TSTP Solution File: SEU151+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU151+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 07:27:48 EDT 2022
% Result : Theorem 16.11s 10.54s
% Output : Proof 16.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU151+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 09:39:19 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 16.11/10.54 % SZS status Theorem
% 16.11/10.54 % SZS output start Proof
% 16.11/10.54 tff(tptp_fun_D_1_type, type, (
% 16.11/10.54 tptp_fun_D_1: $i)).
% 16.11/10.54 tff(tptp_fun_A_4_type, type, (
% 16.11/10.54 tptp_fun_A_4: $i)).
% 16.11/10.54 tff(tptp_fun_C_2_type, type, (
% 16.11/10.54 tptp_fun_C_2: $i)).
% 16.11/10.54 tff(in_type, type, (
% 16.11/10.54 in: ( $i * $i ) > $o)).
% 16.11/10.54 tff(unordered_pair_type, type, (
% 16.11/10.54 unordered_pair: ( $i * $i ) > $i)).
% 16.11/10.54 tff(tptp_fun_B_3_type, type, (
% 16.11/10.54 tptp_fun_B_3: $i)).
% 16.11/10.54 tff(tptp_fun_D_0_type, type, (
% 16.11/10.54 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 16.11/10.54 tff(1,plain,
% 16.11/10.54 ((~(~((unordered_pair(A!4, B!3) = unordered_pair(C!2, D!1)) & (~(A!4 = C!2)) & (~(A!4 = D!1))))) <=> ((unordered_pair(A!4, B!3) = unordered_pair(C!2, D!1)) & (~(A!4 = C!2)) & (~(A!4 = D!1)))),
% 16.11/10.54 inference(rewrite,[status(thm)],[])).
% 16.11/10.54 tff(2,plain,
% 16.11/10.54 ((~![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D)))))),
% 16.11/10.54 inference(rewrite,[status(thm)],[])).
% 16.11/10.54 tff(3,plain,
% 16.11/10.54 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C))) & (~(A = D))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D)))))),
% 16.11/10.54 inference(rewrite,[status(thm)],[])).
% 16.11/10.54 tff(4,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (~(((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C))) & (~(A = D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t10_zfmisc_1')).
% 16.11/10.54 tff(5,plain,
% 16.11/10.54 (~![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D))))),
% 16.11/10.54 inference(modus_ponens,[status(thm)],[4, 3])).
% 16.11/10.54 tff(6,plain,
% 16.11/10.54 (~![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D))))),
% 16.11/10.54 inference(modus_ponens,[status(thm)],[5, 2])).
% 16.11/10.54 tff(7,plain,
% 16.11/10.54 (~![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D))))),
% 16.11/10.54 inference(modus_ponens,[status(thm)],[6, 2])).
% 16.11/10.54 tff(8,plain,
% 16.11/10.54 (~![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D))))),
% 16.11/10.54 inference(modus_ponens,[status(thm)],[7, 2])).
% 16.11/10.54 tff(9,plain,
% 16.11/10.54 (~![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D))))),
% 16.11/10.54 inference(modus_ponens,[status(thm)],[8, 2])).
% 16.11/10.54 tff(10,plain,
% 16.11/10.54 (~![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D))))),
% 16.11/10.54 inference(modus_ponens,[status(thm)],[9, 2])).
% 16.11/10.54 tff(11,plain,
% 16.11/10.54 (~![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D))))),
% 16.11/10.54 inference(modus_ponens,[status(thm)],[10, 2])).
% 16.11/10.54 tff(12,plain,(
% 16.11/10.54 ~(~((unordered_pair(A!4, B!3) = unordered_pair(C!2, D!1)) & (~(A!4 = C!2)) & (~(A!4 = D!1))))),
% 16.11/10.54 inference(skolemize,[status(sab)],[11])).
% 16.11/10.54 tff(13,plain,
% 16.11/10.54 ((unordered_pair(A!4, B!3) = unordered_pair(C!2, D!1)) & (~(A!4 = C!2)) & (~(A!4 = D!1))),
% 16.11/10.54 inference(modus_ponens,[status(thm)],[12, 1])).
% 16.11/10.54 tff(14,plain,
% 16.11/10.54 (~(A!4 = D!1)),
% 16.11/10.54 inference(and_elim,[status(thm)],[13])).
% 16.11/10.54 tff(15,plain,
% 16.11/10.54 (~(A!4 = C!2)),
% 16.11/10.54 inference(and_elim,[status(thm)],[13])).
% 16.11/10.54 tff(16,plain,
% 16.11/10.54 ((~((A!4 = C!2) | (A!4 = D!1))) | (A!4 = C!2) | (A!4 = D!1)),
% 16.11/10.54 inference(tautology,[status(thm)],[])).
% 16.11/10.54 tff(17,plain,
% 16.11/10.54 (~((A!4 = C!2) | (A!4 = D!1))),
% 16.11/10.54 inference(unit_resolution,[status(thm)],[16, 15, 14])).
% 16.11/10.54 tff(18,assumption,((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(C!2, D!1)))) | (~((unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = A!4)))))), introduced(assumption)).
% 16.11/10.54 tff(19,plain,
% 16.11/10.54 (^[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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 16.11/10.54 inference(bind,[status(th)],[])).
% 16.11/10.54 tff(20,plain,
% 16.11/10.54 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 16.11/10.54 inference(quant_intro,[status(thm)],[19])).
% 16.11/10.54 tff(21,plain,
% 16.11/10.54 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 16.11/10.54 inference(pull_quant,[status(thm)],[])).
% 16.11/10.54 tff(22,plain,
% 16.11/10.54 (^[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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))),
% 16.11/10.54 inference(bind,[status(th)],[])).
% 16.11/10.54 tff(23,plain,
% 16.11/10.54 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 16.11/10.54 inference(quant_intro,[status(thm)],[22])).
% 16.11/10.54 tff(24,plain,
% 16.11/10.54 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 16.11/10.54 inference(transitivity,[status(thm)],[23, 21])).
% 16.11/10.54 tff(25,plain,
% 16.11/10.54 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 16.11/10.54 inference(transitivity,[status(thm)],[24, 20])).
% 16.11/10.54 tff(26,plain,
% 16.11/10.54 (^[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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 16.11/10.54 inference(bind,[status(th)],[])).
% 16.11/10.54 tff(27,plain,
% 16.11/10.54 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 16.11/10.54 inference(quant_intro,[status(thm)],[26])).
% 16.11/10.54 tff(28,plain,
% 16.11/10.54 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 16.11/10.54 inference(transitivity,[status(thm)],[27, 25])).
% 16.11/10.54 tff(29,plain,
% 16.11/10.54 (^[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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))),
% 16.11/10.54 inference(bind,[status(th)],[])).
% 16.11/10.54 tff(30,plain,
% 16.11/10.54 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 16.11/10.54 inference(quant_intro,[status(thm)],[29])).
% 16.11/10.54 tff(31,plain,
% 16.11/10.54 (^[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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))),
% 16.11/10.54 inference(bind,[status(th)],[])).
% 16.11/10.54 tff(32,plain,
% 16.11/10.54 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))),
% 16.11/10.54 inference(quant_intro,[status(thm)],[31])).
% 16.11/10.54 tff(33,plain,
% 16.11/10.54 (![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))))),
% 16.11/10.54 inference(rewrite,[status(thm)],[])).
% 16.11/10.54 tff(34,plain,
% 16.11/10.54 (^[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)))))),
% 16.11/10.54 inference(bind,[status(th)],[])).
% 16.11/10.54 tff(35,plain,
% 16.11/10.54 (![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))))),
% 16.11/10.55 inference(quant_intro,[status(thm)],[34])).
% 16.11/10.55 tff(36,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')).
% 16.11/10.55 tff(37,plain,
% 16.11/10.55 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 16.11/10.55 inference(modus_ponens,[status(thm)],[36, 35])).
% 16.11/10.55 tff(38,plain,
% 16.11/10.55 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 16.11/10.55 inference(modus_ponens,[status(thm)],[37, 33])).
% 16.11/10.55 tff(39,plain,(
% 16.11/10.55 ![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))),
% 16.11/10.55 inference(skolemize,[status(sab)],[38])).
% 16.11/10.55 tff(40,plain,
% 16.11/10.55 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))),
% 16.11/10.55 inference(modus_ponens,[status(thm)],[39, 32])).
% 16.11/10.55 tff(41,plain,
% 16.11/10.55 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 16.11/10.55 inference(modus_ponens,[status(thm)],[40, 30])).
% 16.11/10.55 tff(42,plain,
% 16.11/10.55 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 16.11/10.55 inference(modus_ponens,[status(thm)],[41, 28])).
% 16.11/10.55 tff(43,plain,
% 16.11/10.55 (((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(C!2, D!1)))) | (~((unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = A!4)))))))) <=> ((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(C!2, D!1)))) | (~((unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = A!4))))))))),
% 16.11/10.55 inference(rewrite,[status(thm)],[])).
% 16.11/10.55 tff(44,plain,
% 16.11/10.55 ((~((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = B!3) | (A!4 = A!4))))) | (~((unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = A!4))))))) <=> (~((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(C!2, D!1)))) | (~((unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = A!4)))))))),
% 16.11/10.55 inference(rewrite,[status(thm)],[])).
% 16.11/10.55 tff(45,plain,
% 16.11/10.55 (((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = B!3) | (A!4 = A!4))))) | (~((unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = A!4)))))))) <=> ((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(C!2, D!1)))) | (~((unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = A!4))))))))),
% 16.11/10.55 inference(monotonicity,[status(thm)],[44])).
% 16.11/10.55 tff(46,plain,
% 16.11/10.55 (((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = B!3) | (A!4 = A!4))))) | (~((unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = A!4)))))))) <=> ((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(C!2, D!1)))) | (~((unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = A!4))))))))),
% 16.11/10.55 inference(transitivity,[status(thm)],[45, 43])).
% 16.11/10.55 tff(47,plain,
% 16.11/10.55 ((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = B!3) | (A!4 = A!4))))) | (~((unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = A!4)))))))),
% 16.11/10.55 inference(quant_inst,[status(thm)],[])).
% 16.11/10.55 tff(48,plain,
% 16.11/10.55 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(C!2, D!1)))) | (~((unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = A!4)))))))),
% 16.11/10.55 inference(modus_ponens,[status(thm)],[47, 46])).
% 16.11/10.55 tff(49,plain,
% 16.11/10.55 ($false),
% 16.11/10.55 inference(unit_resolution,[status(thm)],[48, 42, 18])).
% 16.11/10.55 tff(50,plain,(~((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(C!2, D!1)))) | (~((unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = A!4))))))), inference(lemma,lemma(discharge,[]))).
% 16.11/10.55 tff(51,plain,
% 16.11/10.55 (((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(C!2, D!1)))) | (~((unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(C!2, D!1), B!3, A!4) = A!4)))))) | ((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(C!2, D!1)))),
% 16.11/10.55 inference(tautology,[status(thm)],[])).
% 16.11/10.55 tff(52,plain,
% 16.11/10.55 ((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(C!2, D!1))),
% 16.11/10.55 inference(unit_resolution,[status(thm)],[51, 50])).
% 16.11/10.55 tff(53,plain,
% 16.11/10.55 (unordered_pair(A!4, B!3) = unordered_pair(C!2, D!1)),
% 16.11/10.55 inference(and_elim,[status(thm)],[13])).
% 16.11/10.55 tff(54,plain,
% 16.11/10.55 (unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3)),
% 16.11/10.55 inference(symmetry,[status(thm)],[53])).
% 16.11/10.55 tff(55,plain,
% 16.11/10.55 ((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(C!2, D!1)))) | (~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(C!2, D!1))),
% 16.11/10.55 inference(tautology,[status(thm)],[])).
% 16.11/10.55 tff(56,plain,
% 16.11/10.55 ((~((~(unordered_pair(C!2, D!1) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(C!2, D!1)))) | in(A!4, unordered_pair(C!2, D!1))),
% 16.11/10.55 inference(unit_resolution,[status(thm)],[55, 54])).
% 16.11/10.55 tff(57,plain,
% 16.11/10.55 (in(A!4, unordered_pair(C!2, D!1))),
% 16.11/10.55 inference(unit_resolution,[status(thm)],[56, 52])).
% 16.11/10.55 tff(58,plain,
% 16.11/10.55 ((~(in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1)))) | (~in(A!4, unordered_pair(C!2, D!1))) | ((A!4 = C!2) | (A!4 = D!1))),
% 16.11/10.55 inference(tautology,[status(thm)],[])).
% 16.11/10.55 tff(59,plain,
% 16.11/10.55 (~(in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1)))),
% 16.11/10.55 inference(unit_resolution,[status(thm)],[58, 57, 17])).
% 16.11/10.55 tff(60,plain,
% 16.11/10.55 (((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1)))) <=> ((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1))))),
% 16.11/10.55 inference(rewrite,[status(thm)],[])).
% 16.11/10.55 tff(61,plain,
% 16.11/10.55 ((~((~in(A!4, unordered_pair(C!2, D!1))) <=> ((A!4 = C!2) | (A!4 = D!1)))) <=> (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1)))),
% 16.11/10.55 inference(rewrite,[status(thm)],[])).
% 16.11/10.55 tff(62,plain,
% 16.11/10.55 ((((~in(A!4, unordered_pair(C!2, D!1))) <=> ((A!4 = C!2) | (A!4 = D!1))) | $false) <=> ((~in(A!4, unordered_pair(C!2, D!1))) <=> ((A!4 = C!2) | (A!4 = D!1)))),
% 16.11/10.55 inference(rewrite,[status(thm)],[])).
% 16.11/10.55 tff(63,plain,
% 16.11/10.55 ((~$true) <=> $false),
% 16.11/10.55 inference(rewrite,[status(thm)],[])).
% 16.11/10.55 tff(64,plain,
% 16.11/10.55 (($true | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1)))) <=> $true),
% 16.11/10.55 inference(rewrite,[status(thm)],[])).
% 16.11/10.55 tff(65,plain,
% 16.11/10.55 (((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2))) <=> ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1)))),
% 16.11/10.55 inference(rewrite,[status(thm)],[])).
% 16.11/10.55 tff(66,plain,
% 16.11/10.55 ((unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1)) <=> $true),
% 16.11/10.55 inference(rewrite,[status(thm)],[])).
% 16.11/10.55 tff(67,plain,
% 16.11/10.55 (((unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2)))) <=> ($true | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1))))),
% 16.11/10.55 inference(monotonicity,[status(thm)],[66, 65])).
% 16.11/10.55 tff(68,plain,
% 16.11/10.55 (((unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2)))) <=> $true),
% 16.11/10.55 inference(transitivity,[status(thm)],[67, 64])).
% 16.11/10.55 tff(69,plain,
% 16.11/10.55 ((~((unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2))))) <=> (~$true)),
% 16.11/10.55 inference(monotonicity,[status(thm)],[68])).
% 16.11/10.55 tff(70,plain,
% 16.11/10.55 ((~((unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2))))) <=> $false),
% 16.11/10.55 inference(transitivity,[status(thm)],[69, 63])).
% 16.11/10.55 tff(71,plain,
% 16.11/10.55 ((~(in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1)))) <=> ((~in(A!4, unordered_pair(C!2, D!1))) <=> ((A!4 = C!2) | (A!4 = D!1)))),
% 16.11/10.55 inference(rewrite,[status(thm)],[])).
% 16.11/10.55 tff(72,plain,
% 16.11/10.55 (($false | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1)))) <=> (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1)))),
% 16.11/10.55 inference(rewrite,[status(thm)],[])).
% 16.11/10.55 tff(73,plain,
% 16.11/10.55 ((in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = D!1) | (A!4 = C!2))) <=> (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1)))),
% 16.11/10.55 inference(rewrite,[status(thm)],[])).
% 16.11/10.55 tff(74,plain,
% 16.11/10.55 ((~(unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1))) <=> (~$true)),
% 16.11/10.55 inference(monotonicity,[status(thm)],[66])).
% 16.11/10.55 tff(75,plain,
% 16.11/10.55 ((~(unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1))) <=> $false),
% 16.11/10.55 inference(transitivity,[status(thm)],[74, 63])).
% 16.11/10.55 tff(76,plain,
% 16.11/10.55 (((~(unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = D!1) | (A!4 = C!2)))) <=> ($false | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1))))),
% 16.11/10.55 inference(monotonicity,[status(thm)],[75, 73])).
% 16.11/10.55 tff(77,plain,
% 16.11/10.55 (((~(unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = D!1) | (A!4 = C!2)))) <=> (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1)))),
% 16.11/10.55 inference(transitivity,[status(thm)],[76, 72])).
% 16.11/10.55 tff(78,plain,
% 16.11/10.55 ((~((~(unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = D!1) | (A!4 = C!2))))) <=> (~(in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1))))),
% 16.11/10.55 inference(monotonicity,[status(thm)],[77])).
% 16.11/10.55 tff(79,plain,
% 16.11/10.55 ((~((~(unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = D!1) | (A!4 = C!2))))) <=> ((~in(A!4, unordered_pair(C!2, D!1))) <=> ((A!4 = C!2) | (A!4 = D!1)))),
% 16.11/10.55 inference(transitivity,[status(thm)],[78, 71])).
% 16.11/10.55 tff(80,plain,
% 16.11/10.55 (((~((~(unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = D!1) | (A!4 = C!2))))) | (~((unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2)))))) <=> (((~in(A!4, unordered_pair(C!2, D!1))) <=> ((A!4 = C!2) | (A!4 = D!1))) | $false)),
% 16.11/10.55 inference(monotonicity,[status(thm)],[79, 70])).
% 16.11/10.55 tff(81,plain,
% 16.11/10.55 (((~((~(unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = D!1) | (A!4 = C!2))))) | (~((unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2)))))) <=> ((~in(A!4, unordered_pair(C!2, D!1))) <=> ((A!4 = C!2) | (A!4 = D!1)))),
% 16.11/10.55 inference(transitivity,[status(thm)],[80, 62])).
% 16.11/10.55 tff(82,plain,
% 16.11/10.55 ((~((~((~(unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = D!1) | (A!4 = C!2))))) | (~((unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2))))))) <=> (~((~in(A!4, unordered_pair(C!2, D!1))) <=> ((A!4 = C!2) | (A!4 = D!1))))),
% 16.11/10.55 inference(monotonicity,[status(thm)],[81])).
% 16.11/10.55 tff(83,plain,
% 16.11/10.55 ((~((~((~(unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = D!1) | (A!4 = C!2))))) | (~((unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2))))))) <=> (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1)))),
% 16.11/10.55 inference(transitivity,[status(thm)],[82, 61])).
% 16.11/10.55 tff(84,plain,
% 16.11/10.55 (((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = D!1) | (A!4 = C!2))))) | (~((unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2)))))))) <=> ((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1))))),
% 16.11/10.55 inference(monotonicity,[status(thm)],[83])).
% 16.11/10.55 tff(85,plain,
% 16.11/10.55 (((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = D!1) | (A!4 = C!2))))) | (~((unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2)))))))) <=> ((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1))))),
% 16.11/10.56 inference(transitivity,[status(thm)],[84, 60])).
% 16.11/10.56 tff(86,plain,
% 16.11/10.56 ((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = D!1) | (A!4 = C!2))))) | (~((unordered_pair(C!2, D!1) = unordered_pair(C!2, D!1)) | ((~in(tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2), unordered_pair(C!2, D!1))) <=> ((tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = D!1) | (tptp_fun_D_0(unordered_pair(C!2, D!1), D!1, C!2) = C!2)))))))),
% 16.11/10.56 inference(quant_inst,[status(thm)],[])).
% 16.11/10.56 tff(87,plain,
% 16.11/10.56 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (in(A!4, unordered_pair(C!2, D!1)) <=> ((A!4 = C!2) | (A!4 = D!1)))),
% 16.11/10.56 inference(modus_ponens,[status(thm)],[86, 85])).
% 16.11/10.56 tff(88,plain,
% 16.11/10.56 ($false),
% 16.11/10.56 inference(unit_resolution,[status(thm)],[87, 42, 59])).
% 16.11/10.56 % SZS output end Proof
%------------------------------------------------------------------------------