TSTP Solution File: SET884+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET884+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 05:08:31 EDT 2022
% Result : Theorem 0.76s 0.76s
% Output : Proof 0.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SET884+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 08:31:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.76/0.76 % SZS status Theorem
% 0.76/0.76 % SZS output start Proof
% 0.76/0.76 tff(in_type, type, (
% 0.76/0.76 in: ( $i * $i ) > $o)).
% 0.76/0.76 tff(unordered_pair_type, type, (
% 0.76/0.76 unordered_pair: ( $i * $i ) > $i)).
% 0.76/0.76 tff(tptp_fun_B_6_type, type, (
% 0.76/0.76 tptp_fun_B_6: $i)).
% 0.76/0.76 tff(tptp_fun_C_5_type, type, (
% 0.76/0.76 tptp_fun_C_5: $i)).
% 0.76/0.76 tff(tptp_fun_A_7_type, type, (
% 0.76/0.76 tptp_fun_A_7: $i)).
% 0.76/0.76 tff(singleton_type, type, (
% 0.76/0.76 singleton: $i > $i)).
% 0.76/0.76 tff(tptp_fun_C_0_type, type, (
% 0.76/0.76 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.76/0.76 tff(subset_type, type, (
% 0.76/0.76 subset: ( $i * $i ) > $o)).
% 0.76/0.76 tff(tptp_fun_C_2_type, type, (
% 0.76/0.76 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.76/0.76 tff(tptp_fun_D_1_type, type, (
% 0.76/0.76 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.76/0.76 tff(1,plain,
% 0.76/0.76 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(2,plain,
% 0.76/0.76 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[1])).
% 0.76/0.76 tff(3,plain,
% 0.76/0.76 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(4,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.76/0.76 tff(5,plain,
% 0.76/0.76 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.76/0.76 tff(6,plain,(
% 0.76/0.76 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.76/0.76 inference(skolemize,[status(sab)],[5])).
% 0.76/0.76 tff(7,plain,
% 0.76/0.76 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.76/0.76 tff(8,plain,
% 0.76/0.76 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(B!6, C!5) = unordered_pair(C!5, B!6))),
% 0.76/0.76 inference(quant_inst,[status(thm)],[])).
% 0.76/0.76 tff(9,plain,
% 0.76/0.76 (unordered_pair(B!6, C!5) = unordered_pair(C!5, B!6)),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.76/0.76 tff(10,plain,
% 0.76/0.76 (unordered_pair(C!5, B!6) = unordered_pair(B!6, C!5)),
% 0.76/0.76 inference(symmetry,[status(thm)],[9])).
% 0.76/0.76 tff(11,plain,
% 0.76/0.76 (in(A!7, unordered_pair(C!5, B!6)) <=> in(A!7, unordered_pair(B!6, C!5))),
% 0.76/0.76 inference(monotonicity,[status(thm)],[10])).
% 0.76/0.76 tff(12,plain,
% 0.76/0.76 (in(A!7, unordered_pair(B!6, C!5)) <=> in(A!7, unordered_pair(C!5, B!6))),
% 0.76/0.76 inference(symmetry,[status(thm)],[11])).
% 0.76/0.76 tff(13,assumption,(~in(A!7, singleton(A!7))), introduced(assumption)).
% 0.76/0.76 tff(14,plain,
% 0.76/0.76 (^[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)))))))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(15,plain,
% 0.76/0.76 (![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))))))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[14])).
% 0.76/0.76 tff(16,plain,
% 0.76/0.76 (![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))))))),
% 0.76/0.76 inference(pull_quant,[status(thm)],[])).
% 0.76/0.76 tff(17,plain,
% 0.76/0.76 (^[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))))))))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(18,plain,
% 0.76/0.76 (![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))))))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[17])).
% 0.76/0.76 tff(19,plain,
% 0.76/0.76 (![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))))))),
% 0.76/0.76 inference(transitivity,[status(thm)],[18, 16])).
% 0.76/0.76 tff(20,plain,
% 0.76/0.76 (![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))))))),
% 0.76/0.76 inference(transitivity,[status(thm)],[19, 15])).
% 0.76/0.76 tff(21,plain,
% 0.76/0.76 (^[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)))))))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(22,plain,
% 0.76/0.76 (![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))))))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[21])).
% 0.76/0.76 tff(23,plain,
% 0.76/0.76 (![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))))))),
% 0.76/0.76 inference(transitivity,[status(thm)],[22, 20])).
% 0.76/0.76 tff(24,plain,
% 0.76/0.76 (^[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))))))))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(25,plain,
% 0.76/0.76 (![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))))))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[24])).
% 0.76/0.76 tff(26,plain,
% 0.76/0.76 (^[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)))))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(27,plain,
% 0.76/0.76 (![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))))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[26])).
% 0.76/0.76 tff(28,plain,
% 0.76/0.76 (![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)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(29,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.76/0.76 tff(30,plain,
% 0.76/0.76 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.76/0.76 tff(31,plain,(
% 0.76/0.76 ![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)))))),
% 0.76/0.76 inference(skolemize,[status(sab)],[30])).
% 0.76/0.76 tff(32,plain,
% 0.76/0.76 (![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))))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.76/0.76 tff(33,plain,
% 0.76/0.76 (![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))))))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.76/0.76 tff(34,plain,
% 0.76/0.76 (![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))))))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.76/0.76 tff(35,plain,
% 0.76/0.76 (((~![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))))))) | in(A!7, singleton(A!7))) <=> ((~![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))))))) | in(A!7, singleton(A!7)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(36,plain,
% 0.76/0.76 ((~(~in(A!7, singleton(A!7)))) <=> in(A!7, singleton(A!7))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(37,plain,
% 0.76/0.76 (((~in(A!7, singleton(A!7))) | $false) <=> (~in(A!7, singleton(A!7)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(38,plain,
% 0.76/0.76 ((~$true) <=> $false),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(39,plain,
% 0.76/0.76 (($true | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))) <=> $true),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(40,plain,
% 0.76/0.76 ((singleton(A!7) = singleton(A!7)) <=> $true),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(41,plain,
% 0.76/0.76 (((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))) <=> ($true | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))),
% 0.76/0.76 inference(monotonicity,[status(thm)],[40])).
% 0.76/0.76 tff(42,plain,
% 0.76/0.76 (((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))) <=> $true),
% 0.76/0.76 inference(transitivity,[status(thm)],[41, 39])).
% 0.76/0.76 tff(43,plain,
% 0.76/0.76 ((~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> (~$true)),
% 0.76/0.76 inference(monotonicity,[status(thm)],[42])).
% 0.76/0.76 tff(44,plain,
% 0.76/0.76 ((~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> $false),
% 0.76/0.76 inference(transitivity,[status(thm)],[43, 38])).
% 0.76/0.76 tff(45,plain,
% 0.76/0.76 ((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) <=> (~in(A!7, singleton(A!7)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(46,plain,
% 0.76/0.76 (((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))) <=> ((~in(A!7, singleton(A!7))) | $false)),
% 0.76/0.76 inference(monotonicity,[status(thm)],[45, 44])).
% 0.76/0.76 tff(47,plain,
% 0.76/0.76 (((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))) <=> (~in(A!7, singleton(A!7)))),
% 0.76/0.76 inference(transitivity,[status(thm)],[46, 37])).
% 0.76/0.76 tff(48,plain,
% 0.76/0.76 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> (~(~in(A!7, singleton(A!7))))),
% 0.76/0.76 inference(monotonicity,[status(thm)],[47])).
% 0.76/0.76 tff(49,plain,
% 0.76/0.76 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> in(A!7, singleton(A!7))),
% 0.76/0.76 inference(transitivity,[status(thm)],[48, 36])).
% 0.76/0.76 tff(50,plain,
% 0.76/0.76 (((~![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))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> ((~![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))))))) | in(A!7, singleton(A!7)))),
% 0.76/0.76 inference(monotonicity,[status(thm)],[49])).
% 0.76/0.76 tff(51,plain,
% 0.76/0.76 (((~![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))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> ((~![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))))))) | in(A!7, singleton(A!7)))),
% 0.76/0.76 inference(transitivity,[status(thm)],[50, 35])).
% 0.76/0.76 tff(52,plain,
% 0.76/0.76 ((~![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))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))),
% 0.76/0.76 inference(quant_inst,[status(thm)],[])).
% 0.76/0.76 tff(53,plain,
% 0.76/0.76 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(A!7, singleton(A!7))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.76/0.76 tff(54,plain,
% 0.76/0.76 ($false),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[53, 34, 13])).
% 0.76/0.76 tff(55,plain,(in(A!7, singleton(A!7))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.76 tff(56,plain,
% 0.76/0.76 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(57,plain,
% 0.76/0.76 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(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_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[56])).
% 0.76/0.76 tff(58,plain,
% 0.76/0.76 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(59,plain,
% 0.76/0.76 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(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_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[58])).
% 0.76/0.76 tff(60,plain,
% 0.76/0.76 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(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_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.85/0.76 inference(transitivity,[status(thm)],[59, 57])).
% 0.85/0.76 tff(61,plain,
% 0.85/0.76 (^[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_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))))),
% 0.85/0.76 inference(bind,[status(th)],[])).
% 0.85/0.76 tff(62,plain,
% 0.85/0.76 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(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_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.85/0.76 inference(quant_intro,[status(thm)],[61])).
% 0.85/0.76 tff(63,plain,
% 0.85/0.76 (![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)))),
% 0.85/0.76 inference(rewrite,[status(thm)],[])).
% 0.85/0.76 tff(64,plain,
% 0.85/0.76 (^[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))))),
% 0.85/0.76 inference(bind,[status(th)],[])).
% 0.85/0.76 tff(65,plain,
% 0.85/0.76 (![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)))),
% 0.85/0.76 inference(quant_intro,[status(thm)],[64])).
% 0.85/0.76 tff(66,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.85/0.76 tff(67,plain,
% 0.85/0.76 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.85/0.76 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.85/0.76 tff(68,plain,
% 0.85/0.76 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.85/0.76 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.85/0.76 tff(69,plain,(
% 0.85/0.76 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))),
% 0.85/0.76 inference(skolemize,[status(sab)],[68])).
% 0.85/0.76 tff(70,plain,
% 0.85/0.76 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.85/0.76 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.85/0.76 tff(71,plain,
% 0.85/0.76 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.85/0.76 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.85/0.76 tff(72,plain,
% 0.85/0.76 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(singleton(A!7), unordered_pair(B!6, C!5))) | ![C: $i] : ((~in(C, singleton(A!7))) | in(C, unordered_pair(B!6, C!5))))) | (~(subset(singleton(A!7), unordered_pair(B!6, C!5)) | (~((~in(tptp_fun_C_2(unordered_pair(B!6, C!5), singleton(A!7)), singleton(A!7))) | in(tptp_fun_C_2(unordered_pair(B!6, C!5), singleton(A!7)), unordered_pair(B!6, C!5))))))))),
% 0.85/0.77 inference(quant_inst,[status(thm)],[])).
% 0.85/0.77 tff(73,plain,
% 0.85/0.77 (~((~((~subset(singleton(A!7), unordered_pair(B!6, C!5))) | ![C: $i] : ((~in(C, singleton(A!7))) | in(C, unordered_pair(B!6, C!5))))) | (~(subset(singleton(A!7), unordered_pair(B!6, C!5)) | (~((~in(tptp_fun_C_2(unordered_pair(B!6, C!5), singleton(A!7)), singleton(A!7))) | in(tptp_fun_C_2(unordered_pair(B!6, C!5), singleton(A!7)), unordered_pair(B!6, C!5)))))))),
% 0.85/0.77 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.85/0.77 tff(74,plain,
% 0.85/0.77 (((~((~subset(singleton(A!7), unordered_pair(B!6, C!5))) | ![C: $i] : ((~in(C, singleton(A!7))) | in(C, unordered_pair(B!6, C!5))))) | (~(subset(singleton(A!7), unordered_pair(B!6, C!5)) | (~((~in(tptp_fun_C_2(unordered_pair(B!6, C!5), singleton(A!7)), singleton(A!7))) | in(tptp_fun_C_2(unordered_pair(B!6, C!5), singleton(A!7)), unordered_pair(B!6, C!5))))))) | ((~subset(singleton(A!7), unordered_pair(B!6, C!5))) | ![C: $i] : ((~in(C, singleton(A!7))) | in(C, unordered_pair(B!6, C!5))))),
% 0.85/0.77 inference(tautology,[status(thm)],[])).
% 0.85/0.77 tff(75,plain,
% 0.85/0.77 ((~subset(singleton(A!7), unordered_pair(B!6, C!5))) | ![C: $i] : ((~in(C, singleton(A!7))) | in(C, unordered_pair(B!6, C!5)))),
% 0.85/0.77 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.85/0.77 tff(76,plain,
% 0.85/0.77 ((~(~(subset(singleton(A!7), unordered_pair(B!6, C!5)) & (~(A!7 = B!6)) & (~(A!7 = C!5))))) <=> (subset(singleton(A!7), unordered_pair(B!6, C!5)) & (~(A!7 = B!6)) & (~(A!7 = C!5)))),
% 0.85/0.77 inference(rewrite,[status(thm)],[])).
% 0.85/0.77 tff(77,plain,
% 0.85/0.77 ((~![A: $i, B: $i, C: $i] : (~(subset(singleton(A), unordered_pair(B, C)) & (~(A = B)) & (~(A = C))))) <=> (~![A: $i, B: $i, C: $i] : (~(subset(singleton(A), unordered_pair(B, C)) & (~(A = B)) & (~(A = C)))))),
% 0.85/0.77 inference(rewrite,[status(thm)],[])).
% 0.85/0.77 tff(78,plain,
% 0.85/0.77 ((~![A: $i, B: $i, C: $i] : (~((subset(singleton(A), unordered_pair(B, C)) & (~(A = B))) & (~(A = C))))) <=> (~![A: $i, B: $i, C: $i] : (~(subset(singleton(A), unordered_pair(B, C)) & (~(A = B)) & (~(A = C)))))),
% 0.85/0.77 inference(rewrite,[status(thm)],[])).
% 0.85/0.77 tff(79,axiom,(~![A: $i, B: $i, C: $i] : (~((subset(singleton(A), unordered_pair(B, C)) & (~(A = B))) & (~(A = C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t25_zfmisc_1')).
% 0.85/0.77 tff(80,plain,
% 0.85/0.77 (~![A: $i, B: $i, C: $i] : (~(subset(singleton(A), unordered_pair(B, C)) & (~(A = B)) & (~(A = C))))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.85/0.77 tff(81,plain,
% 0.85/0.77 (~![A: $i, B: $i, C: $i] : (~(subset(singleton(A), unordered_pair(B, C)) & (~(A = B)) & (~(A = C))))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[80, 77])).
% 0.85/0.77 tff(82,plain,
% 0.85/0.77 (~![A: $i, B: $i, C: $i] : (~(subset(singleton(A), unordered_pair(B, C)) & (~(A = B)) & (~(A = C))))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.85/0.77 tff(83,plain,
% 0.85/0.77 (~![A: $i, B: $i, C: $i] : (~(subset(singleton(A), unordered_pair(B, C)) & (~(A = B)) & (~(A = C))))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[82, 77])).
% 0.85/0.77 tff(84,plain,
% 0.85/0.77 (~![A: $i, B: $i, C: $i] : (~(subset(singleton(A), unordered_pair(B, C)) & (~(A = B)) & (~(A = C))))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[83, 77])).
% 0.85/0.77 tff(85,plain,
% 0.85/0.77 (~![A: $i, B: $i, C: $i] : (~(subset(singleton(A), unordered_pair(B, C)) & (~(A = B)) & (~(A = C))))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.85/0.77 tff(86,plain,
% 0.85/0.77 (~![A: $i, B: $i, C: $i] : (~(subset(singleton(A), unordered_pair(B, C)) & (~(A = B)) & (~(A = C))))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[85, 77])).
% 0.85/0.77 tff(87,plain,(
% 0.85/0.77 ~(~(subset(singleton(A!7), unordered_pair(B!6, C!5)) & (~(A!7 = B!6)) & (~(A!7 = C!5))))),
% 0.85/0.77 inference(skolemize,[status(sab)],[86])).
% 0.85/0.77 tff(88,plain,
% 0.85/0.77 (subset(singleton(A!7), unordered_pair(B!6, C!5)) & (~(A!7 = B!6)) & (~(A!7 = C!5))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[87, 76])).
% 0.85/0.77 tff(89,plain,
% 0.85/0.77 (subset(singleton(A!7), unordered_pair(B!6, C!5))),
% 0.85/0.77 inference(and_elim,[status(thm)],[88])).
% 0.85/0.77 tff(90,plain,
% 0.85/0.77 ((~((~subset(singleton(A!7), unordered_pair(B!6, C!5))) | ![C: $i] : ((~in(C, singleton(A!7))) | in(C, unordered_pair(B!6, C!5))))) | (~subset(singleton(A!7), unordered_pair(B!6, C!5))) | ![C: $i] : ((~in(C, singleton(A!7))) | in(C, unordered_pair(B!6, C!5)))),
% 0.85/0.77 inference(tautology,[status(thm)],[])).
% 0.85/0.77 tff(91,plain,
% 0.85/0.77 ((~((~subset(singleton(A!7), unordered_pair(B!6, C!5))) | ![C: $i] : ((~in(C, singleton(A!7))) | in(C, unordered_pair(B!6, C!5))))) | ![C: $i] : ((~in(C, singleton(A!7))) | in(C, unordered_pair(B!6, C!5)))),
% 0.85/0.77 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.85/0.77 tff(92,plain,
% 0.85/0.77 (![C: $i] : ((~in(C, singleton(A!7))) | in(C, unordered_pair(B!6, C!5)))),
% 0.85/0.77 inference(unit_resolution,[status(thm)],[91, 75])).
% 0.85/0.77 tff(93,plain,
% 0.85/0.77 (((~![C: $i] : ((~in(C, singleton(A!7))) | in(C, unordered_pair(B!6, C!5)))) | ((~in(A!7, singleton(A!7))) | in(A!7, unordered_pair(B!6, C!5)))) <=> ((~![C: $i] : ((~in(C, singleton(A!7))) | in(C, unordered_pair(B!6, C!5)))) | (~in(A!7, singleton(A!7))) | in(A!7, unordered_pair(B!6, C!5)))),
% 0.85/0.77 inference(rewrite,[status(thm)],[])).
% 0.85/0.77 tff(94,plain,
% 0.85/0.77 ((~![C: $i] : ((~in(C, singleton(A!7))) | in(C, unordered_pair(B!6, C!5)))) | ((~in(A!7, singleton(A!7))) | in(A!7, unordered_pair(B!6, C!5)))),
% 0.85/0.77 inference(quant_inst,[status(thm)],[])).
% 0.85/0.77 tff(95,plain,
% 0.85/0.77 ((~![C: $i] : ((~in(C, singleton(A!7))) | in(C, unordered_pair(B!6, C!5)))) | (~in(A!7, singleton(A!7))) | in(A!7, unordered_pair(B!6, C!5))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.85/0.77 tff(96,plain,
% 0.85/0.77 (in(A!7, unordered_pair(B!6, C!5))),
% 0.85/0.77 inference(unit_resolution,[status(thm)],[95, 92, 55])).
% 0.85/0.77 tff(97,plain,
% 0.85/0.77 (in(A!7, unordered_pair(C!5, B!6))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[96, 12])).
% 0.85/0.77 tff(98,plain,
% 0.85/0.77 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.85/0.77 inference(bind,[status(th)],[])).
% 0.85/0.77 tff(99,plain,
% 0.85/0.77 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.85/0.77 inference(quant_intro,[status(thm)],[98])).
% 0.85/0.77 tff(100,plain,
% 0.85/0.77 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.85/0.77 inference(pull_quant,[status(thm)],[])).
% 0.85/0.77 tff(101,plain,
% 0.85/0.77 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 0.85/0.77 inference(bind,[status(th)],[])).
% 0.85/0.77 tff(102,plain,
% 0.85/0.77 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.85/0.77 inference(quant_intro,[status(thm)],[101])).
% 0.85/0.77 tff(103,plain,
% 0.85/0.77 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.85/0.77 inference(transitivity,[status(thm)],[102, 100])).
% 0.85/0.77 tff(104,plain,
% 0.85/0.77 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.85/0.77 inference(transitivity,[status(thm)],[103, 99])).
% 0.85/0.77 tff(105,plain,
% 0.85/0.77 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.85/0.77 inference(bind,[status(th)],[])).
% 0.85/0.77 tff(106,plain,
% 0.85/0.77 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.85/0.77 inference(quant_intro,[status(thm)],[105])).
% 0.85/0.77 tff(107,plain,
% 0.85/0.77 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.85/0.77 inference(transitivity,[status(thm)],[106, 104])).
% 0.85/0.77 tff(108,plain,
% 0.85/0.77 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 0.85/0.77 inference(bind,[status(th)],[])).
% 0.85/0.77 tff(109,plain,
% 0.85/0.77 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.85/0.77 inference(quant_intro,[status(thm)],[108])).
% 0.85/0.77 tff(110,plain,
% 0.85/0.77 (^[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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 0.85/0.77 inference(bind,[status(th)],[])).
% 0.85/0.77 tff(111,plain,
% 0.85/0.77 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))),
% 0.85/0.77 inference(quant_intro,[status(thm)],[110])).
% 0.85/0.77 tff(112,plain,
% 0.85/0.77 (![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))))),
% 0.85/0.77 inference(rewrite,[status(thm)],[])).
% 0.85/0.77 tff(113,plain,
% 0.85/0.77 (^[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)))))),
% 0.85/0.77 inference(bind,[status(th)],[])).
% 0.85/0.77 tff(114,plain,
% 0.85/0.77 (![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))))),
% 0.85/0.77 inference(quant_intro,[status(thm)],[113])).
% 0.85/0.77 tff(115,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_tarski')).
% 0.85/0.77 tff(116,plain,
% 0.85/0.77 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.85/0.77 tff(117,plain,
% 0.85/0.77 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.85/0.77 tff(118,plain,(
% 0.85/0.77 ![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 0.85/0.77 inference(skolemize,[status(sab)],[117])).
% 0.85/0.77 tff(119,plain,
% 0.85/0.77 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.85/0.77 tff(120,plain,
% 0.85/0.77 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[119, 109])).
% 0.85/0.77 tff(121,plain,
% 0.85/0.77 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.85/0.77 inference(modus_ponens,[status(thm)],[120, 107])).
% 0.85/0.77 tff(122,plain,
% 0.85/0.77 (((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5)))) <=> ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))))),
% 0.85/0.77 inference(rewrite,[status(thm)],[])).
% 0.85/0.77 tff(123,plain,
% 0.85/0.77 ((~((~in(A!7, unordered_pair(C!5, B!6))) <=> ((A!7 = B!6) | (A!7 = C!5)))) <=> (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5)))),
% 0.85/0.77 inference(rewrite,[status(thm)],[])).
% 0.85/0.77 tff(124,plain,
% 0.85/0.77 ((((~in(A!7, unordered_pair(C!5, B!6))) <=> ((A!7 = B!6) | (A!7 = C!5))) | $false) <=> ((~in(A!7, unordered_pair(C!5, B!6))) <=> ((A!7 = B!6) | (A!7 = C!5)))),
% 0.85/0.77 inference(rewrite,[status(thm)],[])).
% 0.85/0.77 tff(125,plain,
% 0.85/0.77 (($true | ((~in(tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5), unordered_pair(C!5, B!6))) <=> ((tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = B!6) | (tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = C!5)))) <=> $true),
% 0.85/0.77 inference(rewrite,[status(thm)],[])).
% 0.85/0.77 tff(126,plain,
% 0.85/0.77 ((unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6)) <=> $true),
% 0.85/0.77 inference(rewrite,[status(thm)],[])).
% 0.85/0.77 tff(127,plain,
% 0.85/0.77 (((unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5), unordered_pair(C!5, B!6))) <=> ((tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = B!6) | (tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = C!5)))) <=> ($true | ((~in(tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5), unordered_pair(C!5, B!6))) <=> ((tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = B!6) | (tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = C!5))))),
% 0.85/0.77 inference(monotonicity,[status(thm)],[126])).
% 0.85/0.77 tff(128,plain,
% 0.85/0.77 (((unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5), unordered_pair(C!5, B!6))) <=> ((tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = B!6) | (tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = C!5)))) <=> $true),
% 0.85/0.77 inference(transitivity,[status(thm)],[127, 125])).
% 0.85/0.77 tff(129,plain,
% 0.85/0.77 ((~((unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5), unordered_pair(C!5, B!6))) <=> ((tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = B!6) | (tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = C!5))))) <=> (~$true)),
% 0.85/0.77 inference(monotonicity,[status(thm)],[128])).
% 0.85/0.77 tff(130,plain,
% 0.85/0.77 ((~((unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5), unordered_pair(C!5, B!6))) <=> ((tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = B!6) | (tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = C!5))))) <=> $false),
% 0.85/0.77 inference(transitivity,[status(thm)],[129, 38])).
% 0.85/0.77 tff(131,plain,
% 0.85/0.77 ((~(in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5)))) <=> ((~in(A!7, unordered_pair(C!5, B!6))) <=> ((A!7 = B!6) | (A!7 = C!5)))),
% 0.85/0.77 inference(rewrite,[status(thm)],[])).
% 0.85/0.77 tff(132,plain,
% 0.85/0.77 (($false | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5)))) <=> (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5)))),
% 0.85/0.77 inference(rewrite,[status(thm)],[])).
% 0.85/0.77 tff(133,plain,
% 0.85/0.77 ((~(unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6))) <=> (~$true)),
% 0.85/0.77 inference(monotonicity,[status(thm)],[126])).
% 0.85/0.77 tff(134,plain,
% 0.85/0.77 ((~(unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6))) <=> $false),
% 0.85/0.77 inference(transitivity,[status(thm)],[133, 38])).
% 0.85/0.77 tff(135,plain,
% 0.85/0.77 (((~(unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5)))) <=> ($false | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))))),
% 0.85/0.77 inference(monotonicity,[status(thm)],[134])).
% 0.85/0.77 tff(136,plain,
% 0.85/0.77 (((~(unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5)))) <=> (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5)))),
% 0.85/0.78 inference(transitivity,[status(thm)],[135, 132])).
% 0.85/0.78 tff(137,plain,
% 0.85/0.78 ((~((~(unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))))) <=> (~(in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))))),
% 0.85/0.78 inference(monotonicity,[status(thm)],[136])).
% 0.85/0.78 tff(138,plain,
% 0.85/0.78 ((~((~(unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))))) <=> ((~in(A!7, unordered_pair(C!5, B!6))) <=> ((A!7 = B!6) | (A!7 = C!5)))),
% 0.85/0.78 inference(transitivity,[status(thm)],[137, 131])).
% 0.85/0.78 tff(139,plain,
% 0.85/0.78 (((~((~(unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))))) | (~((unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5), unordered_pair(C!5, B!6))) <=> ((tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = B!6) | (tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = C!5)))))) <=> (((~in(A!7, unordered_pair(C!5, B!6))) <=> ((A!7 = B!6) | (A!7 = C!5))) | $false)),
% 0.85/0.78 inference(monotonicity,[status(thm)],[138, 130])).
% 0.85/0.78 tff(140,plain,
% 0.85/0.78 (((~((~(unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))))) | (~((unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5), unordered_pair(C!5, B!6))) <=> ((tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = B!6) | (tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = C!5)))))) <=> ((~in(A!7, unordered_pair(C!5, B!6))) <=> ((A!7 = B!6) | (A!7 = C!5)))),
% 0.85/0.78 inference(transitivity,[status(thm)],[139, 124])).
% 0.85/0.78 tff(141,plain,
% 0.85/0.78 ((~((~((~(unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))))) | (~((unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5), unordered_pair(C!5, B!6))) <=> ((tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = B!6) | (tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = C!5))))))) <=> (~((~in(A!7, unordered_pair(C!5, B!6))) <=> ((A!7 = B!6) | (A!7 = C!5))))),
% 0.85/0.78 inference(monotonicity,[status(thm)],[140])).
% 0.85/0.78 tff(142,plain,
% 0.85/0.78 ((~((~((~(unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))))) | (~((unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5), unordered_pair(C!5, B!6))) <=> ((tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = B!6) | (tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = C!5))))))) <=> (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5)))),
% 0.85/0.78 inference(transitivity,[status(thm)],[141, 123])).
% 0.85/0.78 tff(143,plain,
% 0.85/0.78 (((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))))) | (~((unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5), unordered_pair(C!5, B!6))) <=> ((tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = B!6) | (tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = C!5)))))))) <=> ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))))),
% 0.85/0.78 inference(monotonicity,[status(thm)],[142])).
% 0.85/0.78 tff(144,plain,
% 0.85/0.78 (((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))))) | (~((unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5), unordered_pair(C!5, B!6))) <=> ((tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = B!6) | (tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = C!5)))))))) <=> ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))))),
% 0.85/0.78 inference(transitivity,[status(thm)],[143, 122])).
% 0.85/0.78 tff(145,plain,
% 0.85/0.78 ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))))) | (~((unordered_pair(C!5, B!6) = unordered_pair(C!5, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5), unordered_pair(C!5, B!6))) <=> ((tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = B!6) | (tptp_fun_D_1(unordered_pair(C!5, B!6), B!6, C!5) = C!5)))))))),
% 0.85/0.78 inference(quant_inst,[status(thm)],[])).
% 0.85/0.78 tff(146,plain,
% 0.85/0.78 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5)))),
% 0.85/0.78 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.85/0.78 tff(147,plain,
% 0.85/0.78 (in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5))),
% 0.85/0.78 inference(unit_resolution,[status(thm)],[146, 121])).
% 0.85/0.78 tff(148,plain,
% 0.85/0.78 (~(A!7 = C!5)),
% 0.85/0.78 inference(and_elim,[status(thm)],[88])).
% 0.85/0.78 tff(149,plain,
% 0.85/0.78 (~(A!7 = B!6)),
% 0.85/0.78 inference(and_elim,[status(thm)],[88])).
% 0.85/0.78 tff(150,plain,
% 0.85/0.78 ((~((A!7 = B!6) | (A!7 = C!5))) | (A!7 = B!6) | (A!7 = C!5)),
% 0.85/0.78 inference(tautology,[status(thm)],[])).
% 0.85/0.78 tff(151,plain,
% 0.85/0.78 (~((A!7 = B!6) | (A!7 = C!5))),
% 0.85/0.78 inference(unit_resolution,[status(thm)],[150, 149, 148])).
% 0.85/0.78 tff(152,plain,
% 0.85/0.78 ((~(in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5)))) | (~in(A!7, unordered_pair(C!5, B!6))) | ((A!7 = B!6) | (A!7 = C!5))),
% 0.85/0.78 inference(tautology,[status(thm)],[])).
% 0.85/0.78 tff(153,plain,
% 0.85/0.78 ((~(in(A!7, unordered_pair(C!5, B!6)) <=> ((A!7 = B!6) | (A!7 = C!5)))) | (~in(A!7, unordered_pair(C!5, B!6)))),
% 0.85/0.78 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.85/0.78 tff(154,plain,
% 0.85/0.78 (~in(A!7, unordered_pair(C!5, B!6))),
% 0.85/0.78 inference(unit_resolution,[status(thm)],[153, 147])).
% 0.85/0.78 tff(155,plain,
% 0.85/0.78 ($false),
% 0.85/0.78 inference(unit_resolution,[status(thm)],[154, 97])).
% 0.85/0.78 % SZS output end Proof
%------------------------------------------------------------------------------