%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU178+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:09 AM UTC 2025
% Result : Theorem 0.39s 0.61s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU178+2 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:13:09 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.39/0.61 % SZS status Theorem
% 0.39/0.61 % SZS output start Proof
% 0.39/0.61 tff(in_type, type, (
% 0.39/0.61 in: ( $i * $i ) > $o)).
% 0.39/0.61 tff(cartesian_product2_type, type, (
% 0.39/0.61 cartesian_product2: ( $i * $i ) > $i)).
% 0.39/0.61 tff(relation_rng_type, type, (
% 0.39/0.61 relation_rng: $i > $i)).
% 0.39/0.61 tff(tptp_fun_A_36_type, type, (
% 0.39/0.61 tptp_fun_A_36: $i)).
% 0.39/0.61 tff(relation_dom_type, type, (
% 0.39/0.61 relation_dom: $i > $i)).
% 0.39/0.61 tff(ordered_pair_type, type, (
% 0.39/0.61 ordered_pair: ( $i * $i ) > $i)).
% 0.39/0.61 tff(tptp_fun_D_0_type, type, (
% 0.39/0.61 tptp_fun_D_0: $i > $i)).
% 0.39/0.61 tff(tptp_fun_C_16_type, type, (
% 0.39/0.61 tptp_fun_C_16: ( $i * $i ) > $i)).
% 0.39/0.61 tff(tptp_fun_C_1_type, type, (
% 0.39/0.61 tptp_fun_C_1: $i > $i)).
% 0.39/0.61 tff(relation_type, type, (
% 0.39/0.61 relation: $i > $o)).
% 0.39/0.61 tff(tptp_fun_B_2_type, type, (
% 0.39/0.61 tptp_fun_B_2: $i > $i)).
% 0.39/0.61 tff(subset_type, type, (
% 0.39/0.61 subset: ( $i * $i ) > $o)).
% 0.39/0.61 tff(1,plain,
% 0.39/0.61 (^[A: $i, B: $i, C: $i, D: $i] : refl((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(2,plain,
% 0.39/0.61 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[1])).
% 0.39/0.61 tff(3,plain,
% 0.39/0.61 (^[A: $i, B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((in(A, C) & in(B, D)) <=> (~((~in(A, C)) | (~in(B, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))), rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))), rewrite((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(4,plain,
% 0.39/0.61 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[3])).
% 0.39/0.61 tff(5,plain,
% 0.39/0.61 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(6,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l55_zfmisc_1')).
% 0.39/0.61 tff(7,plain,
% 0.39/0.61 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.39/0.61 tff(8,plain,(
% 0.39/0.61 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.39/0.61 inference(skolemize,[status(sab)],[7])).
% 0.39/0.61 tff(9,plain,
% 0.39/0.61 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.39/0.61 tff(10,plain,
% 0.39/0.61 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.39/0.61 tff(11,plain,
% 0.39/0.61 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36)))) <=> in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(12,plain,
% 0.39/0.61 (~(((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36)))) <=> in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.39/0.61 tff(13,plain,
% 0.39/0.61 (^[A: $i] : refl((~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(14,plain,
% 0.39/0.61 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[13])).
% 0.39/0.61 tff(15,plain,
% 0.39/0.61 (^[A: $i] : rewrite((~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(16,plain,
% 0.39/0.61 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[15])).
% 0.39/0.61 tff(17,plain,
% 0.39/0.61 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.39/0.61 inference(transitivity,[status(thm)],[16, 14])).
% 0.39/0.61 tff(18,plain,
% 0.39/0.61 (^[A: $i] : trans(monotonicity(rewrite(((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) <=> ((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))), rewrite((relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))) <=> (relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))), ((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))), rewrite((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))), ((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(19,plain,
% 0.39/0.61 (![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[18])).
% 0.39/0.61 tff(20,plain,
% 0.39/0.61 (![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D)))))) <=> ![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(21,axiom,(![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_relat_1')).
% 0.39/0.61 tff(22,plain,
% 0.39/0.61 (![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.39/0.61 tff(23,plain,(
% 0.39/0.61 ![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))),
% 0.39/0.61 inference(skolemize,[status(sab)],[22])).
% 0.39/0.61 tff(24,plain,
% 0.39/0.61 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.39/0.61 tff(25,plain,
% 0.39/0.61 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.39/0.61 tff(26,plain,
% 0.39/0.61 ((~![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))) | (~((~((~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A!36) | (~((~in(tptp_fun_B_2(A!36), A!36)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A!36) = ordered_pair(C, D))))))))))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(27,plain,
% 0.39/0.61 (~((~((~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A!36) | (~((~in(tptp_fun_B_2(A!36), A!36)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A!36) = ordered_pair(C, D)))))))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.39/0.61 tff(28,plain,
% 0.39/0.61 (((~((~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A!36) | (~((~in(tptp_fun_B_2(A!36), A!36)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A!36) = ordered_pair(C, D))))))))) | ((~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))),
% 0.39/0.61 inference(tautology,[status(thm)],[])).
% 0.39/0.61 tff(29,plain,
% 0.39/0.61 ((~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.39/0.61 tff(30,plain,
% 0.39/0.61 ((~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))) <=> (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(31,plain,
% 0.39/0.61 ((~![A: $i] : (relation(A) => subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))) <=> (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(32,axiom,(~![A: $i] : (relation(A) => subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t21_relat_1')).
% 0.39/0.61 tff(33,plain,
% 0.39/0.61 (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.39/0.61 tff(34,plain,
% 0.39/0.61 (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.39/0.61 tff(35,plain,
% 0.39/0.61 (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.39/0.61 tff(36,plain,
% 0.39/0.61 (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[35, 30])).
% 0.39/0.61 tff(37,plain,(
% 0.39/0.61 ~((~relation(A!36)) | subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))))),
% 0.39/0.61 inference(skolemize,[status(sab)],[36])).
% 0.39/0.61 tff(38,plain,
% 0.39/0.61 (relation(A!36)),
% 0.39/0.61 inference(or_elim,[status(thm)],[37])).
% 0.39/0.61 tff(39,plain,
% 0.39/0.61 ((~((~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 0.39/0.61 inference(tautology,[status(thm)],[])).
% 0.39/0.61 tff(40,plain,
% 0.39/0.61 ((~((~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.39/0.61 tff(41,plain,
% 0.39/0.61 (![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[40, 29])).
% 0.39/0.61 tff(42,plain,
% 0.39/0.61 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(43,plain,
% 0.39/0.61 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(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_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[42])).
% 0.39/0.61 tff(44,plain,
% 0.39/0.61 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(45,plain,
% 0.39/0.61 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(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_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[44])).
% 0.39/0.61 tff(46,plain,
% 0.39/0.61 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(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_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 0.39/0.61 inference(transitivity,[status(thm)],[45, 43])).
% 0.39/0.61 tff(47,plain,
% 0.39/0.61 (^[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_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(48,plain,
% 0.39/0.61 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(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_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[47])).
% 0.39/0.61 tff(49,plain,
% 0.39/0.61 (![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)))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(50,plain,
% 0.39/0.61 (^[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))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(51,plain,
% 0.39/0.61 (![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)))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[50])).
% 0.39/0.61 tff(52,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.39/0.61 tff(53,plain,
% 0.39/0.61 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.39/0.61 tff(54,plain,
% 0.39/0.61 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.39/0.61 tff(55,plain,(
% 0.39/0.61 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))),
% 0.39/0.61 inference(skolemize,[status(sab)],[54])).
% 0.39/0.61 tff(56,plain,
% 0.39/0.61 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.39/0.61 tff(57,plain,
% 0.39/0.61 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.39/0.61 tff(58,plain,
% 0.39/0.61 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))) | (~((~((~subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36)))) | ![C: $i] : ((~in(C, A!36)) | in(C, cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))) | (~(subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))))))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(59,plain,
% 0.39/0.61 (~((~((~subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36)))) | ![C: $i] : ((~in(C, A!36)) | in(C, cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))) | (~(subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.39/0.61 tff(60,plain,
% 0.39/0.61 (((~((~subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36)))) | ![C: $i] : ((~in(C, A!36)) | in(C, cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))) | (~(subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))))) | (subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))))),
% 0.39/0.61 inference(tautology,[status(thm)],[])).
% 0.39/0.61 tff(61,plain,
% 0.39/0.61 (subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.39/0.61 tff(62,plain,
% 0.39/0.61 (~subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36)))),
% 0.39/0.61 inference(or_elim,[status(thm)],[37])).
% 0.39/0.61 tff(63,plain,
% 0.39/0.61 ((~(subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))))) | subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))),
% 0.39/0.61 inference(tautology,[status(thm)],[])).
% 0.39/0.61 tff(64,plain,
% 0.39/0.61 ((~(subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.39/0.61 tff(65,plain,
% 0.39/0.61 (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[64, 61])).
% 0.39/0.61 tff(66,plain,
% 0.39/0.61 (((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)),
% 0.39/0.61 inference(tautology,[status(thm)],[])).
% 0.39/0.61 tff(67,plain,
% 0.39/0.61 (in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.39/0.61 tff(68,plain,
% 0.39/0.61 (((~![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | ((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | (tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36) = ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)))))) <=> ((~![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | (~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | (tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36) = ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)))))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(69,plain,
% 0.39/0.61 ((~![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | ((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | (tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36) = ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)))))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(70,plain,
% 0.39/0.61 ((~![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | (~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | (tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36) = ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.39/0.61 tff(71,plain,
% 0.39/0.61 (tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36) = ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[70, 67, 41])).
% 0.39/0.61 tff(72,plain,
% 0.39/0.61 (ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))) = tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)),
% 0.39/0.62 inference(symmetry,[status(thm)],[71])).
% 0.39/0.62 tff(73,plain,
% 0.39/0.62 (in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36))) <=> in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))),
% 0.39/0.62 inference(monotonicity,[status(thm)],[72])).
% 0.39/0.62 tff(74,plain,
% 0.39/0.62 (in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36))) <=> in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))),
% 0.39/0.62 inference(symmetry,[status(thm)],[73])).
% 0.39/0.62 tff(75,plain,
% 0.39/0.62 ((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))) <=> (~in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))),
% 0.39/0.62 inference(monotonicity,[status(thm)],[74])).
% 0.39/0.62 tff(76,plain,
% 0.39/0.62 (((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))) | (~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))),
% 0.39/0.62 inference(tautology,[status(thm)],[])).
% 0.39/0.62 tff(77,plain,
% 0.39/0.62 (~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[76, 65])).
% 0.39/0.62 tff(78,plain,
% 0.39/0.62 (~in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[77, 75])).
% 0.39/0.62 tff(79,plain,
% 0.39/0.62 (in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36) <=> in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)),
% 0.39/0.62 inference(monotonicity,[status(thm)],[72])).
% 0.39/0.62 tff(80,plain,
% 0.39/0.62 (in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36) <=> in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36)),
% 0.39/0.62 inference(symmetry,[status(thm)],[79])).
% 0.39/0.62 tff(81,plain,
% 0.39/0.62 (in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36)),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[67, 80])).
% 0.39/0.62 tff(82,plain,
% 0.39/0.62 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(83,plain,
% 0.39/0.62 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[82])).
% 0.39/0.62 tff(84,plain,
% 0.39/0.62 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(C)) & in(B, relation_rng(C))) <=> (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))), (((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))))), rewrite(((~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))), (((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(85,plain,
% 0.39/0.62 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[84])).
% 0.39/0.62 tff(86,plain,
% 0.39/0.62 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(87,plain,
% 0.39/0.62 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))) <=> ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> (relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))))), rewrite((relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(88,plain,
% 0.39/0.62 (![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[87])).
% 0.39/0.62 tff(89,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t20_relat_1')).
% 0.39/0.62 tff(90,plain,
% 0.39/0.62 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.39/0.62 tff(91,plain,
% 0.39/0.62 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.39/0.62 tff(92,plain,(
% 0.39/0.62 ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.39/0.62 inference(skolemize,[status(sab)],[91])).
% 0.39/0.62 tff(93,plain,
% 0.39/0.62 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.39/0.62 tff(94,plain,
% 0.39/0.62 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.39/0.62 tff(95,plain,
% 0.39/0.62 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | ((~relation(A!36)) | (~in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36)) | (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | (~relation(A!36)) | (~in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36)) | (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36))))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(96,plain,
% 0.39/0.62 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | ((~relation(A!36)) | (~in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36)) | (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36))))))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(97,plain,
% 0.39/0.62 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | (~relation(A!36)) | (~in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36)) | (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36)))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.39/0.62 tff(98,plain,
% 0.39/0.62 ((~in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36)) | (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36)))))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[97, 94, 38])).
% 0.39/0.62 tff(99,plain,
% 0.39/0.62 (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36))))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[98, 81])).
% 0.39/0.62 tff(100,plain,
% 0.39/0.62 ((((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36)))) <=> in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))) | ((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36)))) | in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))),
% 0.39/0.62 inference(tautology,[status(thm)],[])).
% 0.39/0.62 tff(101,plain,
% 0.39/0.62 ($false),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[100, 99, 78, 12])).
% 0.39/0.62 % SZS output end Proof
% 0.39/0.63 % E exiting
%------------------------------------------------------------------------------