TSTP Solution File: SEU243+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU243+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:28:27 EDT 2022
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU243+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 11:11:32 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(disjoint_type, type, (
% 0.14/0.41 disjoint: ( $i * $i ) > $o)).
% 0.14/0.41 tff(tptp_fun_B_1_type, type, (
% 0.14/0.41 tptp_fun_B_1: $i > $i)).
% 0.14/0.41 tff(tptp_fun_A_10_type, type, (
% 0.14/0.41 tptp_fun_A_10: $i)).
% 0.14/0.41 tff(fiber_type, type, (
% 0.14/0.41 fiber: ( $i * $i ) > $i)).
% 0.14/0.41 tff(tptp_fun_D_2_type, type, (
% 0.14/0.41 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.14/0.41 tff(in_type, type, (
% 0.14/0.41 in: ( $i * $i ) > $o)).
% 0.14/0.41 tff(subset_type, type, (
% 0.14/0.41 subset: ( $i * $i ) > $o)).
% 0.14/0.41 tff(set_union2_type, type, (
% 0.14/0.41 set_union2: ( $i * $i ) > $i)).
% 0.14/0.41 tff(relation_rng_type, type, (
% 0.14/0.41 relation_rng: $i > $i)).
% 0.14/0.41 tff(relation_dom_type, type, (
% 0.14/0.41 relation_dom: $i > $i)).
% 0.14/0.41 tff(relation_field_type, type, (
% 0.14/0.41 relation_field: $i > $i)).
% 0.14/0.41 tff(relation_type, type, (
% 0.14/0.41 relation: $i > $o)).
% 0.14/0.41 tff(is_well_founded_in_type, type, (
% 0.14/0.41 is_well_founded_in: ( $i * $i ) > $o)).
% 0.14/0.41 tff(well_founded_relation_type, type, (
% 0.14/0.41 well_founded_relation: $i > $o)).
% 0.14/0.41 tff(empty_set_type, type, (
% 0.14/0.41 empty_set: $i)).
% 0.14/0.41 tff(tptp_fun_C_3_type, type, (
% 0.14/0.41 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.14/0.41 tff(tptp_fun_C_0_type, type, (
% 0.14/0.41 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.14/0.41 tff(1,plain,
% 0.14/0.41 ((~![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)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 ((~![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)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(3,axiom,(~![A: $i] : (relation(A) => (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t5_wellord1')).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 (~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 (~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 (~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.14/0.41 tff(11,plain,(
% 0.14/0.41 ~((~relation(A!10)) | (well_founded_relation(A!10) <=> is_well_founded_in(A!10, relation_field(A!10))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[10])).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (relation(A!10)),
% 0.14/0.41 inference(or_elim,[status(thm)],[11])).
% 0.14/0.41 tff(13,plain,
% 0.14/0.41 (^[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)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 (![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))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 (![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))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(16,plain,
% 0.14/0.41 (^[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)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(17,plain,
% 0.14/0.41 (![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))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.14/0.41 tff(18,axiom,(![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_relat_1')).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.14/0.41 tff(20,plain,
% 0.14/0.41 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.14/0.41 tff(21,plain,(
% 0.14/0.41 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[20])).
% 0.14/0.41 tff(22,plain,
% 0.14/0.41 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.14/0.41 tff(23,plain,
% 0.14/0.41 (((~![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))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 ((~![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))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(25,plain,
% 0.14/0.41 ((~![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)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 (relation_field(A!10) = set_union2(relation_dom(A!10), relation_rng(A!10))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.14/0.41 tff(27,plain,
% 0.14/0.41 (set_union2(relation_dom(A!10), relation_rng(A!10)) = relation_field(A!10)),
% 0.14/0.41 inference(symmetry,[status(thm)],[26])).
% 0.14/0.41 tff(28,plain,
% 0.14/0.41 (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))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[27])).
% 0.14/0.41 tff(29,plain,
% 0.14/0.41 (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)))),
% 0.14/0.41 inference(symmetry,[status(thm)],[28])).
% 0.14/0.41 tff(30,plain,
% 0.14/0.41 (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)))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[26])).
% 0.14/0.41 tff(31,plain,
% 0.14/0.41 (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))),
% 0.14/0.41 inference(symmetry,[status(thm)],[30])).
% 0.14/0.41 tff(32,plain,
% 0.14/0.41 (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))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[27])).
% 0.14/0.41 tff(33,plain,
% 0.14/0.41 (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)))),
% 0.14/0.41 inference(symmetry,[status(thm)],[32])).
% 0.14/0.41 tff(34,plain,
% 0.14/0.41 ((~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))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[33])).
% 0.14/0.41 tff(35,assumption,(~is_well_founded_in(A!10, relation_field(A!10))), introduced(assumption)).
% 0.14/0.41 tff(36,plain,
% 0.14/0.41 (~is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.14/0.41 tff(37,plain,
% 0.14/0.41 (^[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)))))))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(38,plain,
% 0.14/0.41 (![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))))))))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.14/0.41 tff(39,plain,
% 0.14/0.41 (^[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)))))))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(40,plain,
% 0.14/0.41 (![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))))))))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.14/0.41 tff(41,plain,
% 0.14/0.41 (![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))))))))))))),
% 0.14/0.41 inference(transitivity,[status(thm)],[40, 38])).
% 0.14/0.41 tff(42,plain,
% 0.14/0.41 (^[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)))))))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(43,plain,
% 0.14/0.41 (![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))))))))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.14/0.41 tff(44,plain,
% 0.14/0.41 (^[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] : ((~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)))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(45,plain,
% 0.14/0.41 (![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] : ((~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))))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.14/0.41 tff(46,plain,
% 0.14/0.41 (![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)))))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(47,plain,
% 0.14/0.41 (^[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)))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(48,plain,
% 0.14/0.41 (![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)))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.14/0.41 tff(49,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/sandbox2/benchmark/theBenchmark.p','d3_wellord1')).
% 0.14/0.41 tff(50,plain,
% 0.14/0.41 (![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)))))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.14/0.41 tff(51,plain,
% 0.14/0.41 (![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)))))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.14/0.41 tff(52,plain,(
% 0.14/0.41 ![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))))))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[51])).
% 0.14/0.41 tff(53,plain,
% 0.14/0.41 (![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))))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.14/0.42 tff(54,plain,
% 0.14/0.42 (![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))))))))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.14/0.42 tff(55,plain,
% 0.14/0.42 (![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))))))))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[54, 41])).
% 0.14/0.42 tff(56,plain,
% 0.14/0.42 (((~![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) | (~((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))))))))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(57,plain,
% 0.14/0.42 ((~![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))))))))))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(58,plain,
% 0.14/0.42 ((~![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)))))))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.14/0.42 tff(59,plain,
% 0.14/0.42 (![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)))))))))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[58, 55, 12])).
% 0.14/0.42 tff(60,plain,
% 0.14/0.42 (((~![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)))))))))))) | (~((~((~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) | (~((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)))))))))))) | (~((~((~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))))))))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(61,plain,
% 0.14/0.42 ((~((~((~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))) | (~((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))))))) | (~(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)))))))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(62,plain,
% 0.14/0.42 (((~![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)))))))))))) | (~((~((~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))) | (~((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) | (~((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)))))))))))) | (~((~((~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))))))))))))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[61])).
% 0.14/0.42 tff(63,plain,
% 0.14/0.42 (((~![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)))))))))))) | (~((~((~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))) | (~((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) | (~((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)))))))))))) | (~((~((~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))))))))))))),
% 0.14/0.43 inference(transitivity,[status(thm)],[62, 60])).
% 0.14/0.43 tff(64,plain,
% 0.14/0.43 ((~![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)))))))))))) | (~((~((~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))) | (~((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)))))))))))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(65,plain,
% 0.14/0.43 ((~![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)))))))))))) | (~((~((~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)))))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 (~((~((~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))))))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[65, 59])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (((~((~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))))))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (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)))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 ((~(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)))))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 (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)))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 (~((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))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[70, 36])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (((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)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (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)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (subset(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), relation_field(A!10))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[73, 31])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (((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))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (~(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10) = empty_set)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[75, 71])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 ((~(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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (~(well_founded_relation(A!10) <=> is_well_founded_in(A!10, relation_field(A!10)))),
% 0.21/0.43 inference(or_elim,[status(thm)],[11])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 ((~well_founded_relation(A!10)) <=> is_well_founded_in(A!10, relation_field(A!10))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (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))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 (well_founded_relation(A!10) | is_well_founded_in(A!10, relation_field(A!10))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 (well_founded_relation(A!10)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[81, 35])).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 (^[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)))))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 (![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))))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[83])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 (^[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)))))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 (![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))))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[85])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (![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))))))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[86, 84])).
% 0.21/0.44 tff(88,plain,
% 0.21/0.44 (^[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)))))))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(89,plain,
% 0.21/0.44 (![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))))))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[88])).
% 0.21/0.44 tff(90,plain,
% 0.21/0.44 (^[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] : ((~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)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(91,plain,
% 0.21/0.44 (![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] : ((~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))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.44 tff(92,plain,
% 0.21/0.44 (![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)))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(93,plain,
% 0.21/0.44 (^[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)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(94,plain,
% 0.21/0.44 (![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)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.44 tff(95,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/sandbox2/benchmark/theBenchmark.p','d2_wellord1')).
% 0.21/0.44 tff(96,plain,
% 0.21/0.44 (![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)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 (![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)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.21/0.44 tff(98,plain,(
% 0.21/0.44 ![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))))))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[97])).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 (![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))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 (![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))))))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.21/0.44 tff(101,plain,
% 0.21/0.44 (![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))))))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[100, 87])).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 (((~![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) | (~((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))))))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 ((~![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))))))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 ((~![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)))))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 (~((~((~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))))))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[104, 101, 12])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 (((~((~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)))))))))) | ((~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))))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(107,plain,
% 0.21/0.44 ((~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)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 ((~((~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)))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 ((~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)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 (![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)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[109, 82])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 (((~![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))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(112,plain,
% 0.21/0.45 ((~![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))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(113,plain,
% 0.21/0.45 ((~![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)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 ((~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)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[113, 110, 76])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 (~((~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))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[114, 74])).
% 0.21/0.45 tff(116,plain,
% 0.21/0.45 (((~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))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(117,plain,
% 0.21/0.45 (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))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.21/0.45 tff(118,plain,
% 0.21/0.45 (((~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))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 (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))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[118, 115])).
% 0.21/0.45 tff(120,plain,
% 0.21/0.45 (((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))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(121,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[120, 71])).
% 0.21/0.45 tff(122,plain,
% 0.21/0.45 (((~![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))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 ((~![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))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(124,plain,
% 0.21/0.45 ((~![D: $i] : ((~in(D, tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, D), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))))) | (~in(tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10))) | (~disjoint(fiber(A!10, tptp_fun_C_0(tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10), A!10)), tptp_fun_C_3(set_union2(relation_dom(A!10), relation_rng(A!10)), A!10)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.21/0.45 tff(125,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[124, 121, 119, 117])).
% 0.21/0.45 tff(126,plain,(is_well_founded_in(A!10, relation_field(A!10))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(127,plain,
% 0.21/0.45 ((~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))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(128,plain,
% 0.21/0.45 ((~well_founded_relation(A!10)) | (~is_well_founded_in(A!10, relation_field(A!10)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[127, 79])).
% 0.21/0.45 tff(129,plain,
% 0.21/0.45 (~well_founded_relation(A!10)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[128, 126])).
% 0.21/0.45 tff(130,plain,
% 0.21/0.45 (((~((~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)))))))))) | (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))))))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(131,plain,
% 0.21/0.45 (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)))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[130, 105])).
% 0.21/0.45 tff(132,plain,
% 0.21/0.45 ((~(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))))))))) | 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)))))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(133,plain,
% 0.21/0.45 (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)))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.21/0.45 tff(134,plain,
% 0.21/0.45 (~((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))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[133, 129])).
% 0.21/0.45 tff(135,plain,
% 0.21/0.45 (((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)))))) | subset(tptp_fun_B_1(A!10), relation_field(A!10))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(136,plain,
% 0.21/0.45 (subset(tptp_fun_B_1(A!10), relation_field(A!10))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.21/0.45 tff(137,plain,
% 0.21/0.45 (subset(tptp_fun_B_1(A!10), set_union2(relation_dom(A!10), relation_rng(A!10)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[136, 29])).
% 0.21/0.45 tff(138,plain,
% 0.21/0.45 (is_well_founded_in(A!10, set_union2(relation_dom(A!10), relation_rng(A!10)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[126, 33])).
% 0.21/0.45 tff(139,plain,
% 0.21/0.45 (((~((~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))))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(140,plain,
% 0.21/0.45 ((~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)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[139, 66])).
% 0.21/0.45 tff(141,plain,
% 0.21/0.45 ((~((~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)))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(142,plain,
% 0.21/0.45 ((~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)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.21/0.45 tff(143,plain,
% 0.21/0.45 (![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)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[142, 138])).
% 0.21/0.45 tff(144,plain,
% 0.21/0.45 (((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)))))) | (~(tptp_fun_B_1(A!10) = empty_set))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(145,plain,
% 0.21/0.45 (~(tptp_fun_B_1(A!10) = empty_set)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[144, 134])).
% 0.21/0.45 tff(146,plain,
% 0.21/0.45 (((~![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))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(147,plain,
% 0.21/0.45 (((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))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(148,plain,
% 0.21/0.46 (((~![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)))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.46 tff(149,plain,
% 0.21/0.46 (((~![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))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[148, 146])).
% 0.21/0.46 tff(150,plain,
% 0.21/0.46 ((~![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)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(151,plain,
% 0.21/0.46 ((~![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)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.46 tff(152,plain,
% 0.21/0.46 (~((~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))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[151, 145, 143, 137])).
% 0.21/0.46 tff(153,plain,
% 0.21/0.46 (((~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))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(154,plain,
% 0.21/0.46 (disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.21/0.46 tff(155,plain,
% 0.21/0.46 (((~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))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(156,plain,
% 0.21/0.46 (in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[155, 152])).
% 0.21/0.46 tff(157,plain,
% 0.21/0.46 (((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)))))) | ![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(158,plain,
% 0.21/0.46 (![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[157, 134])).
% 0.21/0.46 tff(159,plain,
% 0.21/0.46 (((~![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))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(160,plain,
% 0.21/0.46 ((~![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))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(161,plain,
% 0.21/0.46 ((~![C: $i] : ((~in(C, tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, C), tptp_fun_B_1(A!10))))) | (~in(tptp_fun_D_2(tptp_fun_B_1(A!10), A!10), tptp_fun_B_1(A!10))) | (~disjoint(fiber(A!10, tptp_fun_D_2(tptp_fun_B_1(A!10), A!10)), tptp_fun_B_1(A!10)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.46 tff(162,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[161, 158, 156, 154])).
% 0.21/0.46 % SZS output end Proof
%------------------------------------------------------------------------------