%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM410+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:20:54 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM410+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 01:02:36 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(subset_type, type, (
% 0.11/0.37 subset: ( $i * $i ) > $o)).
% 0.11/0.37 tff(relation_rng_type, type, (
% 0.11/0.37 relation_rng: $i > $i)).
% 0.11/0.37 tff(tptp_fun_A_16_type, type, (
% 0.11/0.37 tptp_fun_A_16: $i)).
% 0.11/0.37 tff(transfinite_sequence_of_type, type, (
% 0.11/0.37 transfinite_sequence_of: ( $i * $i ) > $o)).
% 0.11/0.37 tff(transfinite_sequence_type, type, (
% 0.11/0.37 transfinite_sequence: $i > $o)).
% 0.11/0.37 tff(ordinal_type, type, (
% 0.11/0.37 ordinal: $i > $o)).
% 0.11/0.37 tff(relation_dom_type, type, (
% 0.11/0.37 relation_dom: $i > $i)).
% 0.11/0.37 tff(function_type, type, (
% 0.11/0.37 function: $i > $o)).
% 0.11/0.37 tff(relation_type, type, (
% 0.11/0.37 relation: $i > $o)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 ((~(transfinite_sequence_of(A!16, relation_rng(A!16)) | (~(relation(A!16) & function(A!16))) | (~ordinal(relation_dom(A!16))))) <=> (~(transfinite_sequence_of(A!16, relation_rng(A!16)) | (~(relation(A!16) & function(A!16))) | (~ordinal(relation_dom(A!16)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 ((~![A: $i] : (transfinite_sequence_of(A, relation_rng(A)) | (~(relation(A) & function(A))) | (~ordinal(relation_dom(A))))) <=> (~![A: $i] : (transfinite_sequence_of(A, relation_rng(A)) | (~(relation(A) & function(A))) | (~ordinal(relation_dom(A)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 ((~![A: $i] : ((relation(A) & function(A)) => (ordinal(relation_dom(A)) => transfinite_sequence_of(A, relation_rng(A))))) <=> (~![A: $i] : (transfinite_sequence_of(A, relation_rng(A)) | (~(relation(A) & function(A))) | (~ordinal(relation_dom(A)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(4,axiom,(~![A: $i] : ((relation(A) & function(A)) => (ordinal(relation_dom(A)) => transfinite_sequence_of(A, relation_rng(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t46_ordinal1')).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (~![A: $i] : (transfinite_sequence_of(A, relation_rng(A)) | (~(relation(A) & function(A))) | (~ordinal(relation_dom(A))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (~![A: $i] : (transfinite_sequence_of(A, relation_rng(A)) | (~(relation(A) & function(A))) | (~ordinal(relation_dom(A))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (~![A: $i] : (transfinite_sequence_of(A, relation_rng(A)) | (~(relation(A) & function(A))) | (~ordinal(relation_dom(A))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (~![A: $i] : (transfinite_sequence_of(A, relation_rng(A)) | (~(relation(A) & function(A))) | (~ordinal(relation_dom(A))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.11/0.37 tff(9,plain,(
% 0.11/0.37 ~(transfinite_sequence_of(A!16, relation_rng(A!16)) | (~(relation(A!16) & function(A!16))) | (~ordinal(relation_dom(A!16))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[8])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (~(transfinite_sequence_of(A!16, relation_rng(A!16)) | (~(relation(A!16) & function(A!16))) | (~ordinal(relation_dom(A!16))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (relation(A!16) & function(A!16)),
% 0.11/0.37 inference(or_elim,[status(thm)],[10])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (function(A!16)),
% 0.11/0.37 inference(and_elim,[status(thm)],[11])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (relation(A!16)),
% 0.11/0.37 inference(and_elim,[status(thm)],[11])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (^[A: $i] : refl(((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A))) <=> ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (![A: $i] : ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A))) <=> ![A: $i] : ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), (((~(relation(A) & function(A))) | (transfinite_sequence(A) <=> ordinal(relation_dom(A)))) <=> (((~relation(A)) | (~function(A))) | (transfinite_sequence(A) <=> ordinal(relation_dom(A)))))), rewrite((((~relation(A)) | (~function(A))) | (transfinite_sequence(A) <=> ordinal(relation_dom(A)))) <=> ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A)))), (((~(relation(A) & function(A))) | (transfinite_sequence(A) <=> ordinal(relation_dom(A)))) <=> ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![A: $i] : ((~(relation(A) & function(A))) | (transfinite_sequence(A) <=> ordinal(relation_dom(A)))) <=> ![A: $i] : ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (![A: $i] : ((~(relation(A) & function(A))) | (transfinite_sequence(A) <=> ordinal(relation_dom(A)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (transfinite_sequence(A) <=> ordinal(relation_dom(A))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (^[A: $i] : rewrite(((relation(A) & function(A)) => (transfinite_sequence(A) <=> ordinal(relation_dom(A)))) <=> ((~(relation(A) & function(A))) | (transfinite_sequence(A) <=> ordinal(relation_dom(A)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (![A: $i] : ((relation(A) & function(A)) => (transfinite_sequence(A) <=> ordinal(relation_dom(A)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (transfinite_sequence(A) <=> ordinal(relation_dom(A))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.11/0.37 tff(21,axiom,(![A: $i] : ((relation(A) & function(A)) => (transfinite_sequence(A) <=> ordinal(relation_dom(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_ordinal1')).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (![A: $i] : ((~(relation(A) & function(A))) | (transfinite_sequence(A) <=> ordinal(relation_dom(A))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (![A: $i] : ((~(relation(A) & function(A))) | (transfinite_sequence(A) <=> ordinal(relation_dom(A))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.11/0.37 tff(24,plain,(
% 0.11/0.37 ![A: $i] : ((~(relation(A) & function(A))) | (transfinite_sequence(A) <=> ordinal(relation_dom(A))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[23])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![A: $i] : ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![A: $i] : ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (((~![A: $i] : ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A)))) | ((~relation(A!16)) | (~function(A!16)) | (transfinite_sequence(A!16) <=> ordinal(relation_dom(A!16))))) <=> ((~![A: $i] : ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A)))) | (~relation(A!16)) | (~function(A!16)) | (transfinite_sequence(A!16) <=> ordinal(relation_dom(A!16))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (((transfinite_sequence(A!16) <=> ordinal(relation_dom(A!16))) | (~relation(A!16)) | (~function(A!16))) <=> ((~relation(A!16)) | (~function(A!16)) | (transfinite_sequence(A!16) <=> ordinal(relation_dom(A!16))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (((~![A: $i] : ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A)))) | ((transfinite_sequence(A!16) <=> ordinal(relation_dom(A!16))) | (~relation(A!16)) | (~function(A!16)))) <=> ((~![A: $i] : ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A)))) | ((~relation(A!16)) | (~function(A!16)) | (transfinite_sequence(A!16) <=> ordinal(relation_dom(A!16)))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[28])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (((~![A: $i] : ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A)))) | ((transfinite_sequence(A!16) <=> ordinal(relation_dom(A!16))) | (~relation(A!16)) | (~function(A!16)))) <=> ((~![A: $i] : ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A)))) | (~relation(A!16)) | (~function(A!16)) | (transfinite_sequence(A!16) <=> ordinal(relation_dom(A!16))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[29, 27])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 ((~![A: $i] : ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A)))) | ((transfinite_sequence(A!16) <=> ordinal(relation_dom(A!16))) | (~relation(A!16)) | (~function(A!16)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 ((~![A: $i] : ((transfinite_sequence(A) <=> ordinal(relation_dom(A))) | (~relation(A)) | (~function(A)))) | (~relation(A!16)) | (~function(A!16)) | (transfinite_sequence(A!16) <=> ordinal(relation_dom(A!16)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (transfinite_sequence(A!16) <=> ordinal(relation_dom(A!16))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[32, 26, 13, 12])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (ordinal(relation_dom(A!16))),
% 0.11/0.37 inference(or_elim,[status(thm)],[10])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 ((~(transfinite_sequence(A!16) <=> ordinal(relation_dom(A!16)))) | transfinite_sequence(A!16) | (~ordinal(relation_dom(A!16)))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 ((~(transfinite_sequence(A!16) <=> ordinal(relation_dom(A!16)))) | transfinite_sequence(A!16)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (transfinite_sequence(A!16)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (^[A: $i, B: $i] : refl(((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B))) <=> ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B))) <=> ![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[38])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B) & transfinite_sequence(B)) <=> (~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B))))), ((~(relation(B) & function(B) & transfinite_sequence(B))) <=> (~(~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B))))))), rewrite((~(~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B))))) <=> ((~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))), ((~(relation(B) & function(B) & transfinite_sequence(B))) <=> ((~relation(B)) | (~function(B)) | (~transfinite_sequence(B))))), (((~(relation(B) & function(B) & transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A))) <=> (((~relation(B)) | (~function(B)) | (~transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A))))), rewrite((((~relation(B)) | (~function(B)) | (~transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A))) <=> ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))), (((~(relation(B) & function(B) & transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A))) <=> ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (![A: $i, B: $i] : ((~(relation(B) & function(B) & transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A))) <=> ![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[40])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (![A: $i, B: $i] : ((~(relation(B) & function(B) & transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B) & transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((relation(B) & function(B)) & transfinite_sequence(B)) <=> (relation(B) & function(B) & transfinite_sequence(B))), ((((relation(B) & function(B)) & transfinite_sequence(B)) => (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A))) <=> ((relation(B) & function(B) & transfinite_sequence(B)) => (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A))))), rewrite(((relation(B) & function(B) & transfinite_sequence(B)) => (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A))) <=> ((~(relation(B) & function(B) & transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)))), ((((relation(B) & function(B)) & transfinite_sequence(B)) => (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A))) <=> ((~(relation(B) & function(B) & transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (![A: $i, B: $i] : (((relation(B) & function(B)) & transfinite_sequence(B)) => (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B) & transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.11/0.38 tff(45,axiom,(![A: $i, B: $i] : (((relation(B) & function(B)) & transfinite_sequence(B)) => (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_ordinal1')).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~(relation(B) & function(B) & transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~(relation(B) & function(B) & transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.11/0.38 tff(48,plain,(
% 0.11/0.38 ![A: $i, B: $i] : ((~(relation(B) & function(B) & transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[47])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 (((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | ((~relation(A!16)) | (~function(A!16)) | (~transfinite_sequence(A!16)) | (transfinite_sequence_of(A!16, relation_rng(A!16)) <=> subset(relation_rng(A!16), relation_rng(A!16))))) <=> ((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | (~relation(A!16)) | (~function(A!16)) | (~transfinite_sequence(A!16)) | (transfinite_sequence_of(A!16, relation_rng(A!16)) <=> subset(relation_rng(A!16), relation_rng(A!16))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 (((transfinite_sequence_of(A!16, relation_rng(A!16)) <=> subset(relation_rng(A!16), relation_rng(A!16))) | (~relation(A!16)) | (~function(A!16)) | (~transfinite_sequence(A!16))) <=> ((~relation(A!16)) | (~function(A!16)) | (~transfinite_sequence(A!16)) | (transfinite_sequence_of(A!16, relation_rng(A!16)) <=> subset(relation_rng(A!16), relation_rng(A!16))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 (((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | ((transfinite_sequence_of(A!16, relation_rng(A!16)) <=> subset(relation_rng(A!16), relation_rng(A!16))) | (~relation(A!16)) | (~function(A!16)) | (~transfinite_sequence(A!16)))) <=> ((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | ((~relation(A!16)) | (~function(A!16)) | (~transfinite_sequence(A!16)) | (transfinite_sequence_of(A!16, relation_rng(A!16)) <=> subset(relation_rng(A!16), relation_rng(A!16)))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[52])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 (((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | ((transfinite_sequence_of(A!16, relation_rng(A!16)) <=> subset(relation_rng(A!16), relation_rng(A!16))) | (~relation(A!16)) | (~function(A!16)) | (~transfinite_sequence(A!16)))) <=> ((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | (~relation(A!16)) | (~function(A!16)) | (~transfinite_sequence(A!16)) | (transfinite_sequence_of(A!16, relation_rng(A!16)) <=> subset(relation_rng(A!16), relation_rng(A!16))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[53, 51])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | ((transfinite_sequence_of(A!16, relation_rng(A!16)) <=> subset(relation_rng(A!16), relation_rng(A!16))) | (~relation(A!16)) | (~function(A!16)) | (~transfinite_sequence(A!16)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | (~relation(A!16)) | (~function(A!16)) | (~transfinite_sequence(A!16)) | (transfinite_sequence_of(A!16, relation_rng(A!16)) <=> subset(relation_rng(A!16), relation_rng(A!16)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 ((~transfinite_sequence(A!16)) | (transfinite_sequence_of(A!16, relation_rng(A!16)) <=> subset(relation_rng(A!16), relation_rng(A!16)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[56, 50, 13, 12])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 (transfinite_sequence_of(A!16, relation_rng(A!16)) <=> subset(relation_rng(A!16), relation_rng(A!16))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[57, 37])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 (~transfinite_sequence_of(A!16, relation_rng(A!16))),
% 0.11/0.38 inference(or_elim,[status(thm)],[10])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 ((~(transfinite_sequence_of(A!16, relation_rng(A!16)) <=> subset(relation_rng(A!16), relation_rng(A!16)))) | transfinite_sequence_of(A!16, relation_rng(A!16)) | (~subset(relation_rng(A!16), relation_rng(A!16)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 ((~(transfinite_sequence_of(A!16, relation_rng(A!16)) <=> subset(relation_rng(A!16), relation_rng(A!16)))) | (~subset(relation_rng(A!16), relation_rng(A!16)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 (~subset(relation_rng(A!16), relation_rng(A!16))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 (^[A: $i] : refl(subset(A, A) <=> subset(A, A))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.11/0.38 inference(quant_intro,[status(thm)],[63])).
% 0.11/0.38 tff(65,plain,
% 0.11/0.38 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 (![A: $i, B: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.11/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.11/0.38 tff(67,axiom,(![A: $i, B: $i] : subset(A, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 (![A: $i] : subset(A, A)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (![A: $i] : subset(A, A)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.11/0.38 tff(70,plain,(
% 0.11/0.38 ![A: $i] : subset(A, A)),
% 0.11/0.38 inference(skolemize,[status(sab)],[69])).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 (![A: $i] : subset(A, A)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[70, 64])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 ((~![A: $i] : subset(A, A)) | subset(relation_rng(A!16), relation_rng(A!16))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[72, 71, 62])).
% 0.11/0.38 % SZS output end Proof
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------