%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU243+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:27:22 AM UTC 2025
% Result : Theorem 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU243+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n011.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 06:28:41 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.18/0.36 % SZS status Theorem
% 0.18/0.36 % SZS output start Proof
% 0.18/0.36 tff(disjoint_type, type, (
% 0.18/0.36 disjoint: ( $i * $i ) > $o)).
% 0.18/0.36 tff(tptp_fun_B_1_type, type, (
% 0.18/0.36 tptp_fun_B_1: $i > $i)).
% 0.18/0.36 tff(tptp_fun_A_10_type, type, (
% 0.18/0.36 tptp_fun_A_10: $i)).
% 0.18/0.36 tff(fiber_type, type, (
% 0.18/0.36 fiber: ( $i * $i ) > $i)).
% 0.18/0.36 tff(tptp_fun_D_2_type, type, (
% 0.18/0.36 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.18/0.36 tff(in_type, type, (
% 0.18/0.36 in: ( $i * $i ) > $o)).
% 0.18/0.36 tff(subset_type, type, (
% 0.18/0.36 subset: ( $i * $i ) > $o)).
% 0.18/0.36 tff(set_union2_type, type, (
% 0.18/0.36 set_union2: ( $i * $i ) > $i)).
% 0.18/0.36 tff(relation_rng_type, type, (
% 0.18/0.36 relation_rng: $i > $i)).
% 0.18/0.36 tff(relation_dom_type, type, (
% 0.18/0.36 relation_dom: $i > $i)).
% 0.18/0.36 tff(relation_field_type, type, (
% 0.18/0.36 relation_field: $i > $i)).
% 0.18/0.36 tff(relation_type, type, (
% 0.18/0.36 relation: $i > $o)).
% 0.18/0.36 tff(is_well_founded_in_type, type, (
% 0.18/0.36 is_well_founded_in: ( $i * $i ) > $o)).
% 0.18/0.36 tff(well_founded_relation_type, type, (
% 0.18/0.36 well_founded_relation: $i > $o)).
% 0.18/0.36 tff(empty_set_type, type, (
% 0.18/0.36 empty_set: $i)).
% 0.18/0.36 tff(tptp_fun_C_3_type, type, (
% 0.18/0.36 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.18/0.36 tff(tptp_fun_C_0_type, type, (
% 0.18/0.36 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.18/0.36 tff(1,plain,
% 0.18/0.36 ((~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))) <=> (~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A)))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(2,plain,
% 0.18/0.36 ((~![A: $i] : (relation(A) => (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))) <=> (~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A)))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(3,axiom,(~![A: $i] : (relation(A) => (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_wellord1')).
% 0.18/0.36 tff(4,plain,
% 0.18/0.36 (~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.18/0.36 tff(5,plain,
% 0.18/0.36 (~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.18/0.36 tff(6,plain,
% 0.18/0.36 (~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.18/0.36 tff(7,plain,
% 0.18/0.36 (~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.18/0.36 tff(8,plain,(
% 0.18/0.36 ~((~relation(A!10)) | (well_founded_relation(A!10) <=> is_well_founded_in(A!10, relation_field(A!10))))),
% 0.18/0.36 inference(skolemize,[status(sab)],[7])).
% 0.18/0.36 tff(9,plain,
% 0.18/0.36 (relation(A!10)),
% 0.18/0.36 inference(or_elim,[status(thm)],[8])).
% 0.18/0.36 tff(10,plain,
% 0.18/0.36 (^[A: $i] : refl(((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(11,plain,
% 0.18/0.36 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.18/0.36 tff(12,plain,
% 0.18/0.36 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(13,plain,
% 0.18/0.36 (^[A: $i] : rewrite((relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(14,plain,
% 0.18/0.36 (![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.36 tff(15,axiom,(![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_relat_1')).
% 0.18/0.36 tff(16,plain,
% 0.18/0.36 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.36 tff(17,plain,
% 0.18/0.36 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.18/0.36 tff(18,plain,(
% 0.18/0.36 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.18/0.36 inference(skolemize,[status(sab)],[17])).
% 0.18/0.36 tff(19,plain,
% 0.18/0.36 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.18/0.36 tff(20,plain,
% 0.18/0.36 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!10)) | (relation_field(A!10) = set_union2(relation_dom(A!10), relation_rng(A!10))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!10)) | (relation_field(A!10) = set_union2(relation_dom(A!10), relation_rng(A!10))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(21,plain,
% 0.18/0.36 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!10)) | (relation_field(A!10) = set_union2(relation_dom(A!10), relation_rng(A!10))))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(22,plain,
% 0.18/0.36 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!10)) | (relation_field(A!10) = set_union2(relation_dom(A!10), relation_rng(A!10)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.36 tff(23,plain,
% 0.18/0.36 (relation_field(A!10) = set_union2(relation_dom(A!10), relation_rng(A!10))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.18/0.36 tff(24,plain,
% 0.18/0.36 (set_union2(relation_dom(A!10), relation_rng(A!10)) = relation_field(A!10)),
% 0.18/0.36 inference(symmetry,[status(thm)],[23])).
% 0.18/0.36 tff(25,plain,
% 0.18/0.36 (subset(tptp_fun_B_1(A!10), set_union2(relation_dom(A!10), relation_rng(A!10))) <=> subset(tptp_fun_B_1(A!10), relation_field(A!10))),
% 0.18/0.36 inference(monotonicity,[status(thm)],[24])).
% 0.18/0.36 tff(26,plain,
% 0.18/0.36 (subset(tptp_fun_B_1(A!10), relation_field(A!10)) <=> subset(tptp_fun_B_1(A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))),
% 0.18/0.36 inference(symmetry,[status(thm)],[25])).
% 0.18/0.36 tff(27,plain,
% 0.18/0.36 (subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), relation_field(A!10)) <=> subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))),
% 0.18/0.36 inference(monotonicity,[status(thm)],[23])).
% 0.18/0.36 tff(28,plain,
% 0.18/0.36 (subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10))) <=> subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), relation_field(A!10))),
% 0.18/0.36 inference(symmetry,[status(thm)],[27])).
% 0.18/0.36 tff(29,plain,
% 0.18/0.36 (is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) <=> is_well_founded_in(A!10, relation_field(A!10))),
% 0.18/0.36 inference(monotonicity,[status(thm)],[24])).
% 0.18/0.36 tff(30,plain,
% 0.18/0.36 (is_well_founded_in(A!10, relation_field(A!10)) <=> is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))),
% 0.18/0.36 inference(symmetry,[status(thm)],[29])).
% 0.18/0.36 tff(31,plain,
% 0.18/0.36 ((~is_well_founded_in(A!10, relation_field(A!10))) <=> (~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))))),
% 0.18/0.36 inference(monotonicity,[status(thm)],[30])).
% 0.18/0.36 tff(32,assumption,(~is_well_founded_in(A!10, relation_field(A!10))), introduced(assumption)).
% 0.18/0.36 tff(33,plain,
% 0.18/0.36 (~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.18/0.36 tff(34,plain,
% 0.18/0.36 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A)))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A)))))))))))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(35,plain,
% 0.18/0.36 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A)))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))))))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[34])).
% 0.18/0.36 tff(36,plain,
% 0.18/0.36 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A)))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A)))))))))))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(37,plain,
% 0.18/0.36 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A)))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))))))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[36])).
% 0.18/0.36 tff(38,plain,
% 0.18/0.36 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A)))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))))))),
% 0.18/0.36 inference(transitivity,[status(thm)],[37, 35])).
% 0.18/0.36 tff(39,plain,
% 0.18/0.36 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~is_well_founded_in(A, B)) | ![C: $i] : ((~subset(C, B)) | (C = empty_set) | (in(tptp_fun_D_2(C, A), C) & disjoint(fiber(A, tptp_fun_D_2(C, A)), C)))) & (is_well_founded_in(A, B) | (subset(tptp_fun_C_3(B, A), B) & (~(tptp_fun_C_3(B, A) = empty_set)) & ![D: $i] : (~(in(D, tptp_fun_C_3(B, A)) & disjoint(fiber(A, D), tptp_fun_C_3(B, A)))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A)))))))))))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(40,plain,
% 0.18/0.36 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_well_founded_in(A, B)) | ![C: $i] : ((~subset(C, B)) | (C = empty_set) | (in(tptp_fun_D_2(C, A), C) & disjoint(fiber(A, tptp_fun_D_2(C, A)), C)))) & (is_well_founded_in(A, B) | (subset(tptp_fun_C_3(B, A), B) & (~(tptp_fun_C_3(B, A) = empty_set)) & ![D: $i] : (~(in(D, tptp_fun_C_3(B, A)) & disjoint(fiber(A, D), tptp_fun_C_3(B, A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))))))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[39])).
% 0.18/0.36 tff(41,plain,
% 0.18/0.36 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~(subset(C, B) & (~(C = empty_set)) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~(subset(C, B) & (~(C = empty_set)) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C)))))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(42,plain,
% 0.18/0.36 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((is_well_founded_in(A, B) <=> ![C: $i] : (~((subset(C, B) & (~(C = empty_set))) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C)))))) <=> (is_well_founded_in(A, B) <=> ![C: $i] : (~(subset(C, B) & (~(C = empty_set)) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C)))))))), (![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~((subset(C, B) & (~(C = empty_set))) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C)))))) <=> ![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~(subset(C, B) & (~(C = empty_set)) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C)))))))), ((relation(A) => ![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~((subset(C, B) & (~(C = empty_set))) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C))))))) <=> (relation(A) => ![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~(subset(C, B) & (~(C = empty_set)) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C))))))))), rewrite((relation(A) => ![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~(subset(C, B) & (~(C = empty_set)) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C))))))) <=> ((~relation(A)) | ![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~(subset(C, B) & (~(C = empty_set)) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C)))))))), ((relation(A) => ![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~((subset(C, B) & (~(C = empty_set))) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C))))))) <=> ((~relation(A)) | ![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~(subset(C, B) & (~(C = empty_set)) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C)))))))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(43,plain,
% 0.18/0.36 (![A: $i] : (relation(A) => ![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~((subset(C, B) & (~(C = empty_set))) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~(subset(C, B) & (~(C = empty_set)) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C)))))))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[42])).
% 0.18/0.36 tff(44,axiom,(![A: $i] : (relation(A) => ![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~((subset(C, B) & (~(C = empty_set))) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_wellord1')).
% 0.18/0.36 tff(45,plain,
% 0.18/0.36 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~(subset(C, B) & (~(C = empty_set)) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C)))))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.36 tff(46,plain,
% 0.18/0.36 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_well_founded_in(A, B) <=> ![C: $i] : (~(subset(C, B) & (~(C = empty_set)) & ![D: $i] : (~(in(D, C) & disjoint(fiber(A, D), C)))))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.18/0.36 tff(47,plain,(
% 0.18/0.36 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_well_founded_in(A, B)) | ![C: $i] : ((~subset(C, B)) | (C = empty_set) | (in(tptp_fun_D_2(C, A), C) & disjoint(fiber(A, tptp_fun_D_2(C, A)), C)))) & (is_well_founded_in(A, B) | (subset(tptp_fun_C_3(B, A), B) & (~(tptp_fun_C_3(B, A) = empty_set)) & ![D: $i] : (~(in(D, tptp_fun_C_3(B, A)) & disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))),
% 0.18/0.36 inference(skolemize,[status(sab)],[46])).
% 0.18/0.36 tff(48,plain,
% 0.18/0.36 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.18/0.36 tff(49,plain,
% 0.18/0.36 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.18/0.36 tff(50,plain,
% 0.18/0.36 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))))))) | ((~relation(A!10)) | ![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))))))) | (~relation(A!10)) | ![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set))))))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(51,plain,
% 0.18/0.36 (((~relation(A!10)) | ![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((tptp_fun_C_3(B, A!10) = empty_set) | (~subset(tptp_fun_C_3(B, A!10), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10)))))))))))) <=> ((~relation(A!10)) | ![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set))))))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(52,plain,
% 0.18/0.36 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))))))) | ((~relation(A!10)) | ![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((tptp_fun_C_3(B, A!10) = empty_set) | (~subset(tptp_fun_C_3(B, A!10), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))))))) | ((~relation(A!10)) | ![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set)))))))))),
% 0.18/0.36 inference(monotonicity,[status(thm)],[51])).
% 0.18/0.36 tff(53,plain,
% 0.18/0.36 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))))))) | ((~relation(A!10)) | ![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((tptp_fun_C_3(B, A!10) = empty_set) | (~subset(tptp_fun_C_3(B, A!10), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))))))) | (~relation(A!10)) | ![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set))))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[52, 50])).
% 0.18/0.37 tff(54,plain,
% 0.18/0.37 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))))))) | ((~relation(A!10)) | ![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((tptp_fun_C_3(B, A!10) = empty_set) | (~subset(tptp_fun_C_3(B, A!10), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))))))))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(55,plain,
% 0.18/0.37 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_well_founded_in(A, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A), C)) | (~disjoint(fiber(A, tptp_fun_D_2(C, A)), C))))))) | (~(is_well_founded_in(A, B) | (~((tptp_fun_C_3(B, A) = empty_set) | (~subset(tptp_fun_C_3(B, A), B)) | (~![D: $i] : ((~in(D, tptp_fun_C_3(B, A))) | (~disjoint(fiber(A, D), tptp_fun_C_3(B, A))))))))))))) | (~relation(A!10)) | ![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set)))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.18/0.37 tff(56,plain,
% 0.18/0.37 (![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set)))))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[55, 49, 9])).
% 0.18/0.37 tff(57,plain,
% 0.18/0.37 (((~![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set)))))))) | (~((~((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10))))))) | (~(is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))))))))))) <=> ((~![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set)))))))) | (~((~((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10))))))) | (~(is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))))))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(58,plain,
% 0.18/0.37 ((~((~((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set))))))) <=> (~((~((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10))))))) | (~(is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))))))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(59,plain,
% 0.18/0.37 (((~![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set)))))))) | (~((~((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set)))))))) <=> ((~![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set)))))))) | (~((~((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10))))))) | (~(is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))))))))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[58])).
% 0.18/0.37 tff(60,plain,
% 0.18/0.37 (((~![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set)))))))) | (~((~((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set)))))))) <=> ((~![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set)))))))) | (~((~((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10))))))) | (~(is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))))))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[59, 57])).
% 0.18/0.37 tff(61,plain,
% 0.18/0.37 ((~![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set)))))))) | (~((~((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set)))))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(62,plain,
% 0.18/0.37 ((~![B: $i] : (~((~((~is_well_founded_in(A!10, B)) | ![C: $i] : ((C = empty_set) | (~subset(C, B)) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C))))))) | (~(is_well_founded_in(A!10, B) | (~((~![D: $i] : ((~in(D, tptp_fun_C_3(B, A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(B, A!10))))) | (~subset(tptp_fun_C_3(B, A!10), B)) | (tptp_fun_C_3(B, A!10) = empty_set)))))))) | (~((~((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10))))))) | (~(is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))))))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.18/0.37 tff(63,plain,
% 0.18/0.37 (~((~((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10))))))) | (~(is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))))))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[62, 56])).
% 0.18/0.37 tff(64,plain,
% 0.18/0.37 (((~((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10))))))) | (~(is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))))))))) | (is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))))))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(65,plain,
% 0.18/0.37 (is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.18/0.37 tff(66,plain,
% 0.18/0.37 ((~(is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))))))) | is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))))))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(67,plain,
% 0.18/0.37 (is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.18/0.37 tff(68,plain,
% 0.18/0.37 (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[67, 33])).
% 0.18/0.37 tff(69,plain,
% 0.18/0.37 (((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))))) | subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(70,plain,
% 0.18/0.37 (subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.18/0.37 tff(71,plain,
% 0.18/0.37 (subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), relation_field(A!10))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[70, 28])).
% 0.18/0.37 tff(72,plain,
% 0.18/0.37 (((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))))) | (~(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(73,plain,
% 0.18/0.37 (~(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[72, 68])).
% 0.18/0.37 tff(74,plain,
% 0.18/0.37 (~(well_founded_relation(A!10) <=> is_well_founded_in(A!10, relation_field(A!10)))),
% 0.18/0.37 inference(or_elim,[status(thm)],[8])).
% 0.18/0.37 tff(75,plain,
% 0.18/0.37 ((well_founded_relation(A!10) <=> is_well_founded_in(A!10, relation_field(A!10))) | well_founded_relation(A!10) | is_well_founded_in(A!10, relation_field(A!10))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(76,plain,
% 0.18/0.37 (well_founded_relation(A!10) | is_well_founded_in(A!10, relation_field(A!10))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.18/0.37 tff(77,plain,
% 0.18/0.37 (well_founded_relation(A!10)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[76, 32])).
% 0.18/0.37 tff(78,plain,
% 0.18/0.37 (^[A: $i] : refl(((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A)))))))))))) <=> ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A)))))))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(79,plain,
% 0.18/0.37 (![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A)))))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A))))))))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[78])).
% 0.18/0.37 tff(80,plain,
% 0.18/0.37 (^[A: $i] : rewrite(((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A)))))))))))) <=> ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A)))))))))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(81,plain,
% 0.18/0.38 (![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A)))))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A))))))))))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[80])).
% 0.18/0.38 tff(82,plain,
% 0.18/0.38 (![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A)))))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A))))))))))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[81, 79])).
% 0.18/0.38 tff(83,plain,
% 0.18/0.38 (^[A: $i] : rewrite(((~relation(A)) | (((~well_founded_relation(A)) | ![B: $i] : ((~subset(B, relation_field(A))) | (B = empty_set) | (in(tptp_fun_C_0(B, A), B) & disjoint(fiber(A, tptp_fun_C_0(B, A)), B)))) & (well_founded_relation(A) | (subset(tptp_fun_B_1(A), relation_field(A)) & (~(tptp_fun_B_1(A) = empty_set)) & ![C: $i] : (~(in(C, tptp_fun_B_1(A)) & disjoint(fiber(A, C), tptp_fun_B_1(A)))))))) <=> ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A)))))))))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(84,plain,
% 0.18/0.38 (![A: $i] : ((~relation(A)) | (((~well_founded_relation(A)) | ![B: $i] : ((~subset(B, relation_field(A))) | (B = empty_set) | (in(tptp_fun_C_0(B, A), B) & disjoint(fiber(A, tptp_fun_C_0(B, A)), B)))) & (well_founded_relation(A) | (subset(tptp_fun_B_1(A), relation_field(A)) & (~(tptp_fun_B_1(A) = empty_set)) & ![C: $i] : (~(in(C, tptp_fun_B_1(A)) & disjoint(fiber(A, C), tptp_fun_B_1(A)))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A))))))))))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.38 tff(85,plain,
% 0.18/0.38 (![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> ![B: $i] : (~(subset(B, relation_field(A)) & (~(B = empty_set)) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B))))))) <=> ![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> ![B: $i] : (~(subset(B, relation_field(A)) & (~(B = empty_set)) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B)))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(86,plain,
% 0.18/0.38 (^[A: $i] : trans(monotonicity(rewrite((well_founded_relation(A) <=> ![B: $i] : (~((subset(B, relation_field(A)) & (~(B = empty_set))) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B)))))) <=> (well_founded_relation(A) <=> ![B: $i] : (~(subset(B, relation_field(A)) & (~(B = empty_set)) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B))))))), ((relation(A) => (well_founded_relation(A) <=> ![B: $i] : (~((subset(B, relation_field(A)) & (~(B = empty_set))) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B))))))) <=> (relation(A) => (well_founded_relation(A) <=> ![B: $i] : (~(subset(B, relation_field(A)) & (~(B = empty_set)) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B))))))))), rewrite((relation(A) => (well_founded_relation(A) <=> ![B: $i] : (~(subset(B, relation_field(A)) & (~(B = empty_set)) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B))))))) <=> ((~relation(A)) | (well_founded_relation(A) <=> ![B: $i] : (~(subset(B, relation_field(A)) & (~(B = empty_set)) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B)))))))), ((relation(A) => (well_founded_relation(A) <=> ![B: $i] : (~((subset(B, relation_field(A)) & (~(B = empty_set))) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B))))))) <=> ((~relation(A)) | (well_founded_relation(A) <=> ![B: $i] : (~(subset(B, relation_field(A)) & (~(B = empty_set)) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B)))))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(87,plain,
% 0.18/0.38 (![A: $i] : (relation(A) => (well_founded_relation(A) <=> ![B: $i] : (~((subset(B, relation_field(A)) & (~(B = empty_set))) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B))))))) <=> ![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> ![B: $i] : (~(subset(B, relation_field(A)) & (~(B = empty_set)) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B)))))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.38 tff(88,axiom,(![A: $i] : (relation(A) => (well_founded_relation(A) <=> ![B: $i] : (~((subset(B, relation_field(A)) & (~(B = empty_set))) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_wellord1')).
% 0.18/0.38 tff(89,plain,
% 0.18/0.38 (![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> ![B: $i] : (~(subset(B, relation_field(A)) & (~(B = empty_set)) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B)))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.38 tff(90,plain,
% 0.18/0.38 (![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> ![B: $i] : (~(subset(B, relation_field(A)) & (~(B = empty_set)) & ![C: $i] : (~(in(C, B) & disjoint(fiber(A, C), B)))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.18/0.38 tff(91,plain,(
% 0.18/0.38 ![A: $i] : ((~relation(A)) | (((~well_founded_relation(A)) | ![B: $i] : ((~subset(B, relation_field(A))) | (B = empty_set) | (in(tptp_fun_C_0(B, A), B) & disjoint(fiber(A, tptp_fun_C_0(B, A)), B)))) & (well_founded_relation(A) | (subset(tptp_fun_B_1(A), relation_field(A)) & (~(tptp_fun_B_1(A) = empty_set)) & ![C: $i] : (~(in(C, tptp_fun_B_1(A)) & disjoint(fiber(A, C), tptp_fun_B_1(A))))))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[90])).
% 0.18/0.38 tff(92,plain,
% 0.18/0.38 (![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A))))))))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.18/0.38 tff(93,plain,
% 0.18/0.38 (![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A))))))))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.18/0.38 tff(94,plain,
% 0.18/0.38 (((~![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A))))))))))))) | ((~relation(A!10)) | (~((~((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))) | (~(well_founded_relation(A!10) | (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A))))))))))))) | (~relation(A!10)) | (~((~((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))) | (~(well_founded_relation(A!10) | (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set))))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(95,plain,
% 0.18/0.38 (((~relation(A!10)) | (~((~((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))) | (~(well_founded_relation(A!10) | (~((tptp_fun_B_1(A!10) = empty_set) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10)))))))))))) <=> ((~relation(A!10)) | (~((~((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))) | (~(well_founded_relation(A!10) | (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set))))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(96,plain,
% 0.18/0.38 (((~![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A))))))))))))) | ((~relation(A!10)) | (~((~((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))) | (~(well_founded_relation(A!10) | (~((tptp_fun_B_1(A!10) = empty_set) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A))))))))))))) | ((~relation(A!10)) | (~((~((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))) | (~(well_founded_relation(A!10) | (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set)))))))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[95])).
% 0.18/0.38 tff(97,plain,
% 0.18/0.38 (((~![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A))))))))))))) | ((~relation(A!10)) | (~((~((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))) | (~(well_founded_relation(A!10) | (~((tptp_fun_B_1(A!10) = empty_set) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A))))))))))))) | (~relation(A!10)) | (~((~((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))) | (~(well_founded_relation(A!10) | (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set))))))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[96, 94])).
% 0.18/0.38 tff(98,plain,
% 0.18/0.38 ((~![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A))))))))))))) | ((~relation(A!10)) | (~((~((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))) | (~(well_founded_relation(A!10) | (~((tptp_fun_B_1(A!10) = empty_set) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))))))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(99,plain,
% 0.18/0.38 ((~![A: $i] : ((~relation(A)) | (~((~((~well_founded_relation(A)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A))) | (~((~in(tptp_fun_C_0(B, A), B)) | (~disjoint(fiber(A, tptp_fun_C_0(B, A)), B))))))) | (~(well_founded_relation(A) | (~((tptp_fun_B_1(A) = empty_set) | (~subset(tptp_fun_B_1(A), relation_field(A))) | (~![C: $i] : ((~in(C, tptp_fun_B_1(A))) | (~disjoint(fiber(A, C), tptp_fun_B_1(A))))))))))))) | (~relation(A!10)) | (~((~((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))) | (~(well_founded_relation(A!10) | (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set)))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.38 tff(100,plain,
% 0.18/0.38 (~((~((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))) | (~(well_founded_relation(A!10) | (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[99, 93, 9])).
% 0.18/0.38 tff(101,plain,
% 0.18/0.38 (((~((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))) | (~(well_founded_relation(A!10) | (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set)))))) | ((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(102,plain,
% 0.18/0.38 ((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B)))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.18/0.38 tff(103,plain,
% 0.18/0.38 ((~((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))) | (~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B)))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(104,plain,
% 0.18/0.38 ((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B)))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.18/0.38 tff(105,plain,
% 0.18/0.38 (![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B)))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[104, 77])).
% 0.18/0.38 tff(106,plain,
% 0.18/0.38 (((~![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B)))))) | ((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), relation_field(A!10))) | (~((~in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))))) <=> ((~![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B)))))) | (tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), relation_field(A!10))) | (~((~in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(107,plain,
% 0.18/0.38 ((~![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B)))))) | ((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), relation_field(A!10))) | (~((~in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(108,plain,
% 0.18/0.38 ((~![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B)))))) | (tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), relation_field(A!10))) | (~((~in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.18/0.38 tff(109,plain,
% 0.18/0.38 ((~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), relation_field(A!10))) | (~((~in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[108, 105, 73])).
% 0.18/0.38 tff(110,plain,
% 0.18/0.38 (~((~in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[109, 71])).
% 0.18/0.38 tff(111,plain,
% 0.18/0.38 (((~in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))) | disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(112,plain,
% 0.18/0.38 (disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.18/0.38 tff(113,plain,
% 0.18/0.38 (((~in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))) | in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(114,plain,
% 0.18/0.39 (in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[113, 110])).
% 0.18/0.39 tff(115,plain,
% 0.18/0.39 (((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))))) | ![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(116,plain,
% 0.18/0.39 (![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[115, 68])).
% 0.18/0.39 tff(117,plain,
% 0.18/0.39 (((~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))) | ((~in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))) <=> ((~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))) | (~in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(118,plain,
% 0.18/0.39 ((~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))) | ((~in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(119,plain,
% 0.18/0.39 ((~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))) | (~in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.18/0.39 tff(120,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[119, 116, 114, 112])).
% 0.18/0.39 tff(121,plain,(is_well_founded_in(A!10, relation_field(A!10))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(122,plain,
% 0.18/0.39 ((well_founded_relation(A!10) <=> is_well_founded_in(A!10, relation_field(A!10))) | (~well_founded_relation(A!10)) | (~is_well_founded_in(A!10, relation_field(A!10)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(123,plain,
% 0.18/0.39 ((~well_founded_relation(A!10)) | (~is_well_founded_in(A!10, relation_field(A!10)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[122, 74])).
% 0.18/0.39 tff(124,plain,
% 0.18/0.39 (~well_founded_relation(A!10)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[123, 121])).
% 0.18/0.39 tff(125,plain,
% 0.18/0.39 (((~((~well_founded_relation(A!10)) | ![B: $i] : ((B = empty_set) | (~subset(B, relation_field(A!10))) | (~((~in(tptp_fun_C_0(B, A!10), B)) | (~disjoint(fiber(A!10, tptp_fun_C_0(B, A!10)), B))))))) | (~(well_founded_relation(A!10) | (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set)))))) | (well_founded_relation(A!10) | (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(126,plain,
% 0.18/0.39 (well_founded_relation(A!10) | (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[125, 100])).
% 0.18/0.39 tff(127,plain,
% 0.18/0.39 ((~(well_founded_relation(A!10) | (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set))))) | well_founded_relation(A!10) | (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(128,plain,
% 0.18/0.39 (well_founded_relation(A!10) | (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.18/0.39 tff(129,plain,
% 0.18/0.39 (~((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[128, 124])).
% 0.18/0.39 tff(130,plain,
% 0.18/0.39 (((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set)) | subset(tptp_fun_B_1(A!10), relation_field(A!10))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(131,plain,
% 0.18/0.39 (subset(tptp_fun_B_1(A!10), relation_field(A!10))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.18/0.39 tff(132,plain,
% 0.18/0.39 (subset(tptp_fun_B_1(A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[131, 26])).
% 0.18/0.39 tff(133,plain,
% 0.18/0.39 (is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[121, 30])).
% 0.18/0.39 tff(134,plain,
% 0.18/0.39 (((~((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10))))))) | (~(is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10))) | (~((tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set) | (~subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))))))))) | ((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10))))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(135,plain,
% 0.18/0.39 ((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[134, 63])).
% 0.18/0.39 tff(136,plain,
% 0.18/0.39 ((~((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10))))))) | (~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(137,plain,
% 0.18/0.39 ((~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))) | ![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.18/0.39 tff(138,plain,
% 0.18/0.39 (![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[137, 133])).
% 0.18/0.39 tff(139,plain,
% 0.18/0.39 (((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set)) | (~(tptp_fun_B_1(A!10) = empty_set))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(140,plain,
% 0.18/0.39 (~(tptp_fun_B_1(A!10) = empty_set)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[139, 129])).
% 0.18/0.39 tff(141,plain,
% 0.18/0.39 (((~![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))))) | ((tptp_fun_B_1(A!10) = empty_set) | (~subset(tptp_fun_B_1(A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))))))) <=> ((~![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))))) | (tptp_fun_B_1(A!10) = empty_set) | (~subset(tptp_fun_B_1(A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(142,plain,
% 0.18/0.39 (((tptp_fun_B_1(A!10) = empty_set) | (~((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), set_union2(relation_dom(A!10), relation_rng(A!10))))) <=> ((tptp_fun_B_1(A!10) = empty_set) | (~subset(tptp_fun_B_1(A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(143,plain,
% 0.18/0.39 (((~![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))))) | ((tptp_fun_B_1(A!10) = empty_set) | (~((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))))) <=> ((~![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))))) | ((tptp_fun_B_1(A!10) = empty_set) | (~subset(tptp_fun_B_1(A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10)))))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[142])).
% 0.18/0.39 tff(144,plain,
% 0.18/0.39 (((~![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))))) | ((tptp_fun_B_1(A!10) = empty_set) | (~((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))))) <=> ((~![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))))) | (tptp_fun_B_1(A!10) = empty_set) | (~subset(tptp_fun_B_1(A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[143, 141])).
% 0.18/0.39 tff(145,plain,
% 0.18/0.39 ((~![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))))) | ((tptp_fun_B_1(A!10) = empty_set) | (~((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(146,plain,
% 0.18/0.39 ((~![C: $i] : ((C = empty_set) | (~((~in(tptp_fun_D_2(C, A!10), C)) | (~disjoint(fiber(A!10, tptp_fun_D_2(C, A!10)), C)))) | (~subset(C, set_union2(relation_dom(A!10), relation_rng(A!10)))))) | (tptp_fun_B_1(A!10) = empty_set) | (~subset(tptp_fun_B_1(A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))) | (~((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.18/0.39 tff(147,plain,
% 0.18/0.39 (~((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[146, 140, 138, 132])).
% 0.18/0.39 tff(148,plain,
% 0.18/0.39 (((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10)))) | disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(149,plain,
% 0.18/0.39 (disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.18/0.39 tff(150,plain,
% 0.18/0.39 (((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10)))) | in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(151,plain,
% 0.18/0.39 (in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[150, 147])).
% 0.18/0.39 tff(152,plain,
% 0.18/0.39 (((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~subset(tptp_fun_B_1(A!10), relation_field(A!10))) | (tptp_fun_B_1(A!10) = empty_set)) | ![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(153,plain,
% 0.18/0.39 (![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[152, 129])).
% 0.18/0.39 tff(154,plain,
% 0.18/0.39 (((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | ((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))))) <=> ((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(155,plain,
% 0.18/0.39 ((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | ((~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(156,plain,
% 0.18/0.39 ((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.18/0.39 tff(157,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[156, 153, 151, 149])).
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------