TSTP Solution File: SET962+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 05:08:45 EDT 2022
% Result : Theorem 0.16s 0.38s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.10/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.32 % Computer : n007.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sat Sep 3 08:28:49 EDT 2022
% 0.16/0.32 % CPUTime :
% 0.16/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.32 Usage: tptp [options] [-file:]file
% 0.16/0.32 -h, -? prints this message.
% 0.16/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.32 -m, -model generate model.
% 0.16/0.32 -p, -proof generate proof.
% 0.16/0.32 -c, -core generate unsat core of named formulas.
% 0.16/0.32 -st, -statistics display statistics.
% 0.16/0.32 -t:timeout set timeout (in second).
% 0.16/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.32 -<param>:<value> configuration parameter and value.
% 0.16/0.32 -o:<output-file> file to place output in.
% 0.16/0.38 % SZS status Theorem
% 0.16/0.38 % SZS output start Proof
% 0.16/0.38 tff(in_type, type, (
% 0.16/0.38 in: ( $i * $i ) > $o)).
% 0.16/0.38 tff(cartesian_product2_type, type, (
% 0.16/0.38 cartesian_product2: ( $i * $i ) > $i)).
% 0.16/0.38 tff(tptp_fun_B_2_type, type, (
% 0.16/0.38 tptp_fun_B_2: $i)).
% 0.16/0.38 tff(ordered_pair_type, type, (
% 0.16/0.38 ordered_pair: ( $i * $i ) > $i)).
% 0.16/0.38 tff(tptp_fun_C_4_type, type, (
% 0.16/0.38 tptp_fun_C_4: ( $i * $i ) > $i)).
% 0.16/0.38 tff(tptp_fun_A_3_type, type, (
% 0.16/0.38 tptp_fun_A_3: $i)).
% 0.16/0.38 tff(1,plain,
% 0.16/0.38 ((~![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)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(2,plain,
% 0.16/0.38 ((~![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)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(3,axiom,(~![A: $i, B: $i] : ((cartesian_product2(A, A) = cartesian_product2(B, B)) => (A = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t115_zfmisc_1')).
% 0.16/0.38 tff(4,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~(cartesian_product2(A, A) = cartesian_product2(B, B))) | (A = B))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.16/0.38 tff(5,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~(cartesian_product2(A, A) = cartesian_product2(B, B))) | (A = B))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.16/0.38 tff(6,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~(cartesian_product2(A, A) = cartesian_product2(B, B))) | (A = B))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.16/0.38 tff(7,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~(cartesian_product2(A, A) = cartesian_product2(B, B))) | (A = B))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.16/0.38 tff(8,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~(cartesian_product2(A, A) = cartesian_product2(B, B))) | (A = B))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.16/0.38 tff(9,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~(cartesian_product2(A, A) = cartesian_product2(B, B))) | (A = B))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.16/0.38 tff(10,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~(cartesian_product2(A, A) = cartesian_product2(B, B))) | (A = B))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.16/0.38 tff(11,plain,(
% 0.16/0.38 ~((~(cartesian_product2(A!3, A!3) = cartesian_product2(B!2, B!2))) | (A!3 = B!2))),
% 0.16/0.38 inference(skolemize,[status(sab)],[10])).
% 0.16/0.38 tff(12,plain,
% 0.16/0.38 (cartesian_product2(A!3, A!3) = cartesian_product2(B!2, B!2)),
% 0.16/0.38 inference(or_elim,[status(thm)],[11])).
% 0.16/0.38 tff(13,plain,
% 0.16/0.38 (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) <=> in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[12])).
% 0.16/0.38 tff(14,plain,
% 0.16/0.38 ((~in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3))) <=> (~in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[13])).
% 0.16/0.38 tff(15,assumption,(~in(tptp_fun_C_4(A!3, B!2), A!3)), introduced(assumption)).
% 0.16/0.38 tff(16,plain,
% 0.16/0.38 (^[A: $i, B: $i, C: $i, D: $i] : refl((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))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(17,plain,
% 0.16/0.38 (![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(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.16/0.38 tff(18,plain,
% 0.16/0.38 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((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))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(19,plain,
% 0.16/0.38 (![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(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.16/0.38 tff(20,plain,
% 0.16/0.38 (![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(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(21,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/sandbox2/benchmark/theBenchmark.p','l55_zfmisc_1')).
% 0.16/0.38 tff(22,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.16/0.38 tff(23,plain,(
% 0.16/0.38 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.16/0.38 inference(skolemize,[status(sab)],[22])).
% 0.16/0.38 tff(24,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.16/0.38 tff(25,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.16/0.38 tff(26,plain,
% 0.16/0.38 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) <=> in(tptp_fun_C_4(A!3, B!2), A!3))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) <=> in(tptp_fun_C_4(A!3, B!2), A!3)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(27,plain,
% 0.16/0.38 ((in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) <=> (~((~in(tptp_fun_C_4(A!3, B!2), A!3)) | (~in(tptp_fun_C_4(A!3, B!2), A!3))))) <=> (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) <=> in(tptp_fun_C_4(A!3, B!2), A!3))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(28,plain,
% 0.16/0.38 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) <=> (~((~in(tptp_fun_C_4(A!3, B!2), A!3)) | (~in(tptp_fun_C_4(A!3, B!2), A!3)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) <=> in(tptp_fun_C_4(A!3, B!2), A!3)))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[27])).
% 0.16/0.38 tff(29,plain,
% 0.16/0.38 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) <=> (~((~in(tptp_fun_C_4(A!3, B!2), A!3)) | (~in(tptp_fun_C_4(A!3, B!2), A!3)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) <=> in(tptp_fun_C_4(A!3, B!2), A!3)))),
% 0.16/0.38 inference(transitivity,[status(thm)],[28, 26])).
% 0.16/0.38 tff(30,plain,
% 0.16/0.38 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) <=> (~((~in(tptp_fun_C_4(A!3, B!2), A!3)) | (~in(tptp_fun_C_4(A!3, B!2), A!3)))))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(31,plain,
% 0.16/0.38 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) <=> in(tptp_fun_C_4(A!3, B!2), A!3))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.16/0.39 tff(32,plain,
% 0.16/0.39 (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) <=> in(tptp_fun_C_4(A!3, B!2), A!3)),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.16/0.39 tff(33,plain,
% 0.16/0.39 ((~(in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) <=> in(tptp_fun_C_4(A!3, B!2), A!3))) | (~in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3))) | in(tptp_fun_C_4(A!3, B!2), A!3)),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(34,plain,
% 0.16/0.39 ((~in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3))) | in(tptp_fun_C_4(A!3, B!2), A!3)),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.16/0.39 tff(35,plain,
% 0.16/0.39 (~in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[34, 15])).
% 0.16/0.39 tff(36,plain,
% 0.16/0.39 (~in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[35, 14])).
% 0.16/0.39 tff(37,plain,
% 0.16/0.39 ((B!2 = A!3) <=> (A!3 = B!2)),
% 0.16/0.39 inference(commutativity,[status(thm)],[])).
% 0.16/0.39 tff(38,plain,
% 0.16/0.39 ((A!3 = B!2) <=> (B!2 = A!3)),
% 0.16/0.39 inference(symmetry,[status(thm)],[37])).
% 0.16/0.39 tff(39,plain,
% 0.16/0.39 ((~(A!3 = B!2)) <=> (~(B!2 = A!3))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[38])).
% 0.16/0.39 tff(40,plain,
% 0.16/0.39 (~(A!3 = B!2)),
% 0.16/0.39 inference(or_elim,[status(thm)],[11])).
% 0.16/0.39 tff(41,plain,
% 0.16/0.39 (~(B!2 = A!3)),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.16/0.39 tff(42,plain,
% 0.16/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite((~(in(tptp_fun_C_4(B, A), A) <=> in(tptp_fun_C_4(B, A), B))) <=> ((~in(tptp_fun_C_4(B, A), A)) <=> in(tptp_fun_C_4(B, A), B))), (((~(in(tptp_fun_C_4(B, A), A) <=> in(tptp_fun_C_4(B, A), B))) | (A = B)) <=> (((~in(tptp_fun_C_4(B, A), A)) <=> in(tptp_fun_C_4(B, A), B)) | (A = B)))), rewrite((((~in(tptp_fun_C_4(B, A), A)) <=> in(tptp_fun_C_4(B, A), B)) | (A = B)) <=> ((A = B) | ((~in(tptp_fun_C_4(B, A), A)) <=> in(tptp_fun_C_4(B, A), B)))), (((~(in(tptp_fun_C_4(B, A), A) <=> in(tptp_fun_C_4(B, A), B))) | (A = B)) <=> ((A = B) | ((~in(tptp_fun_C_4(B, A), A)) <=> in(tptp_fun_C_4(B, A), B)))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(43,plain,
% 0.16/0.39 (![A: $i, B: $i] : ((~(in(tptp_fun_C_4(B, A), A) <=> in(tptp_fun_C_4(B, A), B))) | (A = B)) <=> ![A: $i, B: $i] : ((A = B) | ((~in(tptp_fun_C_4(B, A), A)) <=> in(tptp_fun_C_4(B, A), B)))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.16/0.39 tff(44,plain,
% 0.16/0.39 (![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))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(45,plain,
% 0.16/0.39 (^[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)))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(46,plain,
% 0.16/0.39 (![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))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.16/0.39 tff(47,axiom,(![A: $i, B: $i] : (![C: $i] : (in(C, A) <=> in(C, B)) => (A = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_tarski')).
% 0.16/0.39 tff(48,plain,
% 0.16/0.39 (![A: $i, B: $i] : ((~![C: $i] : (in(C, A) <=> in(C, B))) | (A = B))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.16/0.39 tff(49,plain,
% 0.16/0.39 (![A: $i, B: $i] : ((~![C: $i] : (in(C, A) <=> in(C, B))) | (A = B))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.16/0.39 tff(50,plain,(
% 0.16/0.39 ![A: $i, B: $i] : ((~(in(tptp_fun_C_4(B, A), A) <=> in(tptp_fun_C_4(B, A), B))) | (A = B))),
% 0.16/0.39 inference(skolemize,[status(sab)],[49])).
% 0.16/0.39 tff(51,plain,
% 0.16/0.39 (![A: $i, B: $i] : ((A = B) | ((~in(tptp_fun_C_4(B, A), A)) <=> in(tptp_fun_C_4(B, A), B)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.16/0.39 tff(52,plain,
% 0.16/0.39 (((~![A: $i, B: $i] : ((A = B) | ((~in(tptp_fun_C_4(B, A), A)) <=> in(tptp_fun_C_4(B, A), B)))) | ((B!2 = A!3) | ((~in(tptp_fun_C_4(A!3, B!2), B!2)) <=> in(tptp_fun_C_4(A!3, B!2), A!3)))) <=> ((~![A: $i, B: $i] : ((A = B) | ((~in(tptp_fun_C_4(B, A), A)) <=> in(tptp_fun_C_4(B, A), B)))) | (B!2 = A!3) | ((~in(tptp_fun_C_4(A!3, B!2), B!2)) <=> in(tptp_fun_C_4(A!3, B!2), A!3)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(53,plain,
% 0.16/0.39 ((~![A: $i, B: $i] : ((A = B) | ((~in(tptp_fun_C_4(B, A), A)) <=> in(tptp_fun_C_4(B, A), B)))) | ((B!2 = A!3) | ((~in(tptp_fun_C_4(A!3, B!2), B!2)) <=> in(tptp_fun_C_4(A!3, B!2), A!3)))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(54,plain,
% 0.16/0.39 ((~![A: $i, B: $i] : ((A = B) | ((~in(tptp_fun_C_4(B, A), A)) <=> in(tptp_fun_C_4(B, A), B)))) | (B!2 = A!3) | ((~in(tptp_fun_C_4(A!3, B!2), B!2)) <=> in(tptp_fun_C_4(A!3, B!2), A!3))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.16/0.39 tff(55,plain,
% 0.16/0.39 ((B!2 = A!3) | ((~in(tptp_fun_C_4(A!3, B!2), B!2)) <=> in(tptp_fun_C_4(A!3, B!2), A!3))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.16/0.39 tff(56,plain,
% 0.16/0.39 ((~in(tptp_fun_C_4(A!3, B!2), B!2)) <=> in(tptp_fun_C_4(A!3, B!2), A!3)),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[55, 41])).
% 0.16/0.39 tff(57,plain,
% 0.16/0.39 ((~((~in(tptp_fun_C_4(A!3, B!2), B!2)) <=> in(tptp_fun_C_4(A!3, B!2), A!3))) | in(tptp_fun_C_4(A!3, B!2), B!2) | in(tptp_fun_C_4(A!3, B!2), A!3)),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(58,plain,
% 0.16/0.39 (in(tptp_fun_C_4(A!3, B!2), B!2) | in(tptp_fun_C_4(A!3, B!2), A!3)),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.16/0.39 tff(59,plain,
% 0.16/0.39 (in(tptp_fun_C_4(A!3, B!2), B!2)),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[58, 15])).
% 0.16/0.39 tff(60,plain,
% 0.16/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) <=> in(tptp_fun_C_4(A!3, B!2), B!2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) <=> in(tptp_fun_C_4(A!3, B!2), B!2)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(61,plain,
% 0.16/0.39 ((in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) <=> (~((~in(tptp_fun_C_4(A!3, B!2), B!2)) | (~in(tptp_fun_C_4(A!3, B!2), B!2))))) <=> (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) <=> in(tptp_fun_C_4(A!3, B!2), B!2))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(62,plain,
% 0.16/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) <=> (~((~in(tptp_fun_C_4(A!3, B!2), B!2)) | (~in(tptp_fun_C_4(A!3, B!2), B!2)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) <=> in(tptp_fun_C_4(A!3, B!2), B!2)))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[61])).
% 0.16/0.39 tff(63,plain,
% 0.16/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) <=> (~((~in(tptp_fun_C_4(A!3, B!2), B!2)) | (~in(tptp_fun_C_4(A!3, B!2), B!2)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) <=> in(tptp_fun_C_4(A!3, B!2), B!2)))),
% 0.16/0.39 inference(transitivity,[status(thm)],[62, 60])).
% 0.16/0.39 tff(64,plain,
% 0.16/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) <=> (~((~in(tptp_fun_C_4(A!3, B!2), B!2)) | (~in(tptp_fun_C_4(A!3, B!2), B!2)))))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(65,plain,
% 0.16/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) <=> in(tptp_fun_C_4(A!3, B!2), B!2))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.16/0.39 tff(66,plain,
% 0.16/0.39 (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) <=> in(tptp_fun_C_4(A!3, B!2), B!2)),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[65, 25])).
% 0.16/0.39 tff(67,plain,
% 0.16/0.39 ((~(in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) <=> in(tptp_fun_C_4(A!3, B!2), B!2))) | in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) | (~in(tptp_fun_C_4(A!3, B!2), B!2))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(68,plain,
% 0.16/0.39 (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) | (~in(tptp_fun_C_4(A!3, B!2), B!2))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.16/0.39 tff(69,plain,
% 0.16/0.39 (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[68, 59])).
% 0.16/0.39 tff(70,plain,
% 0.16/0.39 ($false),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[69, 36])).
% 0.16/0.39 tff(71,plain,(in(tptp_fun_C_4(A!3, B!2), A!3)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.39 tff(72,plain,
% 0.16/0.39 ((~(in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) <=> in(tptp_fun_C_4(A!3, B!2), A!3))) | in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) | (~in(tptp_fun_C_4(A!3, B!2), A!3))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(73,plain,
% 0.16/0.39 (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3)) | (~in(tptp_fun_C_4(A!3, B!2), A!3))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[72, 32])).
% 0.16/0.39 tff(74,plain,
% 0.16/0.39 (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(A!3, A!3))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[73, 71])).
% 0.16/0.39 tff(75,plain,
% 0.16/0.39 (in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[74, 13])).
% 0.16/0.39 tff(76,plain,
% 0.16/0.39 ((~((~in(tptp_fun_C_4(A!3, B!2), B!2)) <=> in(tptp_fun_C_4(A!3, B!2), A!3))) | (~in(tptp_fun_C_4(A!3, B!2), B!2)) | (~in(tptp_fun_C_4(A!3, B!2), A!3))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(77,plain,
% 0.16/0.39 ((~in(tptp_fun_C_4(A!3, B!2), B!2)) | (~in(tptp_fun_C_4(A!3, B!2), A!3))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[76, 56])).
% 0.16/0.39 tff(78,plain,
% 0.16/0.39 (~in(tptp_fun_C_4(A!3, B!2), B!2)),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[77, 71])).
% 0.16/0.39 tff(79,plain,
% 0.16/0.39 ((~(in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2)) <=> in(tptp_fun_C_4(A!3, B!2), B!2))) | (~in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2))) | in(tptp_fun_C_4(A!3, B!2), B!2)),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(80,plain,
% 0.16/0.39 ((~in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2))) | in(tptp_fun_C_4(A!3, B!2), B!2)),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[79, 66])).
% 0.16/0.39 tff(81,plain,
% 0.16/0.39 (~in(ordered_pair(tptp_fun_C_4(A!3, B!2), tptp_fun_C_4(A!3, B!2)), cartesian_product2(B!2, B!2))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[80, 78])).
% 0.16/0.39 tff(82,plain,
% 0.16/0.39 ($false),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[81, 75])).
% 0.16/0.39 % SZS output end Proof
%------------------------------------------------------------------------------