TSTP Solution File: SEU157+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU157+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 07:27:51 EDT 2022
% Result : Theorem 63.20s 39.10s
% Output : Proof 63.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU157+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 : Sat Sep 3 09:43:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 63.20/39.10 % SZS status Theorem
% 63.20/39.10 % SZS output start Proof
% 63.20/39.10 tff(ordered_pair_type, type, (
% 63.20/39.10 ordered_pair: ( $i * $i ) > $i)).
% 63.20/39.10 tff(tptp_fun_F_0_type, type, (
% 63.20/39.10 tptp_fun_F_0: ( $i * $i * $i ) > $i)).
% 63.20/39.10 tff(tptp_fun_C_6_type, type, (
% 63.20/39.10 tptp_fun_C_6: $i)).
% 63.20/39.10 tff(tptp_fun_D_5_type, type, (
% 63.20/39.10 tptp_fun_D_5: $i)).
% 63.20/39.10 tff(unordered_pair_type, type, (
% 63.20/39.10 unordered_pair: ( $i * $i ) > $i)).
% 63.20/39.10 tff(singleton_type, type, (
% 63.20/39.10 singleton: $i > $i)).
% 63.20/39.10 tff(tptp_fun_A_8_type, type, (
% 63.20/39.10 tptp_fun_A_8: $i)).
% 63.20/39.10 tff(tptp_fun_B_7_type, type, (
% 63.20/39.10 tptp_fun_B_7: $i)).
% 63.20/39.10 tff(tptp_fun_E_1_type, type, (
% 63.20/39.10 tptp_fun_E_1: ( $i * $i * $i ) > $i)).
% 63.20/39.10 tff(in_type, type, (
% 63.20/39.10 in: ( $i * $i ) > $o)).
% 63.20/39.10 tff(cartesian_product2_type, type, (
% 63.20/39.10 cartesian_product2: ( $i * $i ) > $i)).
% 63.20/39.10 tff(tptp_fun_D_2_type, type, (
% 63.20/39.10 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 63.20/39.10 tff(tptp_fun_F_3_type, type, (
% 63.20/39.10 tptp_fun_F_3: ( $i * $i * $i ) > $i)).
% 63.20/39.10 tff(tptp_fun_E_4_type, type, (
% 63.20/39.10 tptp_fun_E_4: ( $i * $i * $i ) > $i)).
% 63.20/39.10 tff(1,plain,
% 63.20/39.10 (^[A: $i, B: $i] : refl((ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))) <=> (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))))),
% 63.20/39.10 inference(bind,[status(th)],[])).
% 63.20/39.10 tff(2,plain,
% 63.20/39.10 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))) <=> ![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 63.20/39.10 inference(quant_intro,[status(thm)],[1])).
% 63.20/39.10 tff(3,plain,
% 63.20/39.10 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))) <=> ![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 63.20/39.10 inference(rewrite,[status(thm)],[])).
% 63.20/39.10 tff(4,axiom,(![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d5_tarski')).
% 63.20/39.10 tff(5,plain,
% 63.20/39.10 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 63.20/39.10 inference(modus_ponens,[status(thm)],[4, 3])).
% 63.20/39.10 tff(6,plain,(
% 63.20/39.10 ![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 63.20/39.10 inference(skolemize,[status(sab)],[5])).
% 63.20/39.10 tff(7,plain,
% 63.20/39.10 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 63.20/39.10 inference(modus_ponens,[status(thm)],[6, 2])).
% 63.20/39.10 tff(8,plain,
% 63.20/39.10 ((~![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))) | (ordered_pair(A!8, B!7) = unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)))),
% 63.20/39.10 inference(quant_inst,[status(thm)],[])).
% 63.20/39.10 tff(9,plain,
% 63.20/39.10 (ordered_pair(A!8, B!7) = unordered_pair(unordered_pair(A!8, B!7), singleton(A!8))),
% 63.20/39.10 inference(unit_resolution,[status(thm)],[8, 7])).
% 63.20/39.10 tff(10,plain,
% 63.20/39.10 ((ordered_pair(A!8, B!7) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))) <=> (unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))),
% 63.20/39.10 inference(monotonicity,[status(thm)],[9])).
% 63.20/39.10 tff(11,plain,
% 63.20/39.10 ((unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))) <=> (ordered_pair(A!8, B!7) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))),
% 63.20/39.10 inference(symmetry,[status(thm)],[10])).
% 63.20/39.10 tff(12,assumption,((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(unordered_pair(B!7, A!8), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, unordered_pair(B!7, A!8))))))), introduced(assumption)).
% 63.20/39.10 tff(13,plain,
% 63.20/39.10 (^[A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : rewrite((~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) <=> (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 63.20/39.10 inference(bind,[status(th)],[])).
% 63.20/39.10 tff(14,plain,
% 63.20/39.10 (![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) <=> ![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))),
% 63.20/39.10 inference(quant_intro,[status(thm)],[13])).
% 63.20/39.10 tff(15,plain,
% 63.20/39.10 (^[A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : refl((~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) <=> (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))))),
% 63.20/39.10 inference(bind,[status(th)],[])).
% 63.20/39.10 tff(16,plain,
% 63.20/39.10 (![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) <=> ![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 63.20/39.10 inference(quant_intro,[status(thm)],[15])).
% 63.20/39.10 tff(17,plain,
% 63.20/39.10 (![A: $i, B: $i, C: $i] : ![E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) <=> ![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 63.20/39.10 inference(pull_quant,[status(thm)],[])).
% 63.20/39.10 tff(18,plain,
% 63.20/39.10 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant((in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))) <=> ![E: $i, F: $i] : (in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))), ((~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))) <=> (~![E: $i, F: $i] : (in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))), pull_quant((~![E: $i, F: $i] : (in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))) <=> ?[E: $i, F: $i] : (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))), ((~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))) <=> ?[E: $i, F: $i] : (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))), (((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))) <=> ((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | ?[E: $i, F: $i] : (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))), pull_quant(((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | ?[E: $i, F: $i] : (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))) <=> ?[E: $i, F: $i] : ((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))), (((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))) <=> ?[E: $i, F: $i] : ((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))), ((~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))) <=> (~?[E: $i, F: $i] : ((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))), pull_quant((~?[E: $i, F: $i] : ((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))) <=> ![E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))), ((~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))) <=> ![E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))))), (![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))) <=> ![D: $i] : ![E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))), pull_quant(![D: $i] : ![E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))) <=> ![D: $i, E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))), (![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))) <=> ![D: $i, E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))), (((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))) <=> ((~(C = cartesian_product2(A, B))) | ![D: $i, E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))))), pull_quant(((~(C = cartesian_product2(A, B))) | ![D: $i, E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))) <=> ![D: $i, E: $i, F: $i] : ((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))), (((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))) <=> ![D: $i, E: $i, F: $i] : ((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))))), ((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) <=> (~![D: $i, E: $i, F: $i] : ((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))))), pull_quant((~![D: $i, E: $i, F: $i] : ((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) <=> ?[D: $i, E: $i, F: $i] : (~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))))), ((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) <=> ?[D: $i, E: $i, F: $i] : (~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))) <=> ![E: $i, F: $i] : ((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))), ((~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))) <=> (~![E: $i, F: $i] : ((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))), pull_quant((~![E: $i, F: $i] : ((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))) <=> ?[E: $i, F: $i] : (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))), ((~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))) <=> ?[E: $i, F: $i] : (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))), (((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))) <=> ((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | ?[E: $i, F: $i] : (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))), pull_quant(((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | ?[E: $i, F: $i] : (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))) <=> ?[E: $i, F: $i] : ((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))), (((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))) <=> ?[E: $i, F: $i] : ((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))), ((~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))) <=> (~?[E: $i, F: $i] : ((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))), pull_quant((~?[E: $i, F: $i] : ((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))) <=> ![E: $i, F: $i] : (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))), ((~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))) <=> ![E: $i, F: $i] : (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))), (((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))) <=> ((C = cartesian_product2(A, B)) | ![E: $i, F: $i] : (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))))), pull_quant(((C = cartesian_product2(A, B)) | ![E: $i, F: $i] : (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))) <=> ![E: $i, F: $i] : ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))), (((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))) <=> ![E: $i, F: $i] : ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))))), ((~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))) <=> (~![E: $i, F: $i] : ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))))), pull_quant((~![E: $i, F: $i] : ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))) <=> ?[E: $i, F: $i] : (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))))), ((~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))) <=> ?[E: $i, F: $i] : (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))))), (((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))))) <=> (?[D: $i, E: $i, F: $i] : (~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | ?[E: $i, F: $i] : (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))))))), pull_quant((?[D: $i, E: $i, F: $i] : (~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | ?[E: $i, F: $i] : (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))))) <=> ?[E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : ((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))), (((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))))) <=> ?[E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : ((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11))))))))))))), ((~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))))) <=> (~?[E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : ((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))))), pull_quant((~?[E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : ((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) <=> ![E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11))))))))))))), ((~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))))) <=> ![E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11))))))))))))))),
% 63.20/39.10 inference(bind,[status(th)],[])).
% 63.20/39.10 tff(19,plain,
% 63.20/39.10 (![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))))) <=> ![A: $i, B: $i, C: $i] : ![E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 63.20/39.11 inference(quant_intro,[status(thm)],[18])).
% 63.20/39.11 tff(20,plain,
% 63.20/39.11 (![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))))) <=> ![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 63.20/39.11 inference(transitivity,[status(thm)],[19, 17])).
% 63.20/39.11 tff(21,plain,
% 63.20/39.11 (![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))))) <=> ![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 63.20/39.11 inference(transitivity,[status(thm)],[20, 16])).
% 63.20/39.11 tff(22,plain,
% 63.20/39.11 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))))) <=> (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))))))),
% 63.20/39.11 inference(bind,[status(th)],[])).
% 63.20/39.11 tff(23,plain,
% 63.20/39.11 (![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))))))),
% 63.20/39.11 inference(quant_intro,[status(thm)],[22])).
% 63.20/39.11 tff(24,plain,
% 63.20/39.11 (![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))))) <=> ![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 63.20/39.11 inference(transitivity,[status(thm)],[23, 21])).
% 63.20/39.11 tff(25,plain,
% 63.20/39.11 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = cartesian_product2(A, B))) | ![D: $i] : (((~in(D, C)) | (in(tptp_fun_E_1(D, B, A), A) & in(tptp_fun_F_0(D, B, A), B) & (D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A))))) & (in(D, C) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (D = ordered_pair(E, F))))))) <=> ((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_E_4(C, B, A), A) & in(tptp_fun_F_3(C, B, A), B) & (tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))) <=> (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))))), ((in(tptp_fun_D_2(C, B, A), C) | (in(tptp_fun_E_4(C, B, A), A) & in(tptp_fun_F_3(C, B, A), B) & (tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))) <=> (in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))))))), rewrite((in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))))) <=> (in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))), ((in(tptp_fun_D_2(C, B, A), C) | (in(tptp_fun_E_4(C, B, A), A) & in(tptp_fun_F_3(C, B, A), B) & (tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))) <=> (in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))))))), rewrite(((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))) <=> ((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))), (((in(tptp_fun_D_2(C, B, A), C) | (in(tptp_fun_E_4(C, B, A), A) & in(tptp_fun_F_3(C, B, A), B) & (tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))) & ((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))) <=> ((in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))))) & ((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))), rewrite(((in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))))) & ((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))) <=> (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))), (((in(tptp_fun_D_2(C, B, A), C) | (in(tptp_fun_E_4(C, B, A), A) & in(tptp_fun_F_3(C, B, A), B) & (tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))) & ((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))) <=> (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))), (((C = cartesian_product2(A, B)) | ((in(tptp_fun_D_2(C, B, A), C) | (in(tptp_fun_E_4(C, B, A), A) & in(tptp_fun_F_3(C, B, A), B) & (tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))) & ((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))) <=> ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))))), rewrite(((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))) <=> ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))), (((C = cartesian_product2(A, B)) | ((in(tptp_fun_D_2(C, B, A), C) | (in(tptp_fun_E_4(C, B, A), A) & in(tptp_fun_F_3(C, B, A), B) & (tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))) & ((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))) <=> ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))))), ((((~(C = cartesian_product2(A, B))) | ![D: $i] : (((~in(D, C)) | (in(tptp_fun_E_1(D, B, A), A) & in(tptp_fun_F_0(D, B, A), B) & (D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A))))) & (in(D, C) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (D = ordered_pair(E, F))))))) & ((C = cartesian_product2(A, B)) | ((in(tptp_fun_D_2(C, B, A), C) | (in(tptp_fun_E_4(C, B, A), A) & in(tptp_fun_F_3(C, B, A), B) & (tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))) & ((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))) <=> (((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))) & ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))))), rewrite((((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))) & ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))))) <=> (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))))))), ((((~(C = cartesian_product2(A, B))) | ![D: $i] : (((~in(D, C)) | (in(tptp_fun_E_1(D, B, A), A) & in(tptp_fun_F_0(D, B, A), B) & (D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A))))) & (in(D, C) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (D = ordered_pair(E, F))))))) & ((C = cartesian_product2(A, B)) | ((in(tptp_fun_D_2(C, B, A), C) | (in(tptp_fun_E_4(C, B, A), A) & in(tptp_fun_F_3(C, B, A), B) & (tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))) & ((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))) <=> (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))))))))),
% 63.20/39.11 inference(bind,[status(th)],[])).
% 63.20/39.11 tff(26,plain,
% 63.20/39.11 (![A: $i, B: $i, C: $i] : (((~(C = cartesian_product2(A, B))) | ![D: $i] : (((~in(D, C)) | (in(tptp_fun_E_1(D, B, A), A) & in(tptp_fun_F_0(D, B, A), B) & (D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A))))) & (in(D, C) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (D = ordered_pair(E, F))))))) & ((C = cartesian_product2(A, B)) | ((in(tptp_fun_D_2(C, B, A), C) | (in(tptp_fun_E_4(C, B, A), A) & in(tptp_fun_F_3(C, B, A), B) & (tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))) & ((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_2(C, B, A) = ordered_pair(E, F)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))))))),
% 63.20/39.11 inference(quant_intro,[status(thm)],[25])).
% 63.20/39.11 tff(27,plain,
% 63.20/39.11 (![A: $i, B: $i, C: $i] : ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : (in(E, A) & in(F, B) & (D = ordered_pair(E, F))))) <=> ![A: $i, B: $i, C: $i] : ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : (in(E, A) & in(F, B) & (D = ordered_pair(E, F)))))),
% 63.20/39.11 inference(rewrite,[status(thm)],[])).
% 63.20/39.11 tff(28,plain,
% 63.20/39.11 (^[A: $i, B: $i, C: $i] : rewrite(((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : ((in(E, A) & in(F, B)) & (D = ordered_pair(E, F))))) <=> ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : (in(E, A) & in(F, B) & (D = ordered_pair(E, F))))))),
% 63.20/39.11 inference(bind,[status(th)],[])).
% 63.20/39.11 tff(29,plain,
% 63.20/39.11 (![A: $i, B: $i, C: $i] : ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : ((in(E, A) & in(F, B)) & (D = ordered_pair(E, F))))) <=> ![A: $i, B: $i, C: $i] : ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : (in(E, A) & in(F, B) & (D = ordered_pair(E, F)))))),
% 63.20/39.11 inference(quant_intro,[status(thm)],[28])).
% 63.20/39.11 tff(30,axiom,(![A: $i, B: $i, C: $i] : ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : ((in(E, A) & in(F, B)) & (D = ordered_pair(E, F)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_zfmisc_1')).
% 63.20/39.11 tff(31,plain,
% 63.20/39.11 (![A: $i, B: $i, C: $i] : ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : (in(E, A) & in(F, B) & (D = ordered_pair(E, F)))))),
% 63.20/39.11 inference(modus_ponens,[status(thm)],[30, 29])).
% 63.20/39.11 tff(32,plain,
% 63.20/39.11 (![A: $i, B: $i, C: $i] : ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : (in(E, A) & in(F, B) & (D = ordered_pair(E, F)))))),
% 63.20/39.11 inference(modus_ponens,[status(thm)],[31, 27])).
% 63.20/39.11 tff(33,plain,(
% 63.20/39.11 ![A: $i, B: $i, C: $i] : (((~(C = cartesian_product2(A, B))) | ![D: $i] : (((~in(D, C)) | (in(tptp_fun_E_1(D, B, A), A) & in(tptp_fun_F_0(D, B, A), B) & (D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A))))) & (in(D, C) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (D = ordered_pair(E, F))))))) & ((C = cartesian_product2(A, B)) | ((in(tptp_fun_D_2(C, B, A), C) | (in(tptp_fun_E_4(C, B, A), A) & in(tptp_fun_F_3(C, B, A), B) & (tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A))))) & ((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))),
% 63.20/39.11 inference(skolemize,[status(sab)],[32])).
% 63.20/39.11 tff(34,plain,
% 63.20/39.11 (![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E, F))))))))))))),
% 63.20/39.11 inference(modus_ponens,[status(thm)],[33, 26])).
% 63.20/39.11 tff(35,plain,
% 63.20/39.11 (![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 63.20/39.11 inference(modus_ponens,[status(thm)],[34, 24])).
% 63.20/39.11 tff(36,plain,
% 63.20/39.11 (![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))),
% 63.20/39.11 inference(modus_ponens,[status(thm)],[35, 14])).
% 63.20/39.11 tff(37,plain,
% 63.20/39.11 (((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(unordered_pair(B!7, A!8), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, unordered_pair(B!7, A!8))))))))) <=> ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(unordered_pair(B!7, A!8), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, unordered_pair(B!7, A!8)))))))))),
% 63.20/39.11 inference(rewrite,[status(thm)],[])).
% 63.20/39.11 tff(38,plain,
% 63.20/39.11 ((~((~((~(cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, unordered_pair(B!7, A!8)))) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(A!8, C!6)) | (~in(unordered_pair(B!7, A!8), D!5)))))))) | (~((cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5)) | (~((~(in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5)) | (~((~in(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), C!6)) | (~in(tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6), D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6)))))))) | (~((~in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5))) | (~in(A!8, C!6)) | (~in(unordered_pair(B!7, A!8), D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(A!8, unordered_pair(B!7, A!8)))))))))))) <=> (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(unordered_pair(B!7, A!8), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, unordered_pair(B!7, A!8))))))))),
% 63.20/39.11 inference(rewrite,[status(thm)],[])).
% 63.20/39.11 tff(39,plain,
% 63.20/39.11 (((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~(cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, unordered_pair(B!7, A!8)))) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(A!8, C!6)) | (~in(unordered_pair(B!7, A!8), D!5)))))))) | (~((cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5)) | (~((~(in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5)) | (~((~in(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), C!6)) | (~in(tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6), D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6)))))))) | (~((~in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5))) | (~in(A!8, C!6)) | (~in(unordered_pair(B!7, A!8), D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(A!8, unordered_pair(B!7, A!8))))))))))))) <=> ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(unordered_pair(B!7, A!8), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, unordered_pair(B!7, A!8)))))))))),
% 63.20/39.11 inference(monotonicity,[status(thm)],[38])).
% 63.20/39.11 tff(40,plain,
% 63.20/39.11 (((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~(cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, unordered_pair(B!7, A!8)))) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(A!8, C!6)) | (~in(unordered_pair(B!7, A!8), D!5)))))))) | (~((cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5)) | (~((~(in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5)) | (~((~in(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), C!6)) | (~in(tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6), D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6)))))))) | (~((~in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5))) | (~in(A!8, C!6)) | (~in(unordered_pair(B!7, A!8), D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(A!8, unordered_pair(B!7, A!8))))))))))))) <=> ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(unordered_pair(B!7, A!8), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, unordered_pair(B!7, A!8)))))))))),
% 63.20/39.11 inference(transitivity,[status(thm)],[39, 37])).
% 63.20/39.11 tff(41,plain,
% 63.20/39.11 ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~(cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, unordered_pair(B!7, A!8)))) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(A!8, C!6)) | (~in(unordered_pair(B!7, A!8), D!5)))))))) | (~((cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5)) | (~((~(in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5)) | (~((~in(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), C!6)) | (~in(tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6), D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6)))))))) | (~((~in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5))) | (~in(A!8, C!6)) | (~in(unordered_pair(B!7, A!8), D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(A!8, unordered_pair(B!7, A!8))))))))))))),
% 63.20/39.12 inference(quant_inst,[status(thm)],[])).
% 63.20/39.12 tff(42,plain,
% 63.20/39.12 ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(unordered_pair(B!7, A!8), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, unordered_pair(B!7, A!8))))))))),
% 63.20/39.12 inference(modus_ponens,[status(thm)],[41, 40])).
% 63.20/39.12 tff(43,plain,
% 63.20/39.12 ($false),
% 63.20/39.12 inference(unit_resolution,[status(thm)],[42, 36, 12])).
% 63.20/39.12 tff(44,plain,(~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(unordered_pair(B!7, A!8), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, unordered_pair(B!7, A!8)))))))), inference(lemma,lemma(discharge,[]))).
% 63.20/39.12 tff(45,plain,
% 63.20/39.12 (((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(unordered_pair(B!7, A!8), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, unordered_pair(B!7, A!8))))))) | ((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))),
% 63.20/39.12 inference(tautology,[status(thm)],[])).
% 63.20/39.12 tff(46,plain,
% 63.20/39.12 ((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))))))),
% 63.20/39.12 inference(unit_resolution,[status(thm)],[45, 44])).
% 63.20/39.12 tff(47,plain,
% 63.20/39.12 (unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7)),
% 63.20/39.12 inference(symmetry,[status(thm)],[9])).
% 63.20/39.12 tff(48,plain,
% 63.20/39.12 (in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) <=> in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5))),
% 63.20/39.12 inference(monotonicity,[status(thm)],[47])).
% 63.20/39.12 tff(49,plain,
% 63.20/39.12 (in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5)) <=> in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))),
% 63.20/39.12 inference(symmetry,[status(thm)],[48])).
% 63.20/39.12 tff(50,plain,
% 63.20/39.12 ((~in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5))) <=> (~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)))),
% 63.20/39.12 inference(monotonicity,[status(thm)],[49])).
% 63.20/39.12 tff(51,assumption,(~((~in(A!8, C!6)) | (~in(B!7, D!5)))), introduced(assumption)).
% 63.20/39.12 tff(52,plain,
% 63.20/39.12 (((~in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5))) <=> (~((~in(A!8, C!6)) | (~in(B!7, D!5))))) <=> (in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5)) <=> ((~in(A!8, C!6)) | (~in(B!7, D!5))))),
% 63.20/39.12 inference(rewrite,[status(thm)],[])).
% 63.20/39.12 tff(53,plain,
% 63.20/39.12 ((in(A!8, C!6) & in(B!7, D!5)) <=> (~((~in(A!8, C!6)) | (~in(B!7, D!5))))),
% 63.20/39.12 inference(rewrite,[status(thm)],[])).
% 63.20/39.12 tff(54,plain,
% 63.20/39.12 (((~in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5))) <=> (in(A!8, C!6) & in(B!7, D!5))) <=> ((~in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5))) <=> (~((~in(A!8, C!6)) | (~in(B!7, D!5)))))),
% 63.20/39.12 inference(monotonicity,[status(thm)],[53])).
% 63.20/39.12 tff(55,plain,
% 63.20/39.12 (((~in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5))) <=> (in(A!8, C!6) & in(B!7, D!5))) <=> (in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5)) <=> ((~in(A!8, C!6)) | (~in(B!7, D!5))))),
% 63.20/39.12 inference(transitivity,[status(thm)],[54, 52])).
% 63.20/39.12 tff(56,plain,
% 63.20/39.12 ((~(in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5)) <=> (in(A!8, C!6) & in(B!7, D!5)))) <=> ((~in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5))) <=> (in(A!8, C!6) & in(B!7, D!5)))),
% 63.20/39.12 inference(rewrite,[status(thm)],[])).
% 63.20/39.12 tff(57,plain,
% 63.20/39.12 ((~![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))))),
% 63.20/39.12 inference(rewrite,[status(thm)],[])).
% 63.20/39.12 tff(58,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')).
% 63.20/39.12 tff(59,plain,
% 63.20/39.12 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 63.20/39.12 inference(modus_ponens,[status(thm)],[58, 57])).
% 63.20/39.12 tff(60,plain,
% 63.20/39.12 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 63.20/39.12 inference(modus_ponens,[status(thm)],[59, 57])).
% 63.20/39.12 tff(61,plain,
% 63.20/39.12 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 63.20/39.12 inference(modus_ponens,[status(thm)],[60, 57])).
% 63.20/39.12 tff(62,plain,
% 63.20/39.12 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 63.20/39.12 inference(modus_ponens,[status(thm)],[61, 57])).
% 63.20/39.12 tff(63,plain,
% 63.20/39.12 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 63.20/39.12 inference(modus_ponens,[status(thm)],[62, 57])).
% 63.20/39.12 tff(64,plain,
% 63.20/39.12 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 63.20/39.12 inference(modus_ponens,[status(thm)],[63, 57])).
% 63.20/39.12 tff(65,plain,
% 63.20/39.12 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 63.20/39.12 inference(modus_ponens,[status(thm)],[64, 57])).
% 63.20/39.12 tff(66,plain,(
% 63.20/39.12 ~(in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5)) <=> (in(A!8, C!6) & in(B!7, D!5)))),
% 63.20/39.12 inference(skolemize,[status(sab)],[65])).
% 63.20/39.12 tff(67,plain,
% 63.20/39.12 ((~in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5))) <=> (in(A!8, C!6) & in(B!7, D!5))),
% 63.20/39.12 inference(modus_ponens,[status(thm)],[66, 56])).
% 63.20/39.12 tff(68,plain,
% 63.20/39.12 (in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5)) <=> ((~in(A!8, C!6)) | (~in(B!7, D!5)))),
% 63.20/39.12 inference(modus_ponens,[status(thm)],[67, 55])).
% 63.20/39.12 tff(69,plain,
% 63.20/39.12 ((~in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5))) | ((~in(A!8, C!6)) | (~in(B!7, D!5))) | (~(in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5)) <=> ((~in(A!8, C!6)) | (~in(B!7, D!5)))))),
% 63.20/39.12 inference(tautology,[status(thm)],[])).
% 63.20/39.12 tff(70,plain,
% 63.20/39.12 ((~in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5))) | ((~in(A!8, C!6)) | (~in(B!7, D!5)))),
% 63.20/39.12 inference(unit_resolution,[status(thm)],[69, 68])).
% 63.20/39.12 tff(71,plain,
% 63.20/39.12 (~in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5))),
% 63.20/39.12 inference(unit_resolution,[status(thm)],[70, 51])).
% 63.20/39.12 tff(72,plain,
% 63.20/39.12 (~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))),
% 63.20/39.12 inference(modus_ponens,[status(thm)],[71, 50])).
% 63.20/39.12 tff(73,plain,
% 63.20/39.12 (((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | (~in(B!7, D!5)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7)))))))) <=> ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | (~in(B!7, D!5)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7))))))))),
% 63.20/39.12 inference(rewrite,[status(thm)],[])).
% 63.20/39.12 tff(74,plain,
% 63.20/39.12 ((~((~((~(cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7))) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(A!8, C!6)) | (~in(B!7, D!5)))))))) | (~((cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5)) | (~((~(in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5)) | (~((~in(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), C!6)) | (~in(tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6), D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6)))))))) | (~((~in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5))) | (~in(A!8, C!6)) | (~in(B!7, D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(A!8, B!7))))))))))) <=> (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | (~in(B!7, D!5)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7)))))))),
% 63.20/39.12 inference(rewrite,[status(thm)],[])).
% 63.20/39.12 tff(75,plain,
% 63.20/39.12 (((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~(cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7))) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(A!8, C!6)) | (~in(B!7, D!5)))))))) | (~((cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5)) | (~((~(in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5)) | (~((~in(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), C!6)) | (~in(tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6), D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6)))))))) | (~((~in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5))) | (~in(A!8, C!6)) | (~in(B!7, D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(A!8, B!7)))))))))))) <=> ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | (~in(B!7, D!5)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7))))))))),
% 63.20/39.12 inference(monotonicity,[status(thm)],[74])).
% 63.20/39.12 tff(76,plain,
% 63.20/39.12 (((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~(cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7))) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(A!8, C!6)) | (~in(B!7, D!5)))))))) | (~((cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5)) | (~((~(in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5)) | (~((~in(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), C!6)) | (~in(tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6), D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6)))))))) | (~((~in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5))) | (~in(A!8, C!6)) | (~in(B!7, D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(A!8, B!7)))))))))))) <=> ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | (~in(B!7, D!5)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7))))))))),
% 63.20/39.12 inference(transitivity,[status(thm)],[75, 73])).
% 63.20/39.12 tff(77,plain,
% 63.20/39.12 ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~(cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7))) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~in(A!8, C!6)) | (~in(B!7, D!5)))))))) | (~((cartesian_product2(C!6, D!5) = cartesian_product2(C!6, D!5)) | (~((~(in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5)) | (~((~in(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), C!6)) | (~in(tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6), D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(tptp_fun_E_4(cartesian_product2(C!6, D!5), D!5, C!6), tptp_fun_F_3(cartesian_product2(C!6, D!5), D!5, C!6)))))))) | (~((~in(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6), cartesian_product2(C!6, D!5))) | (~in(A!8, C!6)) | (~in(B!7, D!5)) | (~(tptp_fun_D_2(cartesian_product2(C!6, D!5), D!5, C!6) = ordered_pair(A!8, B!7)))))))))))),
% 63.20/39.12 inference(quant_inst,[status(thm)],[])).
% 63.20/39.12 tff(78,plain,
% 63.20/39.12 ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | (~in(B!7, D!5)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7)))))))),
% 63.20/39.12 inference(modus_ponens,[status(thm)],[77, 76])).
% 63.20/39.12 tff(79,plain,
% 63.20/39.12 (~((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | (~in(B!7, D!5)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7))))))),
% 63.20/39.12 inference(unit_resolution,[status(thm)],[78, 36])).
% 63.20/39.12 tff(80,plain,
% 63.20/39.12 (((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(A!8, C!6)) | (~in(B!7, D!5)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7)))))) | ((~in(A!8, C!6)) | (~in(B!7, D!5)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7))))),
% 63.20/39.13 inference(tautology,[status(thm)],[])).
% 63.20/39.13 tff(81,plain,
% 63.20/39.13 ((~in(A!8, C!6)) | (~in(B!7, D!5)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7)))),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[80, 79])).
% 63.20/39.13 tff(82,plain,
% 63.20/39.13 (((~in(A!8, C!6)) | (~in(B!7, D!5))) | in(B!7, D!5)),
% 63.20/39.13 inference(tautology,[status(thm)],[])).
% 63.20/39.13 tff(83,plain,
% 63.20/39.13 (in(B!7, D!5)),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[82, 51])).
% 63.20/39.13 tff(84,plain,
% 63.20/39.13 (((~in(A!8, C!6)) | (~in(B!7, D!5))) | in(A!8, C!6)),
% 63.20/39.13 inference(tautology,[status(thm)],[])).
% 63.20/39.13 tff(85,plain,
% 63.20/39.13 (in(A!8, C!6)),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[84, 51])).
% 63.20/39.13 tff(86,plain,
% 63.20/39.13 ((~((~in(A!8, C!6)) | (~in(B!7, D!5)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7))))) | (~in(A!8, C!6)) | (~in(B!7, D!5)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7)))),
% 63.20/39.13 inference(tautology,[status(thm)],[])).
% 63.20/39.13 tff(87,plain,
% 63.20/39.13 ((~((~in(A!8, C!6)) | (~in(B!7, D!5)) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(A!8, B!7))))) | in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[86, 85, 83, 47])).
% 63.20/39.13 tff(88,plain,
% 63.20/39.13 (in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[87, 81])).
% 63.20/39.13 tff(89,plain,
% 63.20/39.13 ($false),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[88, 72])).
% 63.20/39.13 tff(90,plain,((~in(A!8, C!6)) | (~in(B!7, D!5))), inference(lemma,lemma(discharge,[]))).
% 63.20/39.13 tff(91,plain,
% 63.20/39.13 (in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5)) | (~((~in(A!8, C!6)) | (~in(B!7, D!5)))) | (~(in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5)) <=> ((~in(A!8, C!6)) | (~in(B!7, D!5)))))),
% 63.20/39.13 inference(tautology,[status(thm)],[])).
% 63.20/39.13 tff(92,plain,
% 63.20/39.13 (in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5)) | (~((~in(A!8, C!6)) | (~in(B!7, D!5))))),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[91, 68])).
% 63.20/39.13 tff(93,plain,
% 63.20/39.13 (in(ordered_pair(A!8, B!7), cartesian_product2(C!6, D!5))),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[92, 90])).
% 63.20/39.13 tff(94,plain,
% 63.20/39.13 (in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))),
% 63.20/39.13 inference(modus_ponens,[status(thm)],[93, 49])).
% 63.20/39.13 tff(95,assumption,(~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))), introduced(assumption)).
% 63.20/39.13 tff(96,plain,
% 63.20/39.13 ($false),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[95, 94])).
% 63.20/39.13 tff(97,plain,(in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))), inference(lemma,lemma(discharge,[]))).
% 63.20/39.13 tff(98,plain,
% 63.20/39.13 ((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))))))),
% 63.20/39.13 inference(tautology,[status(thm)],[])).
% 63.20/39.13 tff(99,plain,
% 63.20/39.13 ((~((~in(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), cartesian_product2(C!6, D!5))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))))) | (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))))))),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[98, 97])).
% 63.20/39.13 tff(100,plain,
% 63.20/39.13 (~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[99, 46])).
% 63.20/39.13 tff(101,plain,
% 63.20/39.13 (((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))))) | (unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))),
% 63.20/39.13 inference(tautology,[status(thm)],[])).
% 63.20/39.13 tff(102,plain,
% 63.20/39.13 (unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[101, 100])).
% 63.20/39.13 tff(103,plain,
% 63.20/39.13 (ordered_pair(A!8, B!7) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))),
% 63.20/39.13 inference(modus_ponens,[status(thm)],[102, 11])).
% 63.20/39.13 tff(104,assumption,(B!7 = tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)), introduced(assumption)).
% 63.20/39.13 tff(105,plain,
% 63.20/39.13 (in(B!7, D!5) <=> in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)),
% 63.20/39.13 inference(monotonicity,[status(thm)],[104])).
% 63.20/39.13 tff(106,plain,
% 63.20/39.13 (in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5) <=> in(B!7, D!5)),
% 63.20/39.13 inference(symmetry,[status(thm)],[105])).
% 63.20/39.13 tff(107,plain,
% 63.20/39.13 (((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))))) | in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)),
% 63.20/39.13 inference(tautology,[status(thm)],[])).
% 63.20/39.13 tff(108,plain,
% 63.20/39.13 (in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[107, 100])).
% 63.20/39.13 tff(109,plain,
% 63.20/39.13 (in(B!7, D!5)),
% 63.20/39.13 inference(modus_ponens,[status(thm)],[108, 106])).
% 63.20/39.13 tff(110,assumption,(~((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))), introduced(assumption)).
% 63.20/39.13 tff(111,plain,
% 63.20/39.13 (unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[101, 110])).
% 63.20/39.13 tff(112,plain,
% 63.20/39.13 (ordered_pair(A!8, B!7) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))),
% 63.20/39.13 inference(transitivity,[status(thm)],[9, 111])).
% 63.20/39.13 tff(113,plain,
% 63.20/39.13 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D))))) <=> ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 63.20/39.13 inference(bind,[status(th)],[])).
% 63.20/39.13 tff(114,plain,
% 63.20/39.13 (![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 63.20/39.13 inference(quant_intro,[status(thm)],[113])).
% 63.20/39.13 tff(115,plain,
% 63.20/39.13 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D))) <=> ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 63.20/39.13 inference(bind,[status(th)],[])).
% 63.20/39.13 tff(116,plain,
% 63.20/39.13 (![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 63.20/39.13 inference(quant_intro,[status(thm)],[115])).
% 63.20/39.13 tff(117,plain,
% 63.20/39.13 (![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 63.20/39.13 inference(rewrite,[status(thm)],[])).
% 63.20/39.13 tff(118,plain,
% 63.20/39.13 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((ordered_pair(A, B) = ordered_pair(C, D)) => ((A = C) & (B = D))) <=> ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D))))),
% 63.20/39.13 inference(bind,[status(th)],[])).
% 63.20/39.13 tff(119,plain,
% 63.20/39.13 (![A: $i, B: $i, C: $i, D: $i] : ((ordered_pair(A, B) = ordered_pair(C, D)) => ((A = C) & (B = D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 63.20/39.13 inference(quant_intro,[status(thm)],[118])).
% 63.20/39.13 tff(120,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((ordered_pair(A, B) = ordered_pair(C, D)) => ((A = C) & (B = D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t33_zfmisc_1')).
% 63.20/39.13 tff(121,plain,
% 63.20/39.13 (![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 63.20/39.13 inference(modus_ponens,[status(thm)],[120, 119])).
% 63.20/39.13 tff(122,plain,
% 63.20/39.13 (![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 63.20/39.13 inference(modus_ponens,[status(thm)],[121, 117])).
% 63.20/39.13 tff(123,plain,(
% 63.20/39.13 ![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 63.20/39.13 inference(skolemize,[status(sab)],[122])).
% 63.20/39.13 tff(124,plain,
% 63.20/39.13 (![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 63.20/39.13 inference(modus_ponens,[status(thm)],[123, 116])).
% 63.20/39.13 tff(125,plain,
% 63.20/39.13 (![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 63.20/39.13 inference(modus_ponens,[status(thm)],[124, 114])).
% 63.20/39.13 tff(126,plain,
% 63.20/39.13 (((~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))) | ((~(ordered_pair(A!8, B!7) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))) | (~((~(A!8 = tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))) | (~(B!7 = tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))) | (~(ordered_pair(A!8, B!7) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))) | (~((~(A!8 = tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))) | (~(B!7 = tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))))))),
% 63.20/39.13 inference(rewrite,[status(thm)],[])).
% 63.20/39.13 tff(127,plain,
% 63.20/39.13 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))) | ((~(ordered_pair(A!8, B!7) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))) | (~((~(A!8 = tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))) | (~(B!7 = tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))))))),
% 63.20/39.13 inference(quant_inst,[status(thm)],[])).
% 63.20/39.13 tff(128,plain,
% 63.20/39.13 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))) | (~(ordered_pair(A!8, B!7) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))) | (~((~(A!8 = tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))) | (~(B!7 = tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))))),
% 63.20/39.13 inference(modus_ponens,[status(thm)],[127, 126])).
% 63.20/39.13 tff(129,plain,
% 63.20/39.13 (~((~(A!8 = tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))) | (~(B!7 = tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))))),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[128, 125, 112])).
% 63.20/39.13 tff(130,plain,
% 63.20/39.13 (((~(A!8 = tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))) | (~(B!7 = tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))) | (A!8 = tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))),
% 63.20/39.13 inference(tautology,[status(thm)],[])).
% 63.20/39.13 tff(131,plain,
% 63.20/39.13 (A!8 = tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)),
% 63.20/39.13 inference(unit_resolution,[status(thm)],[130, 129])).
% 63.20/39.13 tff(132,plain,
% 63.20/39.13 (in(A!8, C!6) <=> in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)),
% 63.20/39.13 inference(monotonicity,[status(thm)],[131])).
% 63.20/39.13 tff(133,plain,
% 63.20/39.13 (in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6) <=> in(A!8, C!6)),
% 63.20/39.13 inference(symmetry,[status(thm)],[132])).
% 63.20/39.13 tff(134,plain,
% 63.20/39.13 (((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))))) | in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)),
% 63.20/39.15 inference(tautology,[status(thm)],[])).
% 63.20/39.15 tff(135,plain,
% 63.20/39.15 (in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)),
% 63.20/39.15 inference(unit_resolution,[status(thm)],[134, 110])).
% 63.20/39.15 tff(136,plain,
% 63.20/39.15 (in(A!8, C!6)),
% 63.20/39.15 inference(modus_ponens,[status(thm)],[135, 133])).
% 63.20/39.15 tff(137,assumption,(~in(A!8, C!6)), introduced(assumption)).
% 63.20/39.15 tff(138,plain,
% 63.20/39.15 ($false),
% 63.20/39.15 inference(unit_resolution,[status(thm)],[137, 136])).
% 63.20/39.15 tff(139,plain,(((~in(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), C!6)) | (~in(tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), D!5)) | (~(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))))) | in(A!8, C!6)), inference(lemma,lemma(discharge,[]))).
% 63.20/39.15 tff(140,plain,
% 63.20/39.15 (in(A!8, C!6)),
% 63.20/39.15 inference(unit_resolution,[status(thm)],[139, 100])).
% 63.20/39.15 tff(141,plain,
% 63.20/39.15 ((~((~in(A!8, C!6)) | (~in(B!7, D!5)))) | (~in(A!8, C!6)) | (~in(B!7, D!5))),
% 63.20/39.15 inference(tautology,[status(thm)],[])).
% 63.20/39.15 tff(142,plain,
% 63.20/39.15 ((~in(A!8, C!6)) | (~in(B!7, D!5))),
% 63.20/39.15 inference(unit_resolution,[status(thm)],[141, 90])).
% 63.20/39.15 tff(143,plain,
% 63.20/39.15 (~in(B!7, D!5)),
% 63.20/39.15 inference(unit_resolution,[status(thm)],[142, 140])).
% 63.20/39.15 tff(144,plain,
% 63.20/39.15 ($false),
% 63.20/39.15 inference(unit_resolution,[status(thm)],[143, 109])).
% 63.20/39.15 tff(145,plain,(~(B!7 = tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))), inference(lemma,lemma(discharge,[]))).
% 63.20/39.15 tff(146,plain,
% 63.20/39.15 (((~(A!8 = tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))) | (~(B!7 = tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))) | (B!7 = tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))),
% 63.20/39.15 inference(tautology,[status(thm)],[])).
% 63.20/39.15 tff(147,plain,
% 63.20/39.15 ((~(A!8 = tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))) | (~(B!7 = tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))),
% 63.20/39.15 inference(unit_resolution,[status(thm)],[146, 145])).
% 63.20/39.15 tff(148,assumption,(ordered_pair(A!8, B!7) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6))), introduced(assumption)).
% 63.20/39.15 tff(149,plain,
% 63.20/39.15 ($false),
% 63.20/39.15 inference(unit_resolution,[status(thm)],[128, 125, 148, 147])).
% 63.20/39.15 tff(150,plain,(~(ordered_pair(A!8, B!7) = ordered_pair(tptp_fun_E_1(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6), tptp_fun_F_0(unordered_pair(unordered_pair(A!8, B!7), singleton(A!8)), D!5, C!6)))), inference(lemma,lemma(discharge,[]))).
% 63.20/39.15 tff(151,plain,
% 63.20/39.15 ($false),
% 63.20/39.15 inference(unit_resolution,[status(thm)],[150, 103])).
% 63.20/39.15 % SZS output end Proof
%------------------------------------------------------------------------------