%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU262+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:27:25 AM UTC 2025
% Result : Theorem 48.38s 48.62s
% Output : Proof 48.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU262+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 06:31:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 48.38/48.62 % SZS status Theorem
% 48.38/48.62 % SZS output start Proof
% 48.38/48.62 tff(in_type, type, (
% 48.38/48.62 in: ( $i * $i ) > $o)).
% 48.38/48.62 tff(tptp_fun_A_14_type, type, (
% 48.38/48.62 tptp_fun_A_14: $i)).
% 48.38/48.62 tff(tptp_fun_C_0_type, type, (
% 48.38/48.62 tptp_fun_C_0: ( $i * $i ) > $i)).
% 48.38/48.62 tff(relation_dom_type, type, (
% 48.38/48.62 relation_dom: $i > $i)).
% 48.38/48.62 tff(tptp_fun_C_12_type, type, (
% 48.38/48.62 tptp_fun_C_12: $i)).
% 48.38/48.62 tff(subset_type, type, (
% 48.38/48.62 subset: ( $i * $i ) > $o)).
% 48.38/48.62 tff(ordered_pair_type, type, (
% 48.38/48.62 ordered_pair: ( $i * $i ) > $i)).
% 48.38/48.62 tff(tptp_fun_D_1_type, type, (
% 48.38/48.62 tptp_fun_D_1: ( $i * $i ) > $i)).
% 48.38/48.62 tff(tptp_fun_C_2_type, type, (
% 48.38/48.62 tptp_fun_C_2: ( $i * $i ) > $i)).
% 48.38/48.62 tff(tptp_fun_D_3_type, type, (
% 48.38/48.62 tptp_fun_D_3: ( $i * $i ) > $i)).
% 48.38/48.62 tff(relation_type, type, (
% 48.38/48.62 relation: $i > $o)).
% 48.38/48.62 tff(element_type, type, (
% 48.38/48.62 element: ( $i * $i ) > $o)).
% 48.38/48.62 tff(powerset_type, type, (
% 48.38/48.62 powerset: $i > $i)).
% 48.38/48.62 tff(cartesian_product2_type, type, (
% 48.38/48.62 cartesian_product2: ( $i * $i ) > $i)).
% 48.38/48.62 tff(tptp_fun_B_13_type, type, (
% 48.38/48.62 tptp_fun_B_13: $i)).
% 48.38/48.62 tff(relation_of2_as_subset_type, type, (
% 48.38/48.62 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 48.38/48.62 tff(relation_rng_type, type, (
% 48.38/48.62 relation_rng: $i > $i)).
% 48.38/48.62 tff(tptp_fun_D_4_type, type, (
% 48.38/48.62 tptp_fun_D_4: ( $i * $i ) > $i)).
% 48.38/48.62 tff(tptp_fun_C_5_type, type, (
% 48.38/48.62 tptp_fun_C_5: ( $i * $i ) > $i)).
% 48.38/48.62 tff(tptp_fun_D_6_type, type, (
% 48.38/48.62 tptp_fun_D_6: ( $i * $i ) > $i)).
% 48.38/48.62 tff(1,plain,
% 48.38/48.62 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))) <=> (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B))))),
% 48.38/48.62 inference(rewrite,[status(thm)],[])).
% 48.38/48.62 tff(2,plain,
% 48.38/48.62 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => (subset(relation_dom(C), A) & subset(relation_rng(C), B)))) <=> (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B))))),
% 48.38/48.62 inference(rewrite,[status(thm)],[])).
% 48.38/48.62 tff(3,axiom,(~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => (subset(relation_dom(C), A) & subset(relation_rng(C), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_relset_1')).
% 48.38/48.62 tff(4,plain,
% 48.38/48.62 (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[3, 2])).
% 48.38/48.62 tff(5,plain,
% 48.38/48.62 (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[4, 1])).
% 48.38/48.62 tff(6,plain,
% 48.38/48.62 (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[5, 1])).
% 48.38/48.62 tff(7,plain,
% 48.38/48.62 (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[6, 1])).
% 48.38/48.62 tff(8,plain,(
% 48.38/48.62 ~((~relation_of2_as_subset(C!12, A!14, B!13)) | (subset(relation_dom(C!12), A!14) & subset(relation_rng(C!12), B!13)))),
% 48.38/48.62 inference(skolemize,[status(sab)],[7])).
% 48.38/48.62 tff(9,plain,
% 48.38/48.62 (relation_of2_as_subset(C!12, A!14, B!13)),
% 48.38/48.62 inference(or_elim,[status(thm)],[8])).
% 48.38/48.62 tff(10,plain,
% 48.38/48.62 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 48.38/48.62 inference(bind,[status(th)],[])).
% 48.38/48.62 tff(11,plain,
% 48.38/48.62 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 48.38/48.62 inference(quant_intro,[status(thm)],[10])).
% 48.38/48.62 tff(12,plain,
% 48.38/48.62 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 48.38/48.62 inference(rewrite,[status(thm)],[])).
% 48.38/48.62 tff(13,plain,
% 48.38/48.62 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 48.38/48.62 inference(bind,[status(th)],[])).
% 48.38/48.62 tff(14,plain,
% 48.38/48.62 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 48.38/48.62 inference(quant_intro,[status(thm)],[13])).
% 48.38/48.62 tff(15,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 48.38/48.62 tff(16,plain,
% 48.38/48.62 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[15, 14])).
% 48.38/48.62 tff(17,plain,
% 48.38/48.62 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[16, 12])).
% 48.38/48.62 tff(18,plain,(
% 48.38/48.62 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 48.38/48.62 inference(skolemize,[status(sab)],[17])).
% 48.38/48.62 tff(19,plain,
% 48.38/48.62 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[18, 11])).
% 48.38/48.62 tff(20,plain,
% 48.38/48.62 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(C!12, A!14, B!13)) | element(C!12, powerset(cartesian_product2(A!14, B!13))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(C!12, A!14, B!13)) | element(C!12, powerset(cartesian_product2(A!14, B!13))))),
% 48.38/48.62 inference(rewrite,[status(thm)],[])).
% 48.38/48.62 tff(21,plain,
% 48.38/48.62 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(C!12, A!14, B!13)) | element(C!12, powerset(cartesian_product2(A!14, B!13))))),
% 48.38/48.62 inference(quant_inst,[status(thm)],[])).
% 48.38/48.62 tff(22,plain,
% 48.38/48.62 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(C!12, A!14, B!13)) | element(C!12, powerset(cartesian_product2(A!14, B!13)))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[21, 20])).
% 48.38/48.62 tff(23,plain,
% 48.38/48.62 (element(C!12, powerset(cartesian_product2(A!14, B!13)))),
% 48.38/48.62 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 48.38/48.62 tff(24,plain,
% 48.38/48.62 (^[A: $i, B: $i, C: $i] : refl((relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 48.38/48.62 inference(bind,[status(th)],[])).
% 48.38/48.62 tff(25,plain,
% 48.38/48.62 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 48.38/48.62 inference(quant_intro,[status(thm)],[24])).
% 48.38/48.62 tff(26,plain,
% 48.38/48.62 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 48.38/48.62 inference(rewrite,[status(thm)],[])).
% 48.38/48.62 tff(27,plain,
% 48.38/48.62 (^[A: $i, B: $i, C: $i] : rewrite((element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 48.38/48.62 inference(bind,[status(th)],[])).
% 48.38/48.62 tff(28,plain,
% 48.38/48.62 (![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 48.38/48.62 inference(quant_intro,[status(thm)],[27])).
% 48.38/48.62 tff(29,axiom,(![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_relset_1')).
% 48.38/48.62 tff(30,plain,
% 48.38/48.62 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[29, 28])).
% 48.38/48.62 tff(31,plain,
% 48.38/48.62 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[30, 26])).
% 48.38/48.62 tff(32,plain,(
% 48.38/48.62 ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 48.38/48.62 inference(skolemize,[status(sab)],[31])).
% 48.38/48.62 tff(33,plain,
% 48.38/48.62 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[32, 25])).
% 48.38/48.62 tff(34,plain,
% 48.38/48.62 (((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(C!12) | (~element(C!12, powerset(cartesian_product2(A!14, B!13)))))) <=> ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(C!12) | (~element(C!12, powerset(cartesian_product2(A!14, B!13)))))),
% 48.38/48.62 inference(rewrite,[status(thm)],[])).
% 48.38/48.62 tff(35,plain,
% 48.38/48.62 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(C!12) | (~element(C!12, powerset(cartesian_product2(A!14, B!13)))))),
% 48.38/48.62 inference(quant_inst,[status(thm)],[])).
% 48.38/48.62 tff(36,plain,
% 48.38/48.62 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(C!12) | (~element(C!12, powerset(cartesian_product2(A!14, B!13))))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[35, 34])).
% 48.38/48.62 tff(37,plain,
% 48.38/48.62 (relation(C!12)),
% 48.38/48.62 inference(unit_resolution,[status(thm)],[36, 33, 23])).
% 48.38/48.62 tff(38,plain,
% 48.38/48.62 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A))))))))))))),
% 48.38/48.62 inference(bind,[status(th)],[])).
% 48.38/48.62 tff(39,plain,
% 48.38/48.62 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))))))),
% 48.38/48.62 inference(quant_intro,[status(thm)],[38])).
% 48.38/48.62 tff(40,plain,
% 48.38/48.62 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A))))))))))))),
% 48.38/48.62 inference(bind,[status(th)],[])).
% 48.38/48.62 tff(41,plain,
% 48.38/48.62 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))))))),
% 48.38/48.62 inference(quant_intro,[status(thm)],[40])).
% 48.38/48.62 tff(42,plain,
% 48.38/48.62 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))))))),
% 48.38/48.62 inference(transitivity,[status(thm)],[41, 39])).
% 48.38/48.62 tff(43,plain,
% 48.38/48.62 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A)) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A))))))))))))),
% 48.38/48.62 inference(bind,[status(th)],[])).
% 48.38/48.62 tff(44,plain,
% 48.38/48.62 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A)) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))))))),
% 48.38/48.62 inference(quant_intro,[status(thm)],[43])).
% 48.38/48.62 tff(45,plain,
% 48.38/48.62 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 48.38/48.62 inference(rewrite,[status(thm)],[])).
% 48.38/48.62 tff(46,plain,
% 48.38/48.62 (^[A: $i] : rewrite((relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))))),
% 48.38/48.62 inference(bind,[status(th)],[])).
% 48.38/48.62 tff(47,plain,
% 48.38/48.62 (![A: $i] : (relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 48.38/48.62 inference(quant_intro,[status(thm)],[46])).
% 48.38/48.62 tff(48,axiom,(![A: $i] : (relation(A) => ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_relat_1')).
% 48.38/48.62 tff(49,plain,
% 48.38/48.62 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[48, 47])).
% 48.38/48.62 tff(50,plain,
% 48.38/48.62 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_dom(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(C, D), A))))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[49, 45])).
% 48.38/48.62 tff(51,plain,(
% 48.38/48.62 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_dom(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A))))) & ((B = relation_dom(A)) | ((in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A)) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))),
% 48.38/48.62 inference(skolemize,[status(sab)],[50])).
% 48.38/48.62 tff(52,plain,
% 48.38/48.62 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))))))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[51, 44])).
% 48.38/48.62 tff(53,plain,
% 48.38/48.62 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))))))),
% 48.38/48.62 inference(modus_ponens,[status(thm)],[52, 42])).
% 48.38/48.62 tff(54,plain,
% 48.38/48.62 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))))))) | ((~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))))))) | (~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12)))))))),
% 48.38/48.63 inference(rewrite,[status(thm)],[])).
% 48.38/48.63 tff(55,plain,
% 48.38/48.63 (((~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((B = relation_dom(C!12)) | (~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12))))))))))) <=> ((~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12)))))))),
% 48.38/48.63 inference(rewrite,[status(thm)],[])).
% 48.38/48.63 tff(56,plain,
% 48.38/48.63 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))))))) | ((~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((B = relation_dom(C!12)) | (~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))))))) | ((~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12))))))))),
% 48.38/48.63 inference(monotonicity,[status(thm)],[55])).
% 48.38/48.63 tff(57,plain,
% 48.38/48.63 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))))))) | ((~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((B = relation_dom(C!12)) | (~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))))))) | (~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12)))))))),
% 48.38/48.63 inference(transitivity,[status(thm)],[56, 54])).
% 48.38/48.63 tff(58,plain,
% 48.38/48.63 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))))))) | ((~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((B = relation_dom(C!12)) | (~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))))))))),
% 48.38/48.63 inference(quant_inst,[status(thm)],[])).
% 48.38/48.63 tff(59,plain,
% 48.38/48.63 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_dom(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, A)), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), A)))))))) | (~((B = relation_dom(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), A))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, A), D), A)))))))))))) | (~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12))))))),
% 48.38/48.63 inference(modus_ponens,[status(thm)],[58, 57])).
% 48.38/48.63 tff(60,plain,
% 48.38/48.63 (![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12))))))),
% 48.38/48.63 inference(unit_resolution,[status(thm)],[59, 53, 37])).
% 48.38/48.63 tff(61,plain,
% 48.38/48.63 (((~![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))),
% 48.38/48.63 inference(rewrite,[status(thm)],[])).
% 48.38/48.63 tff(62,plain,
% 48.38/48.63 ((~(~![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) <=> ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12))))))),
% 48.38/48.63 inference(rewrite,[status(thm)],[])).
% 48.38/48.63 tff(63,plain,
% 48.38/48.63 (((~![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12))))))) | $false) <=> (~![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))),
% 48.38/48.63 inference(rewrite,[status(thm)],[])).
% 48.38/48.63 tff(64,plain,
% 48.38/48.63 ((~$true) <=> $false),
% 48.38/48.63 inference(rewrite,[status(thm)],[])).
% 48.38/48.63 tff(65,plain,
% 48.38/48.63 (((~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))) | $true) <=> $true),
% 48.38/48.63 inference(rewrite,[status(thm)],[])).
% 48.38/48.63 tff(66,plain,
% 48.38/48.63 ((relation_dom(C!12) = relation_dom(C!12)) <=> $true),
% 48.38/48.63 inference(rewrite,[status(thm)],[])).
% 48.38/48.63 tff(67,plain,
% 48.38/48.63 (((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12))) <=> ((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))),
% 48.38/48.63 inference(rewrite,[status(thm)],[])).
% 48.38/48.63 tff(68,plain,
% 48.38/48.63 ((~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))) <=> (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12))))),
% 48.38/48.63 inference(monotonicity,[status(thm)],[67])).
% 48.38/48.63 tff(69,plain,
% 48.38/48.63 (((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12))))) <=> ((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))),
% 48.38/48.63 inference(monotonicity,[status(thm)],[68])).
% 48.38/48.63 tff(70,plain,
% 48.38/48.63 ((~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))) <=> (~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12))))))),
% 48.38/48.63 inference(monotonicity,[status(thm)],[69])).
% 48.38/48.63 tff(71,plain,
% 48.38/48.63 (((~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))) | (relation_dom(C!12) = relation_dom(C!12))) <=> ((~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))) | $true)),
% 48.38/48.63 inference(monotonicity,[status(thm)],[70, 66])).
% 48.38/48.63 tff(72,plain,
% 48.38/48.63 (((~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))) | (relation_dom(C!12) = relation_dom(C!12))) <=> $true),
% 48.38/48.63 inference(transitivity,[status(thm)],[71, 65])).
% 48.38/48.63 tff(73,plain,
% 48.38/48.63 ((~((~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))) | (relation_dom(C!12) = relation_dom(C!12)))) <=> (~$true)),
% 48.38/48.63 inference(monotonicity,[status(thm)],[72])).
% 48.38/48.63 tff(74,plain,
% 48.38/48.63 ((~((~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))) | (relation_dom(C!12) = relation_dom(C!12)))) <=> $false),
% 48.38/48.63 inference(transitivity,[status(thm)],[73, 64])).
% 48.38/48.63 tff(75,plain,
% 48.38/48.63 ((~((~(relation_dom(C!12) = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) <=> (~![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))),
% 48.38/48.63 inference(rewrite,[status(thm)],[])).
% 48.38/48.63 tff(76,plain,
% 48.38/48.63 (((~((~(relation_dom(C!12) = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))) | (relation_dom(C!12) = relation_dom(C!12))))) <=> ((~![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12))))))) | $false)),
% 48.38/48.63 inference(monotonicity,[status(thm)],[75, 74])).
% 48.38/48.63 tff(77,plain,
% 48.38/48.63 (((~((~(relation_dom(C!12) = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))) | (relation_dom(C!12) = relation_dom(C!12))))) <=> (~![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))),
% 48.38/48.63 inference(transitivity,[status(thm)],[76, 63])).
% 48.38/48.63 tff(78,plain,
% 48.38/48.63 ((~((~((~(relation_dom(C!12) = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))) | (relation_dom(C!12) = relation_dom(C!12)))))) <=> (~(~![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12))))))))),
% 48.38/48.63 inference(monotonicity,[status(thm)],[77])).
% 48.38/48.63 tff(79,plain,
% 48.38/48.63 ((~((~((~(relation_dom(C!12) = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))) | (relation_dom(C!12) = relation_dom(C!12)))))) <=> ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12))))))),
% 48.38/48.63 inference(transitivity,[status(thm)],[78, 62])).
% 48.38/48.63 tff(80,plain,
% 48.38/48.63 (((~![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12))))))) | (~((~((~(relation_dom(C!12) = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))) | (relation_dom(C!12) = relation_dom(C!12))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))),
% 48.38/48.63 inference(monotonicity,[status(thm)],[79])).
% 48.38/48.63 tff(81,plain,
% 48.38/48.63 (((~![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12))))))) | (~((~((~(relation_dom(C!12) = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))) | (relation_dom(C!12) = relation_dom(C!12))))))) <=> ((~![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))),
% 48.38/48.63 inference(transitivity,[status(thm)],[80, 61])).
% 48.38/48.63 tff(82,plain,
% 48.38/48.63 ((~![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12))))))) | (~((~((~(relation_dom(C!12) = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12)) | in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), tptp_fun_D_3(relation_dom(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_2(relation_dom(C!12), C!12), relation_dom(C!12))) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(relation_dom(C!12), C!12), D), C!12)))))) | (relation_dom(C!12) = relation_dom(C!12))))))),
% 48.38/48.63 inference(quant_inst,[status(thm)],[])).
% 48.38/48.63 tff(83,plain,
% 48.38/48.63 ((~![B: $i] : (~((~((~(B = relation_dom(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(C, D), C!12)))))))) | (~((~((~(in(tptp_fun_C_2(B, C!12), B) | in(ordered_pair(tptp_fun_C_2(B, C!12), tptp_fun_D_3(B, C!12)), C!12))) | (~((~in(tptp_fun_C_2(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_2(B, C!12), D), C!12)))))) | (B = relation_dom(C!12))))))) | ![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12))))))),
% 48.38/48.63 inference(modus_ponens,[status(thm)],[82, 81])).
% 48.38/48.63 tff(84,plain,
% 48.38/48.63 (![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12))))))),
% 48.38/48.63 inference(unit_resolution,[status(thm)],[83, 60])).
% 48.38/48.63 tff(85,plain,
% 48.38/48.63 ((~![C: $i] : (~((~((~in(C, relation_dom(C!12))) | in(ordered_pair(C, tptp_fun_D_1(C, C!12)), C!12))) | (~(in(C, relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(C, D), C!12))))))) | (~((~((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), C!12))) | (~(in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), D), C!12))))))),
% 48.38/48.63 inference(quant_inst,[status(thm)],[])).
% 48.38/48.63 tff(86,plain,
% 48.38/48.63 (~((~((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), C!12))) | (~(in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), D), C!12)))))),
% 48.38/48.63 inference(unit_resolution,[status(thm)],[85, 84])).
% 48.38/48.63 tff(87,plain,
% 48.38/48.63 (((~((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), C!12))) | (~(in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12)) | ![D: $i] : (~in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), D), C!12))))) | ((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), C!12))),
% 48.38/48.63 inference(tautology,[status(thm)],[])).
% 48.38/48.63 tff(88,plain,
% 48.38/48.63 ((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), C!12)),
% 48.38/48.63 inference(unit_resolution,[status(thm)],[87, 86])).
% 48.38/48.63 tff(89,assumption,(~((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14))), introduced(assumption)).
% 48.38/48.63 tff(90,plain,
% 48.38/48.63 (((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))),
% 48.38/48.63 inference(tautology,[status(thm)],[])).
% 48.38/48.63 tff(91,plain,
% 48.38/48.63 (in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))),
% 48.38/48.63 inference(unit_resolution,[status(thm)],[90, 89])).
% 48.38/48.63 tff(92,plain,
% 48.38/48.63 ((~((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), C!12))) | (~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), C!12)),
% 48.38/48.63 inference(tautology,[status(thm)],[])).
% 48.38/48.63 tff(93,plain,
% 48.38/48.63 ((~((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), C!12))) | in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), C!12)),
% 48.38/48.63 inference(unit_resolution,[status(thm)],[92, 91])).
% 48.38/48.63 tff(94,plain,
% 48.38/48.63 (in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), C!12)),
% 48.38/48.63 inference(unit_resolution,[status(thm)],[93, 88])).
% 48.38/48.63 tff(95,assumption,(((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13))), introduced(assumption)).
% 48.38/48.63 tff(96,plain,
% 48.38/48.63 (^[A: $i, B: $i, C: $i, D: $i] : refl((~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))),
% 48.38/48.63 inference(bind,[status(th)],[])).
% 48.38/48.63 tff(97,plain,
% 48.38/48.63 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 48.38/48.63 inference(quant_intro,[status(thm)],[96])).
% 48.38/48.63 tff(98,plain,
% 48.38/48.63 (^[A: $i, B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((in(A, C) & in(B, D)) <=> (~((~in(B, D)) | (~in(A, C))))), ((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(B, D)) | (~in(A, C))))))), rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(B, D)) | (~in(A, C))))) <=> (~(((~in(B, D)) | (~in(A, C))) <=> 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(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))), rewrite((~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(B, D)) | (~in(A, C))) <=> 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(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))))),
% 48.38/48.63 inference(bind,[status(th)],[])).
% 48.38/48.63 tff(99,plain,
% 48.38/48.63 (![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(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 48.38/48.63 inference(quant_intro,[status(thm)],[98])).
% 48.38/48.63 tff(100,plain,
% 48.38/48.63 (![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)))),
% 48.38/48.63 inference(rewrite,[status(thm)],[])).
% 48.38/48.63 tff(101,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t106_zfmisc_1')).
% 48.38/48.63 tff(102,plain,
% 48.38/48.63 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 48.38/48.63 inference(modus_ponens,[status(thm)],[101, 100])).
% 48.38/48.63 tff(103,plain,(
% 48.38/48.63 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 48.38/48.63 inference(skolemize,[status(sab)],[102])).
% 48.38/48.63 tff(104,plain,
% 48.38/48.63 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 48.38/48.63 inference(modus_ponens,[status(thm)],[103, 99])).
% 48.38/48.63 tff(105,plain,
% 48.38/48.63 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 48.38/48.63 inference(modus_ponens,[status(thm)],[104, 97])).
% 48.38/48.63 tff(106,plain,
% 48.38/48.63 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13)))))),
% 48.38/48.64 inference(rewrite,[status(thm)],[])).
% 48.38/48.64 tff(107,plain,
% 48.38/48.64 ((~(((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13)))) <=> (~(((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13))))),
% 48.38/48.64 inference(rewrite,[status(thm)],[])).
% 48.38/48.64 tff(108,plain,
% 48.38/48.64 ((((~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13)) | (~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13))) <=> (((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13)))),
% 48.38/48.64 inference(rewrite,[status(thm)],[])).
% 48.38/48.64 tff(109,plain,
% 48.38/48.64 ((~(((~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13)) | (~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13)))) <=> (~(((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13))))),
% 48.38/48.64 inference(monotonicity,[status(thm)],[108])).
% 48.38/48.64 tff(110,plain,
% 48.38/48.64 ((~(((~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13)) | (~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13)))) <=> (~(((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13))))),
% 48.38/48.64 inference(transitivity,[status(thm)],[109, 107])).
% 48.38/48.64 tff(111,plain,
% 48.38/48.64 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13)) | (~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13)))))),
% 48.38/48.64 inference(monotonicity,[status(thm)],[110])).
% 48.38/48.64 tff(112,plain,
% 48.38/48.64 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13)) | (~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13)))))),
% 48.38/48.64 inference(transitivity,[status(thm)],[111, 106])).
% 48.38/48.64 tff(113,plain,
% 48.38/48.64 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13)) | (~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13))))),
% 48.38/48.64 inference(quant_inst,[status(thm)],[])).
% 48.38/48.64 tff(114,plain,
% 48.38/48.64 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13))))),
% 48.38/48.64 inference(modus_ponens,[status(thm)],[113, 112])).
% 48.38/48.64 tff(115,plain,
% 48.38/48.64 ($false),
% 48.38/48.64 inference(unit_resolution,[status(thm)],[114, 105, 95])).
% 48.38/48.64 tff(116,plain,(~(((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13)))), inference(lemma,lemma(discharge,[]))).
% 48.38/48.64 tff(117,plain,
% 48.38/48.64 (((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14))),
% 48.38/48.64 inference(tautology,[status(thm)],[])).
% 48.38/48.64 tff(118,plain,
% 48.38/48.64 (~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)),
% 48.38/48.64 inference(unit_resolution,[status(thm)],[117, 89])).
% 48.38/48.64 tff(119,plain,
% 48.38/48.64 (((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))) | in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)),
% 48.38/48.64 inference(tautology,[status(thm)],[])).
% 48.38/48.64 tff(120,plain,
% 48.38/48.64 ((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))),
% 48.38/48.64 inference(unit_resolution,[status(thm)],[119, 118])).
% 48.38/48.64 tff(121,plain,
% 48.38/48.64 ((((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13))) <=> in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13))) | (~((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)) | (~in(tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12), B!13)))) | (~in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13)))),
% 48.38/48.64 inference(tautology,[status(thm)],[])).
% 48.38/48.64 tff(122,plain,
% 48.38/48.64 (~in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13))),
% 48.38/48.64 inference(unit_resolution,[status(thm)],[121, 120, 116])).
% 48.38/48.64 tff(123,plain,
% 48.38/48.64 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 48.38/48.64 inference(bind,[status(th)],[])).
% 48.38/48.64 tff(124,plain,
% 48.38/48.64 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 48.38/48.64 inference(quant_intro,[status(thm)],[123])).
% 48.38/48.64 tff(125,plain,
% 48.38/48.64 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 48.38/48.64 inference(bind,[status(th)],[])).
% 48.38/48.64 tff(126,plain,
% 48.38/48.64 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 48.38/48.64 inference(quant_intro,[status(thm)],[125])).
% 48.38/48.64 tff(127,plain,
% 48.38/48.64 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 48.38/48.64 inference(transitivity,[status(thm)],[126, 124])).
% 48.38/48.64 tff(128,plain,
% 48.38/48.64 (^[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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 48.38/48.64 inference(bind,[status(th)],[])).
% 48.38/48.64 tff(129,plain,
% 48.38/48.64 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 48.38/48.64 inference(quant_intro,[status(thm)],[128])).
% 48.38/48.64 tff(130,plain,
% 48.38/48.64 (![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)))),
% 48.38/48.64 inference(rewrite,[status(thm)],[])).
% 48.38/48.64 tff(131,plain,
% 48.38/48.64 (^[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))))),
% 48.38/48.64 inference(bind,[status(th)],[])).
% 48.38/48.64 tff(132,plain,
% 48.38/48.64 (![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)))),
% 48.38/48.64 inference(quant_intro,[status(thm)],[131])).
% 48.38/48.64 tff(133,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')).
% 48.38/48.64 tff(134,plain,
% 48.38/48.64 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 48.38/48.64 inference(modus_ponens,[status(thm)],[133, 132])).
% 48.38/48.64 tff(135,plain,
% 48.38/48.64 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 48.38/48.64 inference(modus_ponens,[status(thm)],[134, 130])).
% 48.38/48.64 tff(136,plain,(
% 48.38/48.64 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 48.38/48.64 inference(skolemize,[status(sab)],[135])).
% 48.38/48.64 tff(137,plain,
% 48.38/48.64 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 48.38/48.64 inference(modus_ponens,[status(thm)],[136, 129])).
% 48.38/48.64 tff(138,plain,
% 48.38/48.64 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 48.38/48.64 inference(modus_ponens,[status(thm)],[137, 127])).
% 48.38/48.64 tff(139,plain,
% 48.38/48.64 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(C!12, cartesian_product2(A!14, B!13))) | ![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13))))) | (~(subset(C!12, cartesian_product2(A!14, B!13)) | (~((~in(tptp_fun_C_0(cartesian_product2(A!14, B!13), C!12), C!12)) | in(tptp_fun_C_0(cartesian_product2(A!14, B!13), C!12), cartesian_product2(A!14, B!13))))))))),
% 48.38/48.64 inference(quant_inst,[status(thm)],[])).
% 48.38/48.64 tff(140,plain,
% 48.38/48.64 (~((~((~subset(C!12, cartesian_product2(A!14, B!13))) | ![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13))))) | (~(subset(C!12, cartesian_product2(A!14, B!13)) | (~((~in(tptp_fun_C_0(cartesian_product2(A!14, B!13), C!12), C!12)) | in(tptp_fun_C_0(cartesian_product2(A!14, B!13), C!12), cartesian_product2(A!14, B!13)))))))),
% 48.38/48.64 inference(unit_resolution,[status(thm)],[139, 138])).
% 48.38/48.64 tff(141,plain,
% 48.38/48.64 (((~((~subset(C!12, cartesian_product2(A!14, B!13))) | ![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13))))) | (~(subset(C!12, cartesian_product2(A!14, B!13)) | (~((~in(tptp_fun_C_0(cartesian_product2(A!14, B!13), C!12), C!12)) | in(tptp_fun_C_0(cartesian_product2(A!14, B!13), C!12), cartesian_product2(A!14, B!13))))))) | ((~subset(C!12, cartesian_product2(A!14, B!13))) | ![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13))))),
% 48.38/48.64 inference(tautology,[status(thm)],[])).
% 48.38/48.64 tff(142,plain,
% 48.38/48.64 ((~subset(C!12, cartesian_product2(A!14, B!13))) | ![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13)))),
% 48.38/48.64 inference(unit_resolution,[status(thm)],[141, 140])).
% 48.38/48.64 tff(143,plain,
% 48.38/48.64 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 48.38/48.64 inference(bind,[status(th)],[])).
% 48.38/48.64 tff(144,plain,
% 48.38/48.64 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 48.38/48.64 inference(quant_intro,[status(thm)],[143])).
% 48.38/48.64 tff(145,plain,
% 48.38/48.64 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 48.38/48.64 inference(rewrite,[status(thm)],[])).
% 48.38/48.64 tff(146,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 48.38/48.64 tff(147,plain,
% 48.38/48.64 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 48.38/48.64 inference(modus_ponens,[status(thm)],[146, 145])).
% 48.38/48.64 tff(148,plain,(
% 48.38/48.64 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 48.38/48.64 inference(skolemize,[status(sab)],[147])).
% 48.38/48.64 tff(149,plain,
% 48.38/48.64 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 48.38/48.64 inference(modus_ponens,[status(thm)],[148, 144])).
% 48.38/48.64 tff(150,plain,
% 48.38/48.64 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(C!12, powerset(cartesian_product2(A!14, B!13))) <=> subset(C!12, cartesian_product2(A!14, B!13)))),
% 48.38/48.64 inference(quant_inst,[status(thm)],[])).
% 48.38/48.64 tff(151,plain,
% 48.38/48.64 (element(C!12, powerset(cartesian_product2(A!14, B!13))) <=> subset(C!12, cartesian_product2(A!14, B!13))),
% 48.38/48.64 inference(unit_resolution,[status(thm)],[150, 149])).
% 48.48/48.64 tff(152,plain,
% 48.48/48.64 ((~(element(C!12, powerset(cartesian_product2(A!14, B!13))) <=> subset(C!12, cartesian_product2(A!14, B!13)))) | (~element(C!12, powerset(cartesian_product2(A!14, B!13)))) | subset(C!12, cartesian_product2(A!14, B!13))),
% 48.48/48.64 inference(tautology,[status(thm)],[])).
% 48.48/48.64 tff(153,plain,
% 48.48/48.64 ((~(element(C!12, powerset(cartesian_product2(A!14, B!13))) <=> subset(C!12, cartesian_product2(A!14, B!13)))) | subset(C!12, cartesian_product2(A!14, B!13))),
% 48.48/48.64 inference(unit_resolution,[status(thm)],[152, 23])).
% 48.48/48.64 tff(154,plain,
% 48.48/48.64 (subset(C!12, cartesian_product2(A!14, B!13))),
% 48.48/48.64 inference(unit_resolution,[status(thm)],[153, 151])).
% 48.48/48.64 tff(155,plain,
% 48.48/48.64 ((~((~subset(C!12, cartesian_product2(A!14, B!13))) | ![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13))))) | (~subset(C!12, cartesian_product2(A!14, B!13))) | ![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13)))),
% 48.48/48.64 inference(tautology,[status(thm)],[])).
% 48.48/48.64 tff(156,plain,
% 48.48/48.64 ((~((~subset(C!12, cartesian_product2(A!14, B!13))) | ![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13))))) | ![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13)))),
% 48.48/48.64 inference(unit_resolution,[status(thm)],[155, 154])).
% 48.48/48.64 tff(157,plain,
% 48.48/48.64 (![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13)))),
% 48.48/48.64 inference(unit_resolution,[status(thm)],[156, 142])).
% 48.48/48.64 tff(158,plain,
% 48.48/48.64 (((~![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13)))) | ((~in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), C!12)) | in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13)))) <=> ((~![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13)))) | (~in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), C!12)) | in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13)))),
% 48.48/48.64 inference(rewrite,[status(thm)],[])).
% 48.48/48.64 tff(159,plain,
% 48.48/48.64 ((~![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13)))) | ((~in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), C!12)) | in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13)))),
% 48.48/48.64 inference(quant_inst,[status(thm)],[])).
% 48.48/48.64 tff(160,plain,
% 48.48/48.64 ((~![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13)))) | (~in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), C!12)) | in(ordered_pair(tptp_fun_C_0(A!14, relation_dom(C!12)), tptp_fun_D_1(tptp_fun_C_0(A!14, relation_dom(C!12)), C!12)), cartesian_product2(A!14, B!13))),
% 48.48/48.64 inference(modus_ponens,[status(thm)],[159, 158])).
% 48.48/48.64 tff(161,plain,
% 48.48/48.64 ($false),
% 48.48/48.64 inference(unit_resolution,[status(thm)],[160, 157, 122, 94])).
% 48.48/48.64 tff(162,plain,((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)), inference(lemma,lemma(discharge,[]))).
% 48.48/48.64 tff(163,assumption,((~((~subset(relation_rng(C!12), B!13)) | ![C: $i] : ((~in(C, relation_rng(C!12))) | in(C, B!13)))) | (~(subset(relation_rng(C!12), B!13) | (~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)))))), introduced(assumption)).
% 48.48/48.64 tff(164,plain,
% 48.48/48.64 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(relation_rng(C!12), B!13)) | ![C: $i] : ((~in(C, relation_rng(C!12))) | in(C, B!13)))) | (~(subset(relation_rng(C!12), B!13) | (~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)))))))),
% 48.48/48.64 inference(quant_inst,[status(thm)],[])).
% 48.48/48.64 tff(165,plain,
% 48.48/48.64 ($false),
% 48.48/48.64 inference(unit_resolution,[status(thm)],[164, 138, 163])).
% 48.48/48.64 tff(166,plain,(~((~((~subset(relation_rng(C!12), B!13)) | ![C: $i] : ((~in(C, relation_rng(C!12))) | in(C, B!13)))) | (~(subset(relation_rng(C!12), B!13) | (~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13))))))), inference(lemma,lemma(discharge,[]))).
% 48.48/48.64 tff(167,plain,
% 48.48/48.64 (((~((~subset(relation_rng(C!12), B!13)) | ![C: $i] : ((~in(C, relation_rng(C!12))) | in(C, B!13)))) | (~(subset(relation_rng(C!12), B!13) | (~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)))))) | (subset(relation_rng(C!12), B!13) | (~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13))))),
% 48.48/48.64 inference(tautology,[status(thm)],[])).
% 48.48/48.64 tff(168,plain,
% 48.48/48.64 (subset(relation_rng(C!12), B!13) | (~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)))),
% 48.48/48.64 inference(unit_resolution,[status(thm)],[167, 166])).
% 48.48/48.64 tff(169,plain,
% 48.48/48.64 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A))))))))))))),
% 48.48/48.64 inference(bind,[status(th)],[])).
% 48.48/48.64 tff(170,plain,
% 48.48/48.64 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))))))),
% 48.48/48.64 inference(quant_intro,[status(thm)],[169])).
% 48.48/48.64 tff(171,plain,
% 48.48/48.64 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A))))))))))))),
% 48.48/48.64 inference(bind,[status(th)],[])).
% 48.48/48.64 tff(172,plain,
% 48.48/48.64 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))))))),
% 48.48/48.64 inference(quant_intro,[status(thm)],[171])).
% 48.48/48.64 tff(173,plain,
% 48.48/48.64 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))))))),
% 48.48/48.64 inference(transitivity,[status(thm)],[172, 170])).
% 48.48/48.64 tff(174,plain,
% 48.48/48.64 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A)) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A))))))))))))),
% 48.48/48.64 inference(bind,[status(th)],[])).
% 48.48/48.64 tff(175,plain,
% 48.48/48.64 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A)) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))))))),
% 48.48/48.64 inference(quant_intro,[status(thm)],[174])).
% 48.48/48.64 tff(176,plain,
% 48.48/48.64 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 48.48/48.64 inference(rewrite,[status(thm)],[])).
% 48.48/48.64 tff(177,plain,
% 48.48/48.64 (^[A: $i] : rewrite((relation(A) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))) <=> ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))))),
% 48.48/48.64 inference(bind,[status(th)],[])).
% 48.48/48.64 tff(178,plain,
% 48.48/48.64 (![A: $i] : (relation(A) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 48.48/48.64 inference(quant_intro,[status(thm)],[177])).
% 48.48/48.64 tff(179,axiom,(![A: $i] : (relation(A) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_relat_1')).
% 48.48/48.64 tff(180,plain,
% 48.48/48.64 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 48.48/48.64 inference(modus_ponens,[status(thm)],[179, 178])).
% 48.48/48.64 tff(181,plain,
% 48.48/48.64 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 48.48/48.64 inference(modus_ponens,[status(thm)],[180, 176])).
% 48.48/48.64 tff(182,plain,(
% 48.48/48.64 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A)) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))),
% 48.48/48.64 inference(skolemize,[status(sab)],[181])).
% 48.48/48.64 tff(183,plain,
% 48.48/48.64 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))))))),
% 48.48/48.64 inference(modus_ponens,[status(thm)],[182, 175])).
% 48.48/48.64 tff(184,plain,
% 48.48/48.64 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))))))),
% 48.48/48.64 inference(modus_ponens,[status(thm)],[183, 173])).
% 48.48/48.64 tff(185,plain,
% 48.48/48.64 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))))))) | ((~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))))))) | (~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12)))))))),
% 48.48/48.65 inference(rewrite,[status(thm)],[])).
% 48.48/48.65 tff(186,plain,
% 48.48/48.65 (((~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((B = relation_rng(C!12)) | (~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12))))))))))) <=> ((~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12)))))))),
% 48.48/48.65 inference(rewrite,[status(thm)],[])).
% 48.48/48.65 tff(187,plain,
% 48.48/48.65 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))))))) | ((~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((B = relation_rng(C!12)) | (~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))))))) | ((~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12))))))))),
% 48.48/48.65 inference(monotonicity,[status(thm)],[186])).
% 48.48/48.65 tff(188,plain,
% 48.48/48.65 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))))))) | ((~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((B = relation_rng(C!12)) | (~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))))))) | (~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12)))))))),
% 48.48/48.65 inference(transitivity,[status(thm)],[187, 185])).
% 48.48/48.65 tff(189,plain,
% 48.48/48.65 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))))))) | ((~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((B = relation_rng(C!12)) | (~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))))))))),
% 48.48/48.65 inference(quant_inst,[status(thm)],[])).
% 48.48/48.65 tff(190,plain,
% 48.48/48.65 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | in(ordered_pair(tptp_fun_D_6(B, A), tptp_fun_C_5(B, A)), A))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, A)), A)))))))))))) | (~relation(C!12)) | ![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12))))))),
% 48.48/48.65 inference(modus_ponens,[status(thm)],[189, 188])).
% 48.48/48.65 tff(191,plain,
% 48.48/48.65 (![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12))))))),
% 48.48/48.65 inference(unit_resolution,[status(thm)],[190, 184, 37])).
% 48.48/48.65 tff(192,plain,
% 48.48/48.65 (((~![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))),
% 48.48/48.65 inference(rewrite,[status(thm)],[])).
% 48.48/48.65 tff(193,plain,
% 48.48/48.65 ((~(~![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) <=> ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12))))))),
% 48.48/48.65 inference(rewrite,[status(thm)],[])).
% 48.48/48.65 tff(194,plain,
% 48.48/48.65 (((~![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12))))))) | $false) <=> (~![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))),
% 48.48/48.65 inference(rewrite,[status(thm)],[])).
% 48.48/48.65 tff(195,plain,
% 48.48/48.65 (((~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))) | $true) <=> $true),
% 48.48/48.65 inference(rewrite,[status(thm)],[])).
% 48.48/48.65 tff(196,plain,
% 48.48/48.65 ((relation_rng(C!12) = relation_rng(C!12)) <=> $true),
% 48.48/48.65 inference(rewrite,[status(thm)],[])).
% 48.48/48.65 tff(197,plain,
% 48.48/48.65 (((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) <=> ((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))),
% 48.48/48.65 inference(rewrite,[status(thm)],[])).
% 48.48/48.65 tff(198,plain,
% 48.48/48.65 ((~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))) <=> (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))))),
% 48.48/48.65 inference(monotonicity,[status(thm)],[197])).
% 48.48/48.65 tff(199,plain,
% 48.48/48.65 (((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))))) <=> ((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))),
% 48.48/48.65 inference(monotonicity,[status(thm)],[198])).
% 48.48/48.65 tff(200,plain,
% 48.48/48.65 ((~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))) <=> (~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))))))),
% 48.48/48.65 inference(monotonicity,[status(thm)],[199])).
% 48.48/48.65 tff(201,plain,
% 48.48/48.65 (((~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))) | (relation_rng(C!12) = relation_rng(C!12))) <=> ((~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))) | $true)),
% 48.48/48.65 inference(monotonicity,[status(thm)],[200, 196])).
% 48.48/48.65 tff(202,plain,
% 48.48/48.65 (((~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))) | (relation_rng(C!12) = relation_rng(C!12))) <=> $true),
% 48.48/48.65 inference(transitivity,[status(thm)],[201, 195])).
% 48.48/48.65 tff(203,plain,
% 48.48/48.65 ((~((~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))) | (relation_rng(C!12) = relation_rng(C!12)))) <=> (~$true)),
% 48.48/48.65 inference(monotonicity,[status(thm)],[202])).
% 48.48/48.65 tff(204,plain,
% 48.48/48.65 ((~((~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))) | (relation_rng(C!12) = relation_rng(C!12)))) <=> $false),
% 48.48/48.65 inference(transitivity,[status(thm)],[203, 64])).
% 48.48/48.65 tff(205,plain,
% 48.48/48.65 ((~((~(relation_rng(C!12) = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) <=> (~![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))),
% 48.48/48.65 inference(rewrite,[status(thm)],[])).
% 48.48/48.65 tff(206,plain,
% 48.48/48.65 (((~((~(relation_rng(C!12) = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))) | (relation_rng(C!12) = relation_rng(C!12))))) <=> ((~![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12))))))) | $false)),
% 48.48/48.65 inference(monotonicity,[status(thm)],[205, 204])).
% 48.48/48.65 tff(207,plain,
% 48.48/48.65 (((~((~(relation_rng(C!12) = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))) | (relation_rng(C!12) = relation_rng(C!12))))) <=> (~![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))),
% 48.48/48.65 inference(transitivity,[status(thm)],[206, 194])).
% 48.48/48.65 tff(208,plain,
% 48.48/48.65 ((~((~((~(relation_rng(C!12) = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))) | (relation_rng(C!12) = relation_rng(C!12)))))) <=> (~(~![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12))))))))),
% 48.48/48.65 inference(monotonicity,[status(thm)],[207])).
% 48.48/48.65 tff(209,plain,
% 48.48/48.65 ((~((~((~(relation_rng(C!12) = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))) | (relation_rng(C!12) = relation_rng(C!12)))))) <=> ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12))))))),
% 48.48/48.65 inference(transitivity,[status(thm)],[208, 193])).
% 48.48/48.65 tff(210,plain,
% 48.48/48.65 (((~![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12))))))) | (~((~((~(relation_rng(C!12) = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))) | (relation_rng(C!12) = relation_rng(C!12))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))),
% 48.48/48.65 inference(monotonicity,[status(thm)],[209])).
% 48.48/48.65 tff(211,plain,
% 48.48/48.65 (((~![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12))))))) | (~((~((~(relation_rng(C!12) = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))) | (relation_rng(C!12) = relation_rng(C!12))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))),
% 48.48/48.65 inference(transitivity,[status(thm)],[210, 192])).
% 48.48/48.65 tff(212,plain,
% 48.48/48.65 ((~![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12))))))) | (~((~((~(relation_rng(C!12) = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12)) | in(ordered_pair(tptp_fun_D_6(relation_rng(C!12), C!12), tptp_fun_C_5(relation_rng(C!12), C!12)), C!12))) | (~((~in(tptp_fun_C_5(relation_rng(C!12), C!12), relation_rng(C!12))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(relation_rng(C!12), C!12)), C!12)))))) | (relation_rng(C!12) = relation_rng(C!12))))))),
% 48.48/48.65 inference(quant_inst,[status(thm)],[])).
% 48.48/48.65 tff(213,plain,
% 48.48/48.65 ((~![B: $i] : (~((~((~(B = relation_rng(C!12))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!12)))))))) | (~((~((~(in(tptp_fun_C_5(B, C!12), B) | in(ordered_pair(tptp_fun_D_6(B, C!12), tptp_fun_C_5(B, C!12)), C!12))) | (~((~in(tptp_fun_C_5(B, C!12), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_5(B, C!12)), C!12)))))) | (B = relation_rng(C!12))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12))))))),
% 48.48/48.65 inference(modus_ponens,[status(thm)],[212, 211])).
% 48.48/48.65 tff(214,plain,
% 48.48/48.65 (![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12))))))),
% 48.48/48.65 inference(unit_resolution,[status(thm)],[213, 191])).
% 48.48/48.65 tff(215,plain,
% 48.48/48.65 ((~![C: $i] : (~((~((~in(C, relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(C, C!12), C), C!12))) | (~(in(C, relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, C), C!12))))))) | (~((~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), C!12))) | (~(in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_0(B!13, relation_rng(C!12))), C!12))))))),
% 48.48/48.65 inference(quant_inst,[status(thm)],[])).
% 48.48/48.65 tff(216,plain,
% 48.48/48.65 (~((~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), C!12))) | (~(in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_0(B!13, relation_rng(C!12))), C!12)))))),
% 48.48/48.65 inference(unit_resolution,[status(thm)],[215, 214])).
% 48.48/48.65 tff(217,plain,
% 48.48/48.65 (((~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), C!12))) | (~(in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_0(B!13, relation_rng(C!12))), C!12))))) | ((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), C!12))),
% 48.48/48.65 inference(tautology,[status(thm)],[])).
% 48.48/48.65 tff(218,plain,
% 48.48/48.65 ((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), C!12)),
% 48.48/48.65 inference(unit_resolution,[status(thm)],[217, 216])).
% 48.48/48.65 tff(219,assumption,(~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13))), introduced(assumption)).
% 48.48/48.65 tff(220,plain,
% 48.48/48.65 (((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))),
% 48.48/48.65 inference(tautology,[status(thm)],[])).
% 48.48/48.65 tff(221,plain,
% 48.48/48.65 (in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))),
% 48.48/48.65 inference(unit_resolution,[status(thm)],[220, 219])).
% 48.48/48.65 tff(222,plain,
% 48.48/48.65 ((~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), C!12))) | (~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), C!12)),
% 48.48/48.65 inference(tautology,[status(thm)],[])).
% 48.48/48.65 tff(223,plain,
% 48.48/48.65 ((~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), C!12))) | in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), C!12)),
% 48.48/48.65 inference(unit_resolution,[status(thm)],[222, 221])).
% 48.48/48.65 tff(224,plain,
% 48.48/48.65 (in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), C!12)),
% 48.48/48.65 inference(unit_resolution,[status(thm)],[223, 218])).
% 48.48/48.65 tff(225,assumption,(((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)) | (~in(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), A!14))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), cartesian_product2(A!14, B!13))), introduced(assumption)).
% 48.48/48.65 tff(226,plain,
% 48.48/48.65 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(B, D)) | (~in(A, C))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)) | (~in(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), A!14))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), cartesian_product2(A!14, B!13))))),
% 48.48/48.66 inference(quant_inst,[status(thm)],[])).
% 48.48/48.66 tff(227,plain,
% 48.48/48.66 ($false),
% 48.48/48.66 inference(unit_resolution,[status(thm)],[226, 105, 225])).
% 48.48/48.66 tff(228,plain,(~(((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)) | (~in(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), A!14))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), cartesian_product2(A!14, B!13)))), inference(lemma,lemma(discharge,[]))).
% 48.48/48.66 tff(229,plain,
% 48.48/48.66 (((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)) | (~in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13))),
% 48.48/48.66 inference(tautology,[status(thm)],[])).
% 48.48/48.66 tff(230,plain,
% 48.48/48.66 (~in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)),
% 48.48/48.66 inference(unit_resolution,[status(thm)],[229, 219])).
% 48.48/48.66 tff(231,plain,
% 48.48/48.66 (((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)) | (~in(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), A!14))) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)),
% 48.48/48.66 inference(tautology,[status(thm)],[])).
% 48.48/48.66 tff(232,plain,
% 48.48/48.66 ((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)) | (~in(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), A!14))),
% 48.48/48.66 inference(unit_resolution,[status(thm)],[231, 230])).
% 48.48/48.66 tff(233,plain,
% 48.48/48.66 ((((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)) | (~in(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), A!14))) <=> in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), cartesian_product2(A!14, B!13))) | (~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)) | (~in(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), A!14)))) | (~in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), cartesian_product2(A!14, B!13)))),
% 48.48/48.66 inference(tautology,[status(thm)],[])).
% 48.48/48.66 tff(234,plain,
% 48.48/48.66 (~in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), cartesian_product2(A!14, B!13))),
% 48.48/48.66 inference(unit_resolution,[status(thm)],[233, 232, 228])).
% 48.48/48.66 tff(235,plain,
% 48.48/48.66 (((~![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13)))) | ((~in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), C!12)) | in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), cartesian_product2(A!14, B!13)))) <=> ((~![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13)))) | (~in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), C!12)) | in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), cartesian_product2(A!14, B!13)))),
% 48.48/48.66 inference(rewrite,[status(thm)],[])).
% 48.48/48.66 tff(236,plain,
% 48.48/48.66 ((~![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13)))) | ((~in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), C!12)) | in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), cartesian_product2(A!14, B!13)))),
% 48.48/48.66 inference(quant_inst,[status(thm)],[])).
% 48.48/48.66 tff(237,plain,
% 48.48/48.66 ((~![C: $i] : ((~in(C, C!12)) | in(C, cartesian_product2(A!14, B!13)))) | (~in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), C!12)) | in(ordered_pair(tptp_fun_D_4(tptp_fun_C_0(B!13, relation_rng(C!12)), C!12), tptp_fun_C_0(B!13, relation_rng(C!12))), cartesian_product2(A!14, B!13))),
% 48.48/48.66 inference(modus_ponens,[status(thm)],[236, 235])).
% 48.48/48.66 tff(238,plain,
% 48.48/48.66 ($false),
% 48.48/48.66 inference(unit_resolution,[status(thm)],[237, 157, 234, 224])).
% 48.48/48.66 tff(239,plain,((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)), inference(lemma,lemma(discharge,[]))).
% 48.48/48.66 tff(240,plain,
% 48.48/48.66 ((~(subset(relation_rng(C!12), B!13) | (~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13))))) | subset(relation_rng(C!12), B!13) | (~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13)))),
% 48.48/48.66 inference(tautology,[status(thm)],[])).
% 48.48/48.66 tff(241,plain,
% 48.48/48.66 ((~(subset(relation_rng(C!12), B!13) | (~((~in(tptp_fun_C_0(B!13, relation_rng(C!12)), relation_rng(C!12))) | in(tptp_fun_C_0(B!13, relation_rng(C!12)), B!13))))) | subset(relation_rng(C!12), B!13)),
% 48.48/48.66 inference(unit_resolution,[status(thm)],[240, 239])).
% 48.48/48.66 tff(242,plain,
% 48.48/48.66 (subset(relation_rng(C!12), B!13)),
% 48.48/48.66 inference(unit_resolution,[status(thm)],[241, 168])).
% 48.48/48.66 tff(243,plain,
% 48.48/48.66 ((~(~((~subset(relation_dom(C!12), A!14)) | (~subset(relation_rng(C!12), B!13))))) <=> ((~subset(relation_dom(C!12), A!14)) | (~subset(relation_rng(C!12), B!13)))),
% 48.48/48.66 inference(rewrite,[status(thm)],[])).
% 48.48/48.66 tff(244,plain,
% 48.48/48.66 ((subset(relation_dom(C!12), A!14) & subset(relation_rng(C!12), B!13)) <=> (~((~subset(relation_dom(C!12), A!14)) | (~subset(relation_rng(C!12), B!13))))),
% 48.48/48.66 inference(rewrite,[status(thm)],[])).
% 48.48/48.66 tff(245,plain,
% 48.48/48.66 ((~(subset(relation_dom(C!12), A!14) & subset(relation_rng(C!12), B!13))) <=> (~(~((~subset(relation_dom(C!12), A!14)) | (~subset(relation_rng(C!12), B!13)))))),
% 48.48/48.66 inference(monotonicity,[status(thm)],[244])).
% 48.48/48.66 tff(246,plain,
% 48.48/48.66 ((~(subset(relation_dom(C!12), A!14) & subset(relation_rng(C!12), B!13))) <=> ((~subset(relation_dom(C!12), A!14)) | (~subset(relation_rng(C!12), B!13)))),
% 48.48/48.66 inference(transitivity,[status(thm)],[245, 243])).
% 48.48/48.66 tff(247,plain,
% 48.48/48.66 (~(subset(relation_dom(C!12), A!14) & subset(relation_rng(C!12), B!13))),
% 48.48/48.66 inference(or_elim,[status(thm)],[8])).
% 48.48/48.66 tff(248,plain,
% 48.48/48.66 ((~subset(relation_dom(C!12), A!14)) | (~subset(relation_rng(C!12), B!13))),
% 48.48/48.66 inference(modus_ponens,[status(thm)],[247, 246])).
% 48.48/48.66 tff(249,plain,
% 48.48/48.66 (~subset(relation_dom(C!12), A!14)),
% 48.48/48.66 inference(unit_resolution,[status(thm)],[248, 242])).
% 48.48/48.66 tff(250,plain,
% 48.48/48.66 ((~(subset(relation_dom(C!12), A!14) | (~((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14))))) | subset(relation_dom(C!12), A!14) | (~((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)))),
% 48.48/48.66 inference(tautology,[status(thm)],[])).
% 48.48/48.66 tff(251,plain,
% 48.48/48.66 (~(subset(relation_dom(C!12), A!14) | (~((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14))))),
% 48.48/48.66 inference(unit_resolution,[status(thm)],[250, 249, 162])).
% 48.48/48.66 tff(252,plain,
% 48.48/48.66 (((~((~subset(relation_dom(C!12), A!14)) | ![C: $i] : ((~in(C, relation_dom(C!12))) | in(C, A!14)))) | (~(subset(relation_dom(C!12), A!14) | (~((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)))))) | (subset(relation_dom(C!12), A!14) | (~((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14))))),
% 48.48/48.66 inference(tautology,[status(thm)],[])).
% 48.48/48.66 tff(253,plain,
% 48.48/48.66 ((~((~subset(relation_dom(C!12), A!14)) | ![C: $i] : ((~in(C, relation_dom(C!12))) | in(C, A!14)))) | (~(subset(relation_dom(C!12), A!14) | (~((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)))))),
% 48.48/48.66 inference(unit_resolution,[status(thm)],[252, 251])).
% 48.48/48.66 tff(254,plain,
% 48.48/48.66 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(relation_dom(C!12), A!14)) | ![C: $i] : ((~in(C, relation_dom(C!12))) | in(C, A!14)))) | (~(subset(relation_dom(C!12), A!14) | (~((~in(tptp_fun_C_0(A!14, relation_dom(C!12)), relation_dom(C!12))) | in(tptp_fun_C_0(A!14, relation_dom(C!12)), A!14)))))))),
% 48.48/48.67 inference(quant_inst,[status(thm)],[])).
% 48.48/48.67 tff(255,plain,
% 48.48/48.67 ($false),
% 48.48/48.67 inference(unit_resolution,[status(thm)],[254, 138, 253])).
% 48.48/48.67 % SZS output end Proof
% 48.48/48.68 % E exiting
%------------------------------------------------------------------------------