%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET962+1 : TPTP v9.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:26:43 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET962+1 : TPTP v9.0.0. Bugfixed v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:52:25 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(in_type, type, (
% 0.19/0.38 in: ( $i * $i ) > $o)).
% 0.19/0.38 tff(cartesian_product2_type, type, (
% 0.19/0.38 cartesian_product2: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_A_3_type, type, (
% 0.19/0.38 tptp_fun_A_3: $i)).
% 0.19/0.38 tff(ordered_pair_type, type, (
% 0.19/0.38 ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_C_4_type, type, (
% 0.19/0.38 tptp_fun_C_4: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_B_2_type, type, (
% 0.19/0.38 tptp_fun_B_2: $i)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : ((~(cartesian_product2(A, A) = cartesian_product2(B, B))) | (A = B))) <=> (~![A: $i, B: $i] : ((~(cartesian_product2(A, A) = cartesian_product2(B, B))) | (A = B)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : ((cartesian_product2(A, A) = cartesian_product2(B, B)) => (A = B))) <=> (~![A: $i, B: $i] : ((~(cartesian_product2(A, A) = cartesian_product2(B, B))) | (A = B)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(3,axiom,(~![A: $i, B: $i] : ((cartesian_product2(A, A) = cartesian_product2(B, B)) => (A = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t115_zfmisc_1')).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (~![A: $i, B: $i] : ((~(cartesian_product2(A, A) = cartesian_product2(B, B))) | (A = B))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (~![A: $i, B: $i] : ((~(cartesian_product2(A, A) = cartesian_product2(B, B))) | (A = B))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (~![A: $i, B: $i] : ((~(cartesian_product2(A, A) = cartesian_product2(B, B))) | (A = B))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (~![A: $i, B: $i] : ((~(cartesian_product2(A, A) = cartesian_product2(B, B))) | (A = B))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.38 tff(8,plain,(
% 0.19/0.38 ~((~(cartesian_product2(A!3, A!3) = cartesian_product2(B!2, B!2))) | (A!3 = B!2))),
% 0.19/0.38 inference(skolemize,[status(sab)],[7])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (cartesian_product2(A!3, A!3) = cartesian_product2(B!2, B!2)),
% 0.19/0.38 inference(or_elim,[status(thm)],[8])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (cartesian_product2(B!2, B!2) = cartesian_product2(A!3, A!3)),
% 0.19/0.38 inference(symmetry,[status(thm)],[9])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2)) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (^[A: $i, B: $i, C: $i, D: $i] : refl((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (^[A: $i, B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((in(A, C) & in(B, D)) <=> (~((~in(A, C)) | (~in(B, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))), rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))), rewrite((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(17,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l55_zfmisc_1')).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.39 tff(19,plain,(
% 0.19/0.39 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[18])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 ((~(~(in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))))) <=> (in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 ((~(in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2)))) <=> (~(in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (((~in(tptp_fun_C_4(B!2, A!3), B!2)) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))) <=> (~(in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (((~in(tptp_fun_C_4(B!2, A!3), B!2)) | (~in(tptp_fun_C_4(B!2, A!3), B!2))) <=> (~in(tptp_fun_C_4(B!2, A!3), B!2))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 ((((~in(tptp_fun_C_4(B!2, A!3), B!2)) | (~in(tptp_fun_C_4(B!2, A!3), B!2))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))) <=> ((~in(tptp_fun_C_4(B!2, A!3), B!2)) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 ((((~in(tptp_fun_C_4(B!2, A!3), B!2)) | (~in(tptp_fun_C_4(B!2, A!3), B!2))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))) <=> (~(in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[27, 25])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 ((((~in(tptp_fun_C_4(B!2, A!3), B!2)) | (~in(tptp_fun_C_4(B!2, A!3), B!2))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))) <=> (~(in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[28, 24])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 ((~(((~in(tptp_fun_C_4(B!2, A!3), B!2)) | (~in(tptp_fun_C_4(B!2, A!3), B!2))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2)))) <=> (~(~(in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[29])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 ((~(((~in(tptp_fun_C_4(B!2, A!3), B!2)) | (~in(tptp_fun_C_4(B!2, A!3), B!2))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2)))) <=> (in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[30, 23])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_4(B!2, A!3), B!2)) | (~in(tptp_fun_C_4(B!2, A!3), B!2))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_4(B!2, A!3), B!2)) | (~in(tptp_fun_C_4(B!2, A!3), B!2))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[32, 22])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_4(B!2, A!3), B!2)) | (~in(tptp_fun_C_4(B!2, A!3), B!2))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[35, 21])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 ((~in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))) <=> (~in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[11])).
% 0.19/0.39 tff(38,assumption,(~in(tptp_fun_C_4(B!2, A!3), B!2)), introduced(assumption)).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~(in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2)))) | in(tptp_fun_C_4(B!2, A!3), B!2) | (~in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (~in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[39, 38, 36])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (~in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 ((~(~(in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))))) <=> (in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((~(in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3)))) <=> (~(in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (((~in(tptp_fun_C_4(B!2, A!3), A!3)) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))) <=> (~(in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (((~in(tptp_fun_C_4(B!2, A!3), A!3)) | (~in(tptp_fun_C_4(B!2, A!3), A!3))) <=> (~in(tptp_fun_C_4(B!2, A!3), A!3))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ((((~in(tptp_fun_C_4(B!2, A!3), A!3)) | (~in(tptp_fun_C_4(B!2, A!3), A!3))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))) <=> ((~in(tptp_fun_C_4(B!2, A!3), A!3)) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 ((((~in(tptp_fun_C_4(B!2, A!3), A!3)) | (~in(tptp_fun_C_4(B!2, A!3), A!3))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))) <=> (~(in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ((((~in(tptp_fun_C_4(B!2, A!3), A!3)) | (~in(tptp_fun_C_4(B!2, A!3), A!3))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))) <=> (~(in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[48, 44])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ((~(((~in(tptp_fun_C_4(B!2, A!3), A!3)) | (~in(tptp_fun_C_4(B!2, A!3), A!3))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3)))) <=> (~(~(in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 ((~(((~in(tptp_fun_C_4(B!2, A!3), A!3)) | (~in(tptp_fun_C_4(B!2, A!3), A!3))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3)))) <=> (in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[50, 43])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_4(B!2, A!3), A!3)) | (~in(tptp_fun_C_4(B!2, A!3), A!3))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_4(B!2, A!3), A!3)) | (~in(tptp_fun_C_4(B!2, A!3), A!3))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[52, 42])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_4(B!2, A!3), A!3)) | (~in(tptp_fun_C_4(B!2, A!3), A!3))) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[55, 21])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~![C: $i] : (in(C, A) <=> in(C, B))) | (A = B)) <=> ![A: $i, B: $i] : ((~![C: $i] : (in(C, A) <=> in(C, B))) | (A = B))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (^[A: $i, B: $i] : rewrite((![C: $i] : (in(C, A) <=> in(C, B)) => (A = B)) <=> ((~![C: $i] : (in(C, A) <=> in(C, B))) | (A = B)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![A: $i, B: $i] : (![C: $i] : (in(C, A) <=> in(C, B)) => (A = B)) <=> ![A: $i, B: $i] : ((~![C: $i] : (in(C, A) <=> in(C, B))) | (A = B))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.40 tff(60,axiom,(![A: $i, B: $i] : (![C: $i] : (in(C, A) <=> in(C, B)) => (A = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_tarski')).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~![C: $i] : (in(C, A) <=> in(C, B))) | (A = B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~![C: $i] : (in(C, A) <=> in(C, B))) | (A = B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.40 tff(63,plain,(
% 0.19/0.40 ![A: $i, B: $i] : ((~(in(tptp_fun_C_4(B, A), A) <=> in(tptp_fun_C_4(B, A), B))) | (A = B))),
% 0.19/0.40 inference(skolemize,[status(sab)],[62])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (~(A!3 = B!2)),
% 0.19/0.40 inference(or_elim,[status(thm)],[8])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~(in(tptp_fun_C_4(B, A), A) <=> in(tptp_fun_C_4(B, A), B))) | (A = B))) | ((~(in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(tptp_fun_C_4(B!2, A!3), B!2))) | (A!3 = B!2))) <=> ((~![A: $i, B: $i] : ((~(in(tptp_fun_C_4(B, A), A) <=> in(tptp_fun_C_4(B, A), B))) | (A = B))) | (~(in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(tptp_fun_C_4(B!2, A!3), B!2))) | (A!3 = B!2))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~(in(tptp_fun_C_4(B, A), A) <=> in(tptp_fun_C_4(B, A), B))) | (A = B))) | ((~(in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(tptp_fun_C_4(B!2, A!3), B!2))) | (A!3 = B!2))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~(in(tptp_fun_C_4(B, A), A) <=> in(tptp_fun_C_4(B, A), B))) | (A = B))) | (~(in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(tptp_fun_C_4(B!2, A!3), B!2))) | (A!3 = B!2)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (~(in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(tptp_fun_C_4(B!2, A!3), B!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[67, 64, 63])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 ((in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(tptp_fun_C_4(B!2, A!3), B!2)) | in(tptp_fun_C_4(B!2, A!3), A!3) | in(tptp_fun_C_4(B!2, A!3), B!2)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (in(tptp_fun_C_4(B!2, A!3), A!3) | in(tptp_fun_C_4(B!2, A!3), B!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (in(tptp_fun_C_4(B!2, A!3), A!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[70, 38])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((~(in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3)))) | (~in(tptp_fun_C_4(B!2, A!3), A!3)) | in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[72, 71, 56])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[73, 41])).
% 0.19/0.40 tff(75,plain,(in(tptp_fun_C_4(B!2, A!3), B!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~(in(tptp_fun_C_4(B!2, A!3), B!2) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2)))) | (~in(tptp_fun_C_4(B!2, A!3), B!2)) | in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(B!2, B!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 75, 36])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[77, 11])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 ((in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(tptp_fun_C_4(B!2, A!3), B!2)) | (~in(tptp_fun_C_4(B!2, A!3), A!3)) | (~in(tptp_fun_C_4(B!2, A!3), B!2))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 ((~in(tptp_fun_C_4(B!2, A!3), A!3)) | (~in(tptp_fun_C_4(B!2, A!3), B!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[79, 68])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (~in(tptp_fun_C_4(B!2, A!3), A!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[80, 75])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 ((~(in(tptp_fun_C_4(B!2, A!3), A!3) <=> in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3)))) | in(tptp_fun_C_4(B!2, A!3), A!3) | (~in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (~in(ordered_pair(tptp_fun_C_4(B!2, A!3), tptp_fun_C_4(B!2, A!3)), cartesian_product2(A!3, A!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[82, 81, 56])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[83, 78])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------