![A: $i, B: $i] : subset(A, set_union2(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_xboole_1')).
% 65.27/42.00 tff(157,plain,
% 65.27/42.00 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 65.27/42.00 inference(modus_ponens,[status(thm)],[156, 155])).
% 65.27/42.00 tff(158,plain,(
% 65.27/42.00 ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 65.27/42.00 inference(skolemize,[status(sab)],[157])).
% 65.27/42.00 tff(159,plain,
% 65.27/42.00 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 65.27/42.00 inference(modus_ponens,[status(thm)],[158, 154])).
% 65.27/42.00 tff(160,plain,
% 65.27/42.00 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12)))),
% 65.27/42.00 inference(quant_inst,[status(thm)],[])).
% 65.27/42.00 tff(161,plain,
% 65.27/42.00 (subset(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12)))),
% 65.27/42.00 inference(unit_resolution,[status(thm)],[160, 159])).
% 65.27/42.00 tff(162,plain,
% 65.27/42.00 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 65.27/42.00 inference(bind,[status(th)],[])).
% 65.27/42.00 tff(163,plain,
% 65.27/42.00 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 65.27/42.00 inference(quant_intro,[status(thm)],[162])).
% 65.27/42.00 tff(164,plain,
% 65.27/42.00 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 65.27/42.00 inference(rewrite,[status(thm)],[])).
% 65.27/42.00 tff(165,plain,
% 65.27/42.00 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 65.27/42.00 inference(bind,[status(th)],[])).
% 65.27/42.00 tff(166,plain,
% 65.27/42.00 (![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 65.27/42.00 inference(quant_intro,[status(thm)],[165])).
% 65.27/42.00 tff(167,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t28_xboole_1')).
% 65.27/42.00 tff(168,plain,
% 65.27/42.00 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 65.27/42.00 inference(modus_ponens,[status(thm)],[167, 166])).
% 65.27/42.00 tff(169,plain,
% 65.27/42.00 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 65.27/42.00 inference(modus_ponens,[status(thm)],[168, 164])).
% 65.27/42.00 tff(170,plain,(
% 65.27/42.00 ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 65.27/42.00 inference(skolemize,[status(sab)],[169])).
% 65.27/42.00 tff(171,plain,
% 65.27/42.00 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 65.27/42.00 inference(modus_ponens,[status(thm)],[170, 163])).
% 65.27/42.00 tff(172,plain,
% 65.27/42.00 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12)))) | (set_intersection2(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12))) = unordered_pair(A!12, A!12)))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12)))) | (set_intersection2(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12))) = unordered_pair(A!12, A!12)))),
% 65.27/42.00 inference(rewrite,[status(thm)],[])).
% 65.27/42.00 tff(173,plain,
% 65.27/42.00 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12)))) | (set_intersection2(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12))) = unordered_pair(A!12, A!12)))),
% 65.27/42.00 inference(quant_inst,[status(thm)],[])).
% 65.27/42.00 tff(174,plain,
% 65.27/42.00 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12)))) | (set_intersection2(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12))) = unordered_pair(A!12, A!12))),
% 65.27/42.00 inference(modus_ponens,[status(thm)],[173, 172])).
% 65.27/42.00 tff(175,plain,
% 65.27/42.00 (set_intersection2(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12))) = unordered_pair(A!12, A!12)),
% 65.27/42.00 inference(unit_resolution,[status(thm)],[174, 171, 161])).
% 65.27/42.00 tff(176,plain,
% 65.27/42.00 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(unordered_pair(A!12, A!12), singleton(A!12)) = set_union2(singleton(A!12), unordered_pair(A!12, A!12)))),
% 65.27/42.00 inference(quant_inst,[status(thm)],[])).
% 65.27/42.00 tff(177,plain,
% 65.27/42.00 (set_union2(unordered_pair(A!12, A!12), singleton(A!12)) = set_union2(singleton(A!12), unordered_pair(A!12, A!12))),
% 65.27/42.00 inference(unit_resolution,[status(thm)],[176, 72])).
% 65.27/42.00 tff(178,plain,
% 65.27/42.00 (set_intersection2(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12))) = set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))),
% 65.27/42.00 inference(monotonicity,[status(thm)],[177])).
% 65.27/42.00 tff(179,plain,
% 65.27/42.00 (set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_intersection2(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12)))),
% 65.27/42.00 inference(symmetry,[status(thm)],[178])).
% 65.27/42.00 tff(180,plain,
% 65.27/42.00 (set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))),
% 65.27/42.00 inference(transitivity,[status(thm)],[179, 175, 152])).
% 65.27/42.00 tff(181,plain,
% 65.27/42.00 ((~((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))),
% 65.27/42.00 inference(tautology,[status(thm)],[])).
% 65.27/42.00 tff(182,plain,
% 65.27/42.00 ((~((~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))),
% 65.27/42.00 inference(unit_resolution,[status(thm)],[181, 180])).
% 65.27/42.00 tff(183,plain,
% 65.27/42.00 (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))),
% 65.27/42.00 inference(unit_resolution,[status(thm)],[182, 150])).
% 65.27/42.00 tff(184,plain,
% 65.27/42.00 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (~((set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(A!7, A!12)), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))))),
% 65.27/42.00 inference(quant_inst,[status(thm)],[])).
% 65.27/42.00 tff(185,plain,
% 65.27/42.00 (~((~((~(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (~((set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(A!7, A!12)), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))),
% 65.27/42.00 inference(unit_resolution,[status(thm)],[184, 21])).
% 65.27/42.00 tff(186,plain,
% 65.27/42.00 (((~((~(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (~((set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = singleton(set_union2(A!7, A!12))) | ((~in(tptp_fun_C_0(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(A!7, A!12)), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_0(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))) | ((~(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))),
% 65.27/42.00 inference(tautology,[status(thm)],[])).
% 65.27/42.00 tff(187,plain,
% 65.27/42.00 ((~(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))),
% 65.27/42.00 inference(unit_resolution,[status(thm)],[186, 185])).
% 65.27/42.00 tff(188,plain,
% 65.27/42.00 (set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = singleton(set_union2(A!7, A!12))),
% 65.27/42.00 inference(transitivity,[status(thm)],[117, 78])).
% 65.27/42.00 tff(189,plain,
% 65.27/42.00 ((~((~(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (~(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))),
% 65.27/42.00 inference(tautology,[status(thm)],[])).
% 65.27/42.00 tff(190,plain,
% 65.27/42.00 ((~((~(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))))) | (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))),
% 65.27/42.00 inference(unit_resolution,[status(thm)],[189, 188])).
% 65.27/42.00 tff(191,plain,
% 65.27/42.00 (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))),
% 65.27/42.00 inference(unit_resolution,[status(thm)],[190, 187])).
% 65.27/42.00 tff(192,assumption,(~((~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))), introduced(assumption)).
% 65.27/42.00 tff(193,plain,
% 65.27/42.00 (((~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))),
% 65.27/42.00 inference(tautology,[status(thm)],[])).
% 65.27/42.00 tff(194,plain,
% 65.27/42.00 (~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))),
% 65.27/42.00 inference(unit_resolution,[status(thm)],[193, 192])).
% 65.27/42.00 tff(195,plain,
% 65.27/42.00 ((~(in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))) | in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) | (~(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))),
% 65.27/42.00 inference(tautology,[status(thm)],[])).
% 65.27/42.00 tff(196,plain,
% 65.27/42.00 ((~(in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))) | (~(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))),
% 65.27/42.00 inference(unit_resolution,[status(thm)],[195, 194])).
% 65.27/42.00 tff(197,plain,
% 65.27/42.00 (~(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))),
% 65.27/42.00 inference(unit_resolution,[status(thm)],[196, 191])).
% 65.27/42.00 tff(198,plain,
% 65.27/42.00 (((~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))),
% 65.27/42.01 inference(tautology,[status(thm)],[])).
% 65.27/42.01 tff(199,plain,
% 65.27/42.01 (in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))),
% 65.27/42.01 inference(unit_resolution,[status(thm)],[198, 192])).
% 65.27/42.01 tff(200,plain,
% 65.27/42.01 ((~(in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))) | (~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))),
% 65.27/42.01 inference(tautology,[status(thm)],[])).
% 65.27/42.01 tff(201,plain,
% 65.27/42.01 ((~(in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12)))) | (tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_union2(A!7, A!12))),
% 65.27/42.01 inference(unit_resolution,[status(thm)],[200, 199])).
% 65.27/42.01 tff(202,plain,
% 65.27/42.01 ($false),
% 65.27/42.01 inference(unit_resolution,[status(thm)],[201, 197, 183])).
% 65.27/42.01 tff(203,plain,((~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))), inference(lemma,lemma(discharge,[]))).
% 65.27/42.01 tff(204,plain,
% 65.27/42.01 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))))),
% 65.27/42.01 inference(bind,[status(th)],[])).
% 65.27/42.01 tff(205,plain,
% 65.27/42.01 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 65.27/42.01 inference(quant_intro,[status(thm)],[204])).
% 65.27/42.01 tff(206,plain,
% 65.27/42.01 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))))),
% 65.27/42.01 inference(bind,[status(th)],[])).
% 65.27/42.01 tff(207,plain,
% 65.27/42.01 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 65.27/42.01 inference(quant_intro,[status(thm)],[206])).
% 65.27/42.01 tff(208,plain,
% 65.27/42.01 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 65.27/42.01 inference(transitivity,[status(thm)],[207, 205])).
% 65.27/42.01 tff(209,plain,
% 65.27/42.01 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))))),
% 65.27/42.01 inference(bind,[status(th)],[])).
% 65.27/42.01 tff(210,plain,
% 65.27/42.01 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 65.27/42.01 inference(quant_intro,[status(thm)],[209])).
% 65.27/42.01 tff(211,plain,
% 65.27/42.01 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 65.27/42.01 inference(rewrite,[status(thm)],[])).
% 65.27/42.01 tff(212,plain,
% 65.27/42.01 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 65.27/42.01 inference(bind,[status(th)],[])).
% 65.27/42.01 tff(213,plain,
% 65.27/42.01 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 65.27/42.01 inference(quant_intro,[status(thm)],[212])).
% 65.27/42.01 tff(214,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 65.27/42.01 tff(215,plain,
% 65.27/42.01 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 65.27/42.01 inference(modus_ponens,[status(thm)],[214, 213])).
% 65.27/42.01 tff(216,plain,
% 65.27/42.01 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 65.27/42.01 inference(modus_ponens,[status(thm)],[215, 211])).
% 65.27/42.01 tff(217,plain,(
% 65.27/42.01 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))),
% 65.27/42.01 inference(skolemize,[status(sab)],[216])).
% 65.27/42.01 tff(218,plain,
% 65.27/42.01 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 65.27/42.01 inference(modus_ponens,[status(thm)],[217, 210])).
% 65.27/42.01 tff(219,plain,
% 65.27/42.01 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 65.27/42.01 inference(modus_ponens,[status(thm)],[218, 208])).
% 65.27/42.01 tff(220,plain,
% 65.27/42.01 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))) | (~((~((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | ![C: $i] : ((~in(C, set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(C, set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))) | (~(subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) | (~((~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))))))),
% 65.27/42.01 inference(quant_inst,[status(thm)],[])).
% 65.27/42.01 tff(221,plain,
% 65.27/42.01 (~((~((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | ![C: $i] : ((~in(C, set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(C, set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))) | (~(subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) | (~((~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))))))),
% 65.27/42.01 inference(unit_resolution,[status(thm)],[220, 219])).
% 65.27/42.01 tff(222,plain,
% 65.27/42.01 (((~((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | ![C: $i] : ((~in(C, set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(C, set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))) | (~(subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) | (~((~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))))) | (subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) | (~((~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))))),
% 65.27/42.01 inference(tautology,[status(thm)],[])).
% 65.27/42.01 tff(223,plain,
% 65.27/42.01 (subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) | (~((~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))),
% 65.27/42.01 inference(unit_resolution,[status(thm)],[222, 221])).
% 65.27/42.01 tff(224,plain,
% 65.27/42.01 ((~(subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) | (~((~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))))) | subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) | (~((~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))),
% 65.27/42.01 inference(tautology,[status(thm)],[])).
% 65.27/42.01 tff(225,plain,
% 65.27/42.01 (subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) | (~((~in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | in(tptp_fun_C_4(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))),
% 65.27/42.01 inference(unit_resolution,[status(thm)],[224, 223])).
% 65.27/42.01 tff(226,plain,
% 65.27/42.01 (subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))),
% 65.27/42.01 inference(unit_resolution,[status(thm)],[225, 203])).
% 65.27/42.01 tff(227,plain,
% 65.27/42.01 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = set_union2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = set_union2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))))),
% 65.27/42.01 inference(rewrite,[status(thm)],[])).
% 65.27/42.01 tff(228,plain,
% 65.27/42.01 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = set_union2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))))),
% 65.27/42.01 inference(quant_inst,[status(thm)],[])).
% 65.27/42.01 tff(229,plain,
% 65.27/42.01 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = set_union2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))))),
% 65.27/42.01 inference(modus_ponens,[status(thm)],[228, 227])).
% 65.27/42.01 tff(230,plain,
% 65.27/42.01 ((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = set_union2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))))),
% 65.27/42.01 inference(unit_resolution,[status(thm)],[229, 112])).
% 65.27/42.01 tff(231,plain,
% 65.27/42.01 (set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))) = set_union2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))),
% 65.27/42.01 inference(unit_resolution,[status(thm)],[230, 226])).
% 65.27/42.01 tff(232,plain,
% 65.27/42.01 (set_union2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) = set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))),
% 65.27/42.01 inference(symmetry,[status(thm)],[231])).
% 65.27/42.01 tff(233,plain,
% 65.27/42.01 (set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = set_union2(unordered_pair(A!12, A!12), singleton(A!12))),
% 65.27/42.01 inference(symmetry,[status(thm)],[177])).
% 65.27/42.01 tff(234,plain,
% 65.27/42.01 (set_union2(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), unordered_pair(A!12, A!12)) = set_union2(singleton(A!12), unordered_pair(A!12, A!12))),
% 65.27/42.01 inference(monotonicity,[status(thm)],[117])).
% 65.27/42.01 tff(235,plain,
% 65.27/42.01 (set_union2(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), unordered_pair(A!12, A!12)) = set_union2(unordered_pair(A!12, A!12), singleton(A!12))),
% 65.27/42.01 inference(transitivity,[status(thm)],[234, 233])).
% 65.27/42.01 tff(236,plain,
% 65.27/42.01 (set_difference(set_union2(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), unordered_pair(A!12, A!12)), unordered_pair(A!12, A!12)) = set_difference(set_union2(unordered_pair(A!12, A!12), singleton(A!12)), unordered_pair(A!12, A!12))),
% 65.27/42.01 inference(monotonicity,[status(thm)],[235])).
% 65.27/42.01 tff(237,plain,
% 65.27/42.01 (^[A: $i, B: $i] : refl((set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> (set_difference(set_union2(A, B), B) = set_difference(A, B)))),
% 65.27/42.01 inference(bind,[status(th)],[])).
% 65.27/42.01 tff(238,plain,
% 65.27/42.01 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 65.27/42.01 inference(quant_intro,[status(thm)],[237])).
% 65.27/42.01 tff(239,plain,
% 65.27/42.01 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 65.27/42.01 inference(rewrite,[status(thm)],[])).
% 65.27/42.01 tff(240,axiom,(![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t40_xboole_1')).
% 65.27/42.01 tff(241,plain,
% 65.27/42.01 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 65.27/42.01 inference(modus_ponens,[status(thm)],[240, 239])).
% 65.27/42.01 tff(242,plain,(
% 65.27/42.01 ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 65.27/42.01 inference(skolemize,[status(sab)],[241])).
% 65.40/42.01 tff(243,plain,
% 65.40/42.01 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 65.40/42.01 inference(modus_ponens,[status(thm)],[242, 238])).
% 65.40/42.01 tff(244,plain,
% 65.40/42.01 ((~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))) | (set_difference(set_union2(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), unordered_pair(A!12, A!12)), unordered_pair(A!12, A!12)) = set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), unordered_pair(A!12, A!12)))),
% 65.40/42.01 inference(quant_inst,[status(thm)],[])).
% 65.40/42.01 tff(245,plain,
% 65.40/42.01 (set_difference(set_union2(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), unordered_pair(A!12, A!12)), unordered_pair(A!12, A!12)) = set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), unordered_pair(A!12, A!12))),
% 65.40/42.01 inference(unit_resolution,[status(thm)],[244, 243])).
% 65.40/42.01 tff(246,plain,
% 65.40/42.01 (set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), unordered_pair(A!12, A!12)) = set_difference(set_union2(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), unordered_pair(A!12, A!12)), unordered_pair(A!12, A!12))),
% 65.40/42.01 inference(symmetry,[status(thm)],[245])).
% 65.40/42.01 tff(247,plain,
% 65.40/42.01 (set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = unordered_pair(A!12, A!12)),
% 65.40/42.01 inference(transitivity,[status(thm)],[179, 175])).
% 65.40/42.01 tff(248,plain,
% 65.40/42.01 (set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), unordered_pair(A!12, A!12))),
% 65.40/42.01 inference(monotonicity,[status(thm)],[247])).
% 65.40/42.01 tff(249,plain,
% 65.40/42.01 (set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) = set_difference(set_union2(unordered_pair(A!12, A!12), singleton(A!12)), unordered_pair(A!12, A!12))),
% 65.40/42.01 inference(transitivity,[status(thm)],[248, 246, 236])).
% 65.40/42.01 tff(250,plain,
% 65.40/42.01 (set_union2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) = set_union2(unordered_pair(A!12, A!12), set_difference(set_union2(unordered_pair(A!12, A!12), singleton(A!12)), unordered_pair(A!12, A!12)))),
% 65.40/42.01 inference(monotonicity,[status(thm)],[247, 249])).
% 65.40/42.01 tff(251,plain,
% 65.40/42.01 (set_union2(unordered_pair(A!12, A!12), set_difference(set_union2(unordered_pair(A!12, A!12), singleton(A!12)), unordered_pair(A!12, A!12))) = set_union2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_difference(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))),
% 65.40/42.01 inference(symmetry,[status(thm)],[250])).
% 65.40/42.01 tff(252,plain,
% 65.40/42.01 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12)))) | (set_union2(unordered_pair(A!12, A!12), singleton(A!12)) = set_union2(unordered_pair(A!12, A!12), set_difference(set_union2(unordered_pair(A!12, A!12), singleton(A!12)), unordered_pair(A!12, A!12)))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12)))) | (set_union2(unordered_pair(A!12, A!12), singleton(A!12)) = set_union2(unordered_pair(A!12, A!12), set_difference(set_union2(unordered_pair(A!12, A!12), singleton(A!12)), unordered_pair(A!12, A!12)))))),
% 65.40/42.02 inference(rewrite,[status(thm)],[])).
% 65.40/42.02 tff(253,plain,
% 65.40/42.02 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12)))) | (set_union2(unordered_pair(A!12, A!12), singleton(A!12)) = set_union2(unordered_pair(A!12, A!12), set_difference(set_union2(unordered_pair(A!12, A!12), singleton(A!12)), unordered_pair(A!12, A!12)))))),
% 65.40/42.02 inference(quant_inst,[status(thm)],[])).
% 65.40/42.02 tff(254,plain,
% 65.40/42.02 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12)))) | (set_union2(unordered_pair(A!12, A!12), singleton(A!12)) = set_union2(unordered_pair(A!12, A!12), set_difference(set_union2(unordered_pair(A!12, A!12), singleton(A!12)), unordered_pair(A!12, A!12))))),
% 65.40/42.02 inference(modus_ponens,[status(thm)],[253, 252])).
% 65.40/42.02 tff(255,plain,
% 65.40/42.02 (set_union2(unordered_pair(A!12, A!12), singleton(A!12)) = set_union2(unordered_pair(A!12, A!12), set_difference(set_union2(unordered_pair(A!12, A!12), singleton(A!12)), unordered_pair(A!12, A!12)))),
% 65.40/42.02 inference(unit_resolution,[status(thm)],[254, 112, 161])).
% 65.40/42.02 tff(256,plain,
% 65.40/42.02 (set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12))),
% 65.40/42.02 inference(transitivity,[status(thm)],[233, 255, 251, 232, 117, 78])).
% 65.40/42.02 tff(257,plain,
% 65.40/42.02 ((~((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))),
% 65.40/42.02 inference(tautology,[status(thm)],[])).
% 65.40/42.02 tff(258,plain,
% 65.40/42.02 ((~((~(set_union2(singleton(A!12), unordered_pair(A!12, A!12)) = singleton(set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))),
% 65.40/42.02 inference(unit_resolution,[status(thm)],[257, 256])).
% 65.40/42.02 tff(259,plain,
% 65.40/42.02 (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))),
% 65.40/42.02 inference(unit_resolution,[status(thm)],[258, 30])).
% 65.40/42.02 tff(260,plain,
% 65.40/42.02 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (~((set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) <=> (tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (~((set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) <=> (tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))))),
% 65.40/42.02 inference(rewrite,[status(thm)],[])).
% 65.40/42.02 tff(261,plain,
% 65.40/42.02 ((~((~((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> ((tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)) | (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))))) | (~((set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) <=> ((tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)) | (tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))))) <=> (~((~((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (~((set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) <=> (tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))))),
% 65.40/42.02 inference(rewrite,[status(thm)],[])).
% 65.40/42.02 tff(262,plain,
% 65.40/42.02 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> ((tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)) | (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))))) | (~((set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) <=> ((tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)) | (tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (~((set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) <=> (tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))))),
% 65.40/42.02 inference(monotonicity,[status(thm)],[261])).
% 65.40/42.02 tff(263,plain,
% 65.40/42.02 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> ((tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)) | (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))))) | (~((set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) <=> ((tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)) | (tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (~((set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) <=> (tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))))),
% 65.40/42.03 inference(transitivity,[status(thm)],[262, 260])).
% 65.40/42.03 tff(264,plain,
% 65.40/42.03 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> ((tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)) | (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))))) | (~((set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) <=> ((tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)) | (tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))))),
% 65.40/42.03 inference(quant_inst,[status(thm)],[])).
% 65.40/42.03 tff(265,plain,
% 65.40/42.03 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))) | (~((~((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (~((set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) <=> (tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))))),
% 65.40/42.03 inference(modus_ponens,[status(thm)],[264, 263])).
% 65.40/42.03 tff(266,plain,
% 65.40/42.03 (~((~((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (~((set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) <=> (tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12))))))),
% 65.40/42.03 inference(unit_resolution,[status(thm)],[265, 141])).
% 65.40/42.03 tff(267,plain,
% 65.40/42.03 (((~((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (~((set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) | ((~in(tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) <=> (tptp_fun_D_2(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_union2(A!7, A!12)))))) | ((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))),
% 65.40/42.03 inference(tautology,[status(thm)],[])).
% 65.40/42.03 tff(268,plain,
% 65.40/42.03 ((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))),
% 65.40/42.03 inference(unit_resolution,[status(thm)],[267, 266])).
% 65.40/42.03 tff(269,plain,
% 65.40/42.03 (unordered_pair(A!12, A!12) = set_intersection2(unordered_pair(A!12, A!12), set_union2(unordered_pair(A!12, A!12), singleton(A!12)))),
% 65.40/42.03 inference(symmetry,[status(thm)],[175])).
% 65.40/42.03 tff(270,plain,
% 65.40/42.03 (unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)) = set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))),
% 65.40/42.03 inference(transitivity,[status(thm)],[151, 269, 178])).
% 65.40/42.03 tff(271,plain,
% 65.40/42.03 ((set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))) <=> (set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))),
% 65.40/42.03 inference(monotonicity,[status(thm)],[270])).
% 65.40/42.03 tff(272,plain,
% 65.40/42.03 ((set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) <=> (set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))),
% 65.40/42.03 inference(symmetry,[status(thm)],[271])).
% 65.40/42.03 tff(273,plain,
% 65.40/42.03 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))),
% 65.40/42.03 inference(rewrite,[status(thm)],[])).
% 65.40/42.03 tff(274,plain,
% 65.40/42.03 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))),
% 65.40/42.03 inference(quant_inst,[status(thm)],[])).
% 65.40/42.03 tff(275,plain,
% 65.40/42.03 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))),
% 65.40/42.03 inference(modus_ponens,[status(thm)],[274, 273])).
% 65.40/42.03 tff(276,plain,
% 65.40/42.03 ((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))),
% 65.40/42.03 inference(unit_resolution,[status(thm)],[275, 171])).
% 65.40/42.03 tff(277,plain,
% 65.40/42.03 (set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))),
% 65.40/42.03 inference(unit_resolution,[status(thm)],[276, 226])).
% 65.40/42.03 tff(278,plain,
% 65.40/42.03 (set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12))),
% 65.40/42.03 inference(modus_ponens,[status(thm)],[277, 272])).
% 65.40/42.03 tff(279,plain,
% 65.40/42.03 ((~((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))),
% 65.40/42.03 inference(tautology,[status(thm)],[])).
% 65.40/42.03 tff(280,plain,
% 65.40/42.03 ((~((~(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) = unordered_pair(set_union2(A!7, A!12), set_union2(A!7, A!12)))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))))) | (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))),
% 65.40/42.03 inference(unit_resolution,[status(thm)],[279, 278])).
% 65.40/42.03 tff(281,plain,
% 65.40/42.03 (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))),
% 65.40/42.03 inference(unit_resolution,[status(thm)],[280, 268])).
% 65.40/42.03 tff(282,plain,
% 65.40/42.03 ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | ((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (~((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))))))),
% 65.40/42.03 inference(quant_inst,[status(thm)],[])).
% 65.40/42.03 tff(283,plain,
% 65.40/42.03 ((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (~((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))))),
% 65.40/42.03 inference(unit_resolution,[status(thm)],[282, 88])).
% 65.40/42.03 tff(284,plain,
% 65.40/42.03 ((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (unordered_pair(A!12, A!12) = singleton(A!12))),
% 65.40/42.03 inference(monotonicity,[status(thm)],[247, 117])).
% 65.40/42.03 tff(285,plain,
% 65.40/42.03 ((unordered_pair(A!12, A!12) = singleton(A!12)) <=> (set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))),
% 65.40/42.03 inference(symmetry,[status(thm)],[284])).
% 65.40/42.03 tff(286,plain,
% 65.40/42.03 ((~(unordered_pair(A!12, A!12) = singleton(A!12))) <=> (~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))),
% 65.40/42.03 inference(monotonicity,[status(thm)],[285])).
% 65.40/42.03 tff(287,plain,
% 65.40/42.03 ((~![A: $i] : (unordered_pair(A, A) = singleton(A))) <=> (~![A: $i] : (unordered_pair(A, A) = singleton(A)))),
% 65.40/42.03 inference(rewrite,[status(thm)],[])).
% 65.40/42.03 tff(288,axiom,(~![A: $i] : (unordered_pair(A, A) = singleton(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t69_enumset1')).
% 65.40/42.03 tff(289,plain,
% 65.40/42.03 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 65.40/42.03 inference(modus_ponens,[status(thm)],[288, 287])).
% 65.40/42.03 tff(290,plain,
% 65.40/42.03 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 65.40/42.03 inference(modus_ponens,[status(thm)],[289, 287])).
% 65.40/42.03 tff(291,plain,
% 65.40/42.03 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 65.40/42.03 inference(modus_ponens,[status(thm)],[290, 287])).
% 65.40/42.03 tff(292,plain,
% 65.40/42.03 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 65.40/42.03 inference(modus_ponens,[status(thm)],[291, 287])).
% 65.40/42.04 tff(293,plain,
% 65.40/42.04 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 65.40/42.04 inference(modus_ponens,[status(thm)],[292, 287])).
% 65.40/42.04 tff(294,plain,
% 65.40/42.04 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 65.40/42.04 inference(modus_ponens,[status(thm)],[293, 287])).
% 65.40/42.04 tff(295,plain,
% 65.40/42.04 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 65.40/42.04 inference(modus_ponens,[status(thm)],[294, 287])).
% 65.40/42.04 tff(296,plain,(
% 65.40/42.04 ~(unordered_pair(A!12, A!12) = singleton(A!12))),
% 65.40/42.04 inference(skolemize,[status(sab)],[295])).
% 65.40/42.04 tff(297,plain,
% 65.40/42.04 (~(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))),
% 65.40/42.04 inference(modus_ponens,[status(thm)],[296, 286])).
% 65.40/42.04 tff(298,plain,
% 65.40/42.04 ((~((set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) <=> (~((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))))))) | (set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))) | ((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))))),
% 65.40/42.04 inference(tautology,[status(thm)],[])).
% 65.40/42.04 tff(299,plain,
% 65.40/42.04 ((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))),
% 65.40/42.04 inference(unit_resolution,[status(thm)],[298, 297, 283])).
% 65.40/42.04 tff(300,plain,
% 65.40/42.04 ((~((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))))) | (~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))),
% 65.40/42.04 inference(tautology,[status(thm)],[])).
% 65.40/42.04 tff(301,plain,
% 65.40/42.04 ((~subset(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))),
% 65.40/42.04 inference(unit_resolution,[status(thm)],[300, 299])).
% 65.40/42.04 tff(302,plain,
% 65.40/42.04 (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))),
% 65.40/42.04 inference(unit_resolution,[status(thm)],[301, 226])).
% 65.40/42.04 tff(303,plain,
% 65.40/42.04 (subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), unordered_pair(A!12, A!12))) <=> subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))),
% 65.40/42.04 inference(monotonicity,[status(thm)],[234])).
% 65.40/42.04 tff(304,plain,
% 65.40/42.04 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), unordered_pair(A!12, A!12)))),
% 65.40/42.04 inference(quant_inst,[status(thm)],[])).
% 65.40/42.04 tff(305,plain,
% 65.40/42.04 (subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), unordered_pair(A!12, A!12)))),
% 65.40/42.04 inference(unit_resolution,[status(thm)],[304, 159])).
% 65.40/42.04 tff(306,plain,
% 65.40/42.04 (subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))),
% 65.40/42.04 inference(modus_ponens,[status(thm)],[305, 303])).
% 65.40/42.04 tff(307,plain,
% 65.40/42.04 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 65.40/42.04 inference(rewrite,[status(thm)],[])).
% 65.40/42.04 tff(308,plain,
% 65.40/42.04 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(B, C)) <=> (~((~subset(B, C)) | (~subset(A, B))))), ((~(subset(A, B) & subset(B, C))) <=> (~(~((~subset(B, C)) | (~subset(A, B))))))), rewrite((~(~((~subset(B, C)) | (~subset(A, B))))) <=> ((~subset(B, C)) | (~subset(A, B)))), ((~(subset(A, B) & subset(B, C))) <=> ((~subset(B, C)) | (~subset(A, B))))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (((~subset(B, C)) | (~subset(A, B))) | subset(A, C)))), rewrite((((~subset(B, C)) | (~subset(A, B))) | subset(A, C)) <=> (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))))),
% 65.40/42.04 inference(bind,[status(th)],[])).
% 65.40/42.04 tff(309,plain,
% 65.40/42.04 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 65.40/42.04 inference(quant_intro,[status(thm)],[308])).
% 65.40/42.04 tff(310,plain,
% 65.40/42.04 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 65.40/42.04 inference(rewrite,[status(thm)],[])).
% 65.40/42.04 tff(311,plain,
% 65.40/42.04 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ((~(subset(A, B) & subset(B, C))) | subset(A, C)))),
% 65.40/42.04 inference(bind,[status(th)],[])).
% 65.40/42.04 tff(312,plain,
% 65.40/42.04 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 65.40/42.04 inference(quant_intro,[status(thm)],[311])).
% 65.40/42.04 tff(313,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_xboole_1')).
% 65.40/42.04 tff(314,plain,
% 65.40/42.04 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 65.40/42.04 inference(modus_ponens,[status(thm)],[313, 312])).
% 65.40/42.04 tff(315,plain,
% 65.40/42.04 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 65.40/42.04 inference(modus_ponens,[status(thm)],[314, 310])).
% 65.40/42.04 tff(316,plain,(
% 65.40/42.04 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 65.40/42.04 inference(skolemize,[status(sab)],[315])).
% 65.40/42.04 tff(317,plain,
% 65.40/42.04 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 65.40/42.04 inference(modus_ponens,[status(thm)],[316, 309])).
% 65.40/42.04 tff(318,plain,
% 65.40/42.04 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 65.40/42.04 inference(modus_ponens,[status(thm)],[317, 307])).
% 65.40/42.04 tff(319,plain,
% 65.40/42.04 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | ((~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))),
% 65.40/42.04 inference(rewrite,[status(thm)],[])).
% 65.40/42.04 tff(320,plain,
% 65.40/42.04 ((subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) <=> ((~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))),
% 65.40/42.04 inference(rewrite,[status(thm)],[])).
% 65.40/42.04 tff(321,plain,
% 65.40/42.04 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | ((~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))))),
% 65.40/42.04 inference(monotonicity,[status(thm)],[320])).
% 65.40/42.04 tff(322,plain,
% 65.40/42.04 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))),
% 65.40/42.04 inference(transitivity,[status(thm)],[321, 319])).
% 65.40/42.04 tff(323,plain,
% 65.40/42.04 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))))),
% 65.40/42.04 inference(quant_inst,[status(thm)],[])).
% 65.40/42.04 tff(324,plain,
% 65.40/42.04 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))),
% 65.40/42.04 inference(modus_ponens,[status(thm)],[323, 322])).
% 65.40/42.04 tff(325,plain,
% 65.40/42.04 ((~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | subset(set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))),
% 65.40/42.04 inference(unit_resolution,[status(thm)],[324, 318, 306])).
% 65.40/42.04 tff(326,plain,
% 65.40/42.04 (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))),
% 65.40/42.04 inference(unit_resolution,[status(thm)],[325, 302])).
% 65.40/42.04 tff(327,plain,
% 65.40/42.04 (^[A: $i, B: $i] : refl(subset(set_intersection2(A, B), A) <=> subset(set_intersection2(A, B), A))),
% 65.40/42.04 inference(bind,[status(th)],[])).
% 65.40/42.04 tff(328,plain,
% 65.40/42.04 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 65.40/42.04 inference(quant_intro,[status(thm)],[327])).
% 65.40/42.04 tff(329,plain,
% 65.40/42.04 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 65.40/42.04 inference(rewrite,[status(thm)],[])).
% 65.40/42.04 tff(330,axiom,(![A: $i, B: $i] : subset(set_intersection2(A, B), A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t17_xboole_1')).
% 65.40/42.04 tff(331,plain,
% 65.40/42.04 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 65.40/42.04 inference(modus_ponens,[status(thm)],[330, 329])).
% 65.40/42.04 tff(332,plain,(
% 65.40/42.04 ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 65.40/42.04 inference(skolemize,[status(sab)],[331])).
% 65.40/42.04 tff(333,plain,
% 65.40/42.04 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 65.40/42.04 inference(modus_ponens,[status(thm)],[332, 328])).
% 65.40/42.04 tff(334,plain,
% 65.40/42.04 ((~![A: $i, B: $i] : subset(set_intersection2(A, B), A)) | subset(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))),
% 65.40/42.04 inference(quant_inst,[status(thm)],[])).
% 65.40/42.04 tff(335,plain,
% 65.40/42.04 (subset(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))),
% 65.40/42.04 inference(unit_resolution,[status(thm)],[334, 333])).
% 65.40/42.04 tff(336,plain,
% 65.40/42.04 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))))),
% 65.40/42.04 inference(rewrite,[status(thm)],[])).
% 65.40/42.04 tff(337,plain,
% 65.40/42.04 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))))),
% 65.40/42.04 inference(quant_inst,[status(thm)],[])).
% 65.40/42.04 tff(338,plain,
% 65.40/42.04 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))),
% 65.40/42.04 inference(modus_ponens,[status(thm)],[337, 336])).
% 65.40/42.04 tff(339,plain,
% 65.40/42.04 (subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))),
% 65.40/42.04 inference(unit_resolution,[status(thm)],[338, 318, 335])).
% 65.40/42.04 tff(340,plain,
% 65.40/42.04 (~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))),
% 65.40/42.04 inference(unit_resolution,[status(thm)],[339, 326])).
% 65.40/42.04 tff(341,plain,
% 65.40/42.04 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))) | (~((~((~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) | ![C: $i] : ((~in(C, set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | in(C, set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))))) | (~(subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~((~in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))))))))),
% 65.40/42.04 inference(quant_inst,[status(thm)],[])).
% 65.40/42.04 tff(342,plain,
% 65.40/42.04 (~((~((~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) | ![C: $i] : ((~in(C, set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | in(C, set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))))) | (~(subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~((~in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))))))),
% 65.40/42.04 inference(unit_resolution,[status(thm)],[341, 219])).
% 65.40/42.04 tff(343,plain,
% 65.40/42.04 (((~((~subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) | ![C: $i] : ((~in(C, set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | in(C, set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))))) | (~(subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~((~in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))))))) | (subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~((~in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))))),
% 65.40/42.05 inference(tautology,[status(thm)],[])).
% 65.40/42.05 tff(344,plain,
% 65.40/42.05 (subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~((~in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))))),
% 65.40/42.05 inference(unit_resolution,[status(thm)],[343, 342])).
% 65.40/42.05 tff(345,plain,
% 65.40/42.05 ((~(subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~((~in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))))) | subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~((~in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))))),
% 65.40/42.05 inference(tautology,[status(thm)],[])).
% 65.40/42.05 tff(346,plain,
% 65.40/42.05 (subset(set_union2(singleton(A!12), unordered_pair(A!12, A!12)), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~((~in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))))),
% 65.40/42.05 inference(unit_resolution,[status(thm)],[345, 344])).
% 65.40/42.05 tff(347,plain,
% 65.40/42.05 (~((~in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))),
% 65.40/42.05 inference(unit_resolution,[status(thm)],[346, 340])).
% 65.40/42.05 tff(348,plain,
% 65.40/42.05 (((~in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) | (~in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))))),
% 65.40/42.05 inference(tautology,[status(thm)],[])).
% 65.40/42.05 tff(349,plain,
% 65.40/42.05 (~in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))),
% 65.40/42.05 inference(unit_resolution,[status(thm)],[348, 347])).
% 65.40/42.05 tff(350,plain,
% 65.40/42.05 ((~(in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))) | in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) | (~(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))),
% 65.40/42.05 inference(tautology,[status(thm)],[])).
% 65.40/42.05 tff(351,plain,
% 65.40/42.05 ((~(in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12))))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))) | (~(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))),
% 65.40/42.05 inference(unit_resolution,[status(thm)],[350, 349])).
% 65.40/42.05 tff(352,plain,
% 65.40/42.05 (~(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))),
% 65.40/42.05 inference(unit_resolution,[status(thm)],[351, 281])).
% 65.40/42.05 tff(353,plain,
% 65.40/42.05 (((~in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))))) | in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))),
% 65.56/42.19 inference(tautology,[status(thm)],[])).
% 65.56/42.19 tff(354,plain,
% 65.56/42.19 (in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))),
% 65.56/42.19 inference(unit_resolution,[status(thm)],[353, 347])).
% 65.56/42.19 tff(355,plain,
% 65.56/42.19 ((~(in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))) | (~in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12)))) | (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))),
% 65.56/42.19 inference(tautology,[status(thm)],[])).
% 65.56/42.19 tff(356,plain,
% 65.56/42.19 ((~(in(tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) <=> (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12)))) | (tptp_fun_C_4(set_intersection2(set_intersection2(unordered_pair(A!12, A!12), set_union2(singleton(A!12), unordered_pair(A!12, A!12))), set_union2(singleton(A!12), set_difference(singleton(A!12), singleton(A!12)))), set_union2(singleton(A!12), unordered_pair(A!12, A!12))) = set_union2(A!7, A!12))),
% 65.56/42.19 inference(unit_resolution,[status(thm)],[355, 354])).
% 65.56/42.19 tff(357,plain,
% 65.56/42.19 ($false),
% 65.56/42.19 inference(unit_resolution,[status(thm)],[356, 352, 259])).
% 65.56/42.19 % SZS output end Proof
%------------------------------------------------------------------------------