TSTP Solution File: SET950+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:08:43 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 08:04:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(in_type, type, (
% 0.20/0.41 in: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_B_10_type, type, (
% 0.20/0.41 tptp_fun_B_10: $i)).
% 0.20/0.41 tff(tptp_fun_A_11_type, type, (
% 0.20/0.41 tptp_fun_A_11: $i)).
% 0.20/0.41 tff(tptp_fun_C_9_type, type, (
% 0.20/0.41 tptp_fun_C_9: $i)).
% 0.20/0.41 tff(tptp_fun_D_8_type, type, (
% 0.20/0.41 tptp_fun_D_8: $i)).
% 0.20/0.41 tff(ordered_pair_type, type, (
% 0.20/0.41 ordered_pair: ( $i * $i ) > $i)).
% 0.20/0.41 tff(cartesian_product2_type, type, (
% 0.20/0.41 cartesian_product2: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_F_0_type, type, (
% 0.20/0.41 tptp_fun_F_0: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_E_1_type, type, (
% 0.20/0.41 tptp_fun_E_1: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_D_2_type, type, (
% 0.20/0.41 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_F_3_type, type, (
% 0.20/0.41 tptp_fun_F_3: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_E_4_type, type, (
% 0.20/0.41 tptp_fun_E_4: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(subset_type, type, (
% 0.20/0.41 subset: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_C_5_type, type, (
% 0.20/0.41 tptp_fun_C_5: ( $i * $i ) > $i)).
% 0.20/0.41 tff(1,assumption,((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~(in(D!8, cartesian_product2(B!10, C!9)) | (~(D!8 = ordered_pair(A!11, D!8))) | (~in(D!8, C!9)) | (~in(A!11, B!10))))), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))) <=> (~((~((~(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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12))))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))) <=> ![A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))) <=> (~((~((~(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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))) <=> ![A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12))))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ![E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))) <=> ![A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12))))))))))))),
% 0.20/0.42 inference(pull_quant,[status(thm)],[])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (^[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_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))), (((~((~(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_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12))))))))))))), ((~((~((~(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_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))))), pull_quant((~?[E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))) <=> ![E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12))))))))))))), ((~((~((~(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_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12))))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![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_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12))))))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 (![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_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12))))))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[8, 6])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (![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_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12))))))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[9, 5])).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 (^[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)))))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 (![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))))))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 (![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_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12))))))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[12, 10])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (^[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))))))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 (![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))))))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (![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)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (^[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))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (![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)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.43 tff(19,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/sandbox/benchmark/theBenchmark.p','d2_zfmisc_1')).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (![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)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (![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)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.43 tff(22,plain,(
% 0.20/0.43 ![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))))))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[21])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 (![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))))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12))))))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[24, 3])).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 (((~![A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))) | (~((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~(in(D!8, cartesian_product2(B!10, C!9)) | (~(D!8 = ordered_pair(A!11, D!8))) | (~in(D!8, C!9)) | (~in(A!11, B!10))))))) <=> ((~![A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))) | (~((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~(in(D!8, cartesian_product2(B!10, C!9)) | (~(D!8 = ordered_pair(A!11, D!8))) | (~in(D!8, C!9)) | (~in(A!11, B!10)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 ((~((~((~(cartesian_product2(B!10, C!9) = cartesian_product2(B!10, C!9))) | (~((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~((~(D!8 = ordered_pair(A!11, D!8))) | in(D!8, cartesian_product2(B!10, C!9)) | (~in(A!11, B!10)) | (~in(D!8, C!9)))))))) | (~((cartesian_product2(B!10, C!9) = cartesian_product2(B!10, C!9)) | (~((~(in(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10), cartesian_product2(B!10, C!9)) | (~((~in(tptp_fun_E_4(cartesian_product2(B!10, C!9), C!9, B!10), B!10)) | (~in(tptp_fun_F_3(cartesian_product2(B!10, C!9), C!9, B!10), C!9)) | (~(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10) = ordered_pair(tptp_fun_E_4(cartesian_product2(B!10, C!9), C!9, B!10), tptp_fun_F_3(cartesian_product2(B!10, C!9), C!9, B!10)))))))) | (~((~in(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10), cartesian_product2(B!10, C!9))) | (~in(A!11, B!10)) | (~in(D!8, C!9)) | (~(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10) = ordered_pair(A!11, D!8))))))))))) <=> (~((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~(in(D!8, cartesian_product2(B!10, C!9)) | (~(D!8 = ordered_pair(A!11, D!8))) | (~in(D!8, C!9)) | (~in(A!11, B!10))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (((~![A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))) | (~((~((~(cartesian_product2(B!10, C!9) = cartesian_product2(B!10, C!9))) | (~((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~((~(D!8 = ordered_pair(A!11, D!8))) | in(D!8, cartesian_product2(B!10, C!9)) | (~in(A!11, B!10)) | (~in(D!8, C!9)))))))) | (~((cartesian_product2(B!10, C!9) = cartesian_product2(B!10, C!9)) | (~((~(in(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10), cartesian_product2(B!10, C!9)) | (~((~in(tptp_fun_E_4(cartesian_product2(B!10, C!9), C!9, B!10), B!10)) | (~in(tptp_fun_F_3(cartesian_product2(B!10, C!9), C!9, B!10), C!9)) | (~(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10) = ordered_pair(tptp_fun_E_4(cartesian_product2(B!10, C!9), C!9, B!10), tptp_fun_F_3(cartesian_product2(B!10, C!9), C!9, B!10)))))))) | (~((~in(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10), cartesian_product2(B!10, C!9))) | (~in(A!11, B!10)) | (~in(D!8, C!9)) | (~(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10) = ordered_pair(A!11, D!8)))))))))))) <=> ((~![A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))) | (~((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~(in(D!8, cartesian_product2(B!10, C!9)) | (~(D!8 = ordered_pair(A!11, D!8))) | (~in(D!8, C!9)) | (~in(A!11, B!10)))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 (((~![A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))) | (~((~((~(cartesian_product2(B!10, C!9) = cartesian_product2(B!10, C!9))) | (~((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~((~(D!8 = ordered_pair(A!11, D!8))) | in(D!8, cartesian_product2(B!10, C!9)) | (~in(A!11, B!10)) | (~in(D!8, C!9)))))))) | (~((cartesian_product2(B!10, C!9) = cartesian_product2(B!10, C!9)) | (~((~(in(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10), cartesian_product2(B!10, C!9)) | (~((~in(tptp_fun_E_4(cartesian_product2(B!10, C!9), C!9, B!10), B!10)) | (~in(tptp_fun_F_3(cartesian_product2(B!10, C!9), C!9, B!10), C!9)) | (~(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10) = ordered_pair(tptp_fun_E_4(cartesian_product2(B!10, C!9), C!9, B!10), tptp_fun_F_3(cartesian_product2(B!10, C!9), C!9, B!10)))))))) | (~((~in(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10), cartesian_product2(B!10, C!9))) | (~in(A!11, B!10)) | (~in(D!8, C!9)) | (~(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10) = ordered_pair(A!11, D!8)))))))))))) <=> ((~![A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))) | (~((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~(in(D!8, cartesian_product2(B!10, C!9)) | (~(D!8 = ordered_pair(A!11, D!8))) | (~in(D!8, C!9)) | (~in(A!11, B!10)))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[28, 26])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 ((~![A: $i, B: $i, C: $i, E_13: $i, F_12: $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_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))) | (~((~((~(cartesian_product2(B!10, C!9) = cartesian_product2(B!10, C!9))) | (~((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~((~(D!8 = ordered_pair(A!11, D!8))) | in(D!8, cartesian_product2(B!10, C!9)) | (~in(A!11, B!10)) | (~in(D!8, C!9)))))))) | (~((cartesian_product2(B!10, C!9) = cartesian_product2(B!10, C!9)) | (~((~(in(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10), cartesian_product2(B!10, C!9)) | (~((~in(tptp_fun_E_4(cartesian_product2(B!10, C!9), C!9, B!10), B!10)) | (~in(tptp_fun_F_3(cartesian_product2(B!10, C!9), C!9, B!10), C!9)) | (~(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10) = ordered_pair(tptp_fun_E_4(cartesian_product2(B!10, C!9), C!9, B!10), tptp_fun_F_3(cartesian_product2(B!10, C!9), C!9, B!10)))))))) | (~((~in(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10), cartesian_product2(B!10, C!9))) | (~in(A!11, B!10)) | (~in(D!8, C!9)) | (~(tptp_fun_D_2(cartesian_product2(B!10, C!9), C!9, B!10) = ordered_pair(A!11, D!8)))))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 ((~![A: $i, B: $i, C: $i, E_13: $i, F_12: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_1(D, B, A), A)) | (~in(tptp_fun_F_0(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_1(D, B, A), tptp_fun_F_0(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_2(C, B, A), C) | (~((~in(tptp_fun_E_4(C, B, A), A)) | (~in(tptp_fun_F_3(C, B, A), B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(tptp_fun_E_4(C, B, A), tptp_fun_F_3(C, B, A)))))))) | (~((~in(tptp_fun_D_2(C, B, A), C)) | (~in(E_13, A)) | (~in(F_12, B)) | (~(tptp_fun_D_2(C, B, A) = ordered_pair(E_13, F_12)))))))))))) | (~((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~(in(D!8, cartesian_product2(B!10, C!9)) | (~(D!8 = ordered_pair(A!11, D!8))) | (~in(D!8, C!9)) | (~in(A!11, B!10))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[31, 25, 1])).
% 0.20/0.45 tff(33,plain,(~((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~(in(D!8, cartesian_product2(B!10, C!9)) | (~(D!8 = ordered_pair(A!11, D!8))) | (~in(D!8, C!9)) | (~in(A!11, B!10)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(34,assumption,(~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))), introduced(assumption)).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 (((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10))))) | (D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 (D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 (((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10))))) | in(tptp_fun_F_0(D!8, C!9, B!10), C!9)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (in(tptp_fun_F_0(D!8, C!9, B!10), C!9)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10))))) | in(tptp_fun_E_1(D!8, C!9, B!10), B!10)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (in(tptp_fun_E_1(D!8, C!9, B!10), B!10)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[39, 34])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (^[E: $i, F: $i] : refl(((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F)))) <=> ((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 (![E: $i, F: $i] : ((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F)))) <=> ![E: $i, F: $i] : ((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (^[E: $i, F: $i] : trans(monotonicity(rewrite((in(E, B!10) & in(F, C!9) & (D!8 = ordered_pair(E, F))) <=> (~((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F)))))), ((~(in(E, B!10) & in(F, C!9) & (D!8 = ordered_pair(E, F)))) <=> (~(~((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F)))))))), rewrite((~(~((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F)))))) <=> ((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F))))), ((~(in(E, B!10) & in(F, C!9) & (D!8 = ordered_pair(E, F)))) <=> ((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (![E: $i, F: $i] : (~(in(E, B!10) & in(F, C!9) & (D!8 = ordered_pair(E, F)))) <=> ![E: $i, F: $i] : ((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 ((subset(A!11, cartesian_product2(B!10, C!9)) & in(D!8, A!11) & ![E: $i, F: $i] : (~(in(E, B!10) & in(F, C!9) & (D!8 = ordered_pair(E, F))))) <=> (subset(A!11, cartesian_product2(B!10, C!9)) & in(D!8, A!11) & ![E: $i, F: $i] : (~(in(E, B!10) & in(F, C!9) & (D!8 = ordered_pair(E, F)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 ((~![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F))))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F)))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 ((~![A: $i, B: $i, C: $i, D: $i] : (~((subset(A, cartesian_product2(B, C)) & in(D, A)) & ![E: $i, F: $i] : (~((in(E, B) & in(F, C)) & (D = ordered_pair(E, F))))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F)))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(48,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (~((subset(A, cartesian_product2(B, C)) & in(D, A)) & ![E: $i, F: $i] : (~((in(E, B) & in(F, C)) & (D = ordered_pair(E, F))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t103_zfmisc_1')).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[51, 46])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[52, 46])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[54, 46])).
% 0.20/0.45 tff(56,plain,(
% 0.20/0.45 $oeq((~(~(subset(A!11, cartesian_product2(B!10, C!9)) & in(D!8, A!11) & ![E: $i, F: $i] : (~(in(E, B!10) & in(F, C!9) & (D!8 = ordered_pair(E, F))))))), (subset(A!11, cartesian_product2(B!10, C!9)) & in(D!8, A!11) & ![E: $i, F: $i] : (~(in(E, B!10) & in(F, C!9) & (D!8 = ordered_pair(E, F))))))),
% 0.20/0.45 inference(transitivity,[status(sab)],[55])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (subset(A!11, cartesian_product2(B!10, C!9)) & in(D!8, A!11) & ![E: $i, F: $i] : (~(in(E, B!10) & in(F, C!9) & (D!8 = ordered_pair(E, F))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[56, 45])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (![E: $i, F: $i] : (~(in(E, B!10) & in(F, C!9) & (D!8 = ordered_pair(E, F))))),
% 0.20/0.45 inference(and_elim,[status(thm)],[57])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (![E: $i, F: $i] : ((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[58, 44])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 (![E: $i, F: $i] : ((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[59, 42])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (((~![E: $i, F: $i] : ((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F))))) | ((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))) <=> ((~![E: $i, F: $i] : ((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F))))) | (~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 ((~![E: $i, F: $i] : ((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F))))) | ((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 ((~![E: $i, F: $i] : ((~in(E, B!10)) | (~in(F, C!9)) | (~(D!8 = ordered_pair(E, F))))) | (~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[63, 60, 40, 38, 36])).
% 0.20/0.45 tff(65,plain,((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(69,plain,
% 0.20/0.46 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.46 tff(70,plain,
% 0.20/0.46 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[69, 67])).
% 0.20/0.46 tff(71,plain,
% 0.20/0.46 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.46 tff(73,plain,
% 0.20/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(75,plain,
% 0.20/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.46 tff(76,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.20/0.46 tff(79,plain,(
% 0.20/0.46 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[78])).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))) | (~((~((~subset(A!11, cartesian_product2(B!10, C!9))) | ![C: $i] : ((~in(C, A!11)) | in(C, cartesian_product2(B!10, C!9))))) | (~(subset(A!11, cartesian_product2(B!10, C!9)) | (~((~in(tptp_fun_C_5(cartesian_product2(B!10, C!9), A!11), A!11)) | in(tptp_fun_C_5(cartesian_product2(B!10, C!9), A!11), cartesian_product2(B!10, C!9))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 (~((~((~subset(A!11, cartesian_product2(B!10, C!9))) | ![C: $i] : ((~in(C, A!11)) | in(C, cartesian_product2(B!10, C!9))))) | (~(subset(A!11, cartesian_product2(B!10, C!9)) | (~((~in(tptp_fun_C_5(cartesian_product2(B!10, C!9), A!11), A!11)) | in(tptp_fun_C_5(cartesian_product2(B!10, C!9), A!11), cartesian_product2(B!10, C!9)))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 (((~((~subset(A!11, cartesian_product2(B!10, C!9))) | ![C: $i] : ((~in(C, A!11)) | in(C, cartesian_product2(B!10, C!9))))) | (~(subset(A!11, cartesian_product2(B!10, C!9)) | (~((~in(tptp_fun_C_5(cartesian_product2(B!10, C!9), A!11), A!11)) | in(tptp_fun_C_5(cartesian_product2(B!10, C!9), A!11), cartesian_product2(B!10, C!9))))))) | ((~subset(A!11, cartesian_product2(B!10, C!9))) | ![C: $i] : ((~in(C, A!11)) | in(C, cartesian_product2(B!10, C!9))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 ((~subset(A!11, cartesian_product2(B!10, C!9))) | ![C: $i] : ((~in(C, A!11)) | in(C, cartesian_product2(B!10, C!9)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 (subset(A!11, cartesian_product2(B!10, C!9))),
% 0.20/0.46 inference(and_elim,[status(thm)],[57])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 ((~((~subset(A!11, cartesian_product2(B!10, C!9))) | ![C: $i] : ((~in(C, A!11)) | in(C, cartesian_product2(B!10, C!9))))) | (~subset(A!11, cartesian_product2(B!10, C!9))) | ![C: $i] : ((~in(C, A!11)) | in(C, cartesian_product2(B!10, C!9)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 ((~((~subset(A!11, cartesian_product2(B!10, C!9))) | ![C: $i] : ((~in(C, A!11)) | in(C, cartesian_product2(B!10, C!9))))) | ![C: $i] : ((~in(C, A!11)) | in(C, cartesian_product2(B!10, C!9)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (![C: $i] : ((~in(C, A!11)) | in(C, cartesian_product2(B!10, C!9)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[88, 85])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (in(D!8, A!11)),
% 0.20/0.46 inference(and_elim,[status(thm)],[57])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (((~![C: $i] : ((~in(C, A!11)) | in(C, cartesian_product2(B!10, C!9)))) | ((~in(D!8, A!11)) | in(D!8, cartesian_product2(B!10, C!9)))) <=> ((~![C: $i] : ((~in(C, A!11)) | in(C, cartesian_product2(B!10, C!9)))) | (~in(D!8, A!11)) | in(D!8, cartesian_product2(B!10, C!9)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 ((~![C: $i] : ((~in(C, A!11)) | in(C, cartesian_product2(B!10, C!9)))) | ((~in(D!8, A!11)) | in(D!8, cartesian_product2(B!10, C!9)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 ((~![C: $i] : ((~in(C, A!11)) | in(C, cartesian_product2(B!10, C!9)))) | (~in(D!8, A!11)) | in(D!8, cartesian_product2(B!10, C!9))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (in(D!8, cartesian_product2(B!10, C!9))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[93, 90, 89])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 ((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[95, 94, 65])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 (((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~(in(D!8, cartesian_product2(B!10, C!9)) | (~(D!8 = ordered_pair(A!11, D!8))) | (~in(D!8, C!9)) | (~in(A!11, B!10))))) | ((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 ((~((~in(D!8, cartesian_product2(B!10, C!9))) | (~((~in(tptp_fun_E_1(D!8, C!9, B!10), B!10)) | (~in(tptp_fun_F_0(D!8, C!9, B!10), C!9)) | (~(D!8 = ordered_pair(tptp_fun_E_1(D!8, C!9, B!10), tptp_fun_F_0(D!8, C!9, B!10)))))))) | (~(in(D!8, cartesian_product2(B!10, C!9)) | (~(D!8 = ordered_pair(A!11, D!8))) | (~in(D!8, C!9)) | (~in(A!11, B!10))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[98, 33])).
% 0.20/0.46 % SZS output end Proof
%------------------------------------------------------------------------------