%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM411+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM411+1 : TPTP v9.0.0. Released v3.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n015.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:02:43 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(subset_type, type, (
% 0.19/0.37 subset: ( $i * $i ) > $o)).
% 0.19/0.37 tff(tptp_fun_B_16_type, type, (
% 0.19/0.37 tptp_fun_B_16: $i)).
% 0.19/0.37 tff(relation_rng_type, type, (
% 0.19/0.37 relation_rng: $i > $i)).
% 0.19/0.37 tff(tptp_fun_C_18_type, type, (
% 0.19/0.37 tptp_fun_C_18: $i)).
% 0.19/0.37 tff(transfinite_sequence_of_type, type, (
% 0.19/0.37 transfinite_sequence_of: ( $i * $i ) > $o)).
% 0.19/0.37 tff(relation_type, type, (
% 0.19/0.37 relation: $i > $o)).
% 0.19/0.37 tff(transfinite_sequence_type, type, (
% 0.19/0.37 transfinite_sequence: $i > $o)).
% 0.19/0.37 tff(function_type, type, (
% 0.19/0.37 function: $i > $o)).
% 0.19/0.37 tff(tptp_fun_A_17_type, type, (
% 0.19/0.37 tptp_fun_A_17: $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : ((~subset(A, B)) | ![C: $i] : ((~transfinite_sequence_of(C, A)) | transfinite_sequence_of(C, B)))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | ![C: $i] : ((~transfinite_sequence_of(C, A)) | transfinite_sequence_of(C, B))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : (subset(A, B) => ![C: $i] : (transfinite_sequence_of(C, A) => transfinite_sequence_of(C, B)))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | ![C: $i] : ((~transfinite_sequence_of(C, A)) | transfinite_sequence_of(C, B))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(3,axiom,(~![A: $i, B: $i] : (subset(A, B) => ![C: $i] : (transfinite_sequence_of(C, A) => transfinite_sequence_of(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t47_ordinal1')).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (~![A: $i, B: $i] : ((~subset(A, B)) | ![C: $i] : ((~transfinite_sequence_of(C, A)) | transfinite_sequence_of(C, B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (~![A: $i, B: $i] : ((~subset(A, B)) | ![C: $i] : ((~transfinite_sequence_of(C, A)) | transfinite_sequence_of(C, B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (~![A: $i, B: $i] : ((~subset(A, B)) | ![C: $i] : ((~transfinite_sequence_of(C, A)) | transfinite_sequence_of(C, B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (~![A: $i, B: $i] : ((~subset(A, B)) | ![C: $i] : ((~transfinite_sequence_of(C, A)) | transfinite_sequence_of(C, B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (~((~transfinite_sequence_of(C!18, A!17)) | transfinite_sequence_of(C!18, B!16))),
% 0.19/0.37 inference(and_elim,[status(thm)],[7])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (transfinite_sequence_of(C!18, A!17)),
% 0.19/0.37 inference(or_elim,[status(thm)],[8])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (^[A: $i, B: $i] : refl(((~transfinite_sequence_of(B, A)) | (~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B))))) <=> ((~transfinite_sequence_of(B, A)) | (~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B))))) <=> ![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (^[A: $i, B: $i] : rewrite(((~transfinite_sequence_of(B, A)) | (relation(B) & function(B) & transfinite_sequence(B))) <=> ((~transfinite_sequence_of(B, A)) | (~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (relation(B) & function(B) & transfinite_sequence(B))) <=> ![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (relation(B) & function(B) & transfinite_sequence(B))) <=> ![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (relation(B) & function(B) & transfinite_sequence(B)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((relation(B) & function(B)) & transfinite_sequence(B)) <=> (relation(B) & function(B) & transfinite_sequence(B))), ((transfinite_sequence_of(B, A) => ((relation(B) & function(B)) & transfinite_sequence(B))) <=> (transfinite_sequence_of(B, A) => (relation(B) & function(B) & transfinite_sequence(B))))), rewrite((transfinite_sequence_of(B, A) => (relation(B) & function(B) & transfinite_sequence(B))) <=> ((~transfinite_sequence_of(B, A)) | (relation(B) & function(B) & transfinite_sequence(B)))), ((transfinite_sequence_of(B, A) => ((relation(B) & function(B)) & transfinite_sequence(B))) <=> ((~transfinite_sequence_of(B, A)) | (relation(B) & function(B) & transfinite_sequence(B)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (![A: $i, B: $i] : (transfinite_sequence_of(B, A) => ((relation(B) & function(B)) & transfinite_sequence(B))) <=> ![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (relation(B) & function(B) & transfinite_sequence(B)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.37 tff(17,axiom,(![A: $i, B: $i] : (transfinite_sequence_of(B, A) => ((relation(B) & function(B)) & transfinite_sequence(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_ordinal1')).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (relation(B) & function(B) & transfinite_sequence(B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (relation(B) & function(B) & transfinite_sequence(B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.37 tff(20,plain,(
% 0.19/0.37 ![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (relation(B) & function(B) & transfinite_sequence(B)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[19])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (((~![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))))) | ((~transfinite_sequence_of(C!18, A!17)) | (~((~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)))))) <=> ((~![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))))) | (~transfinite_sequence_of(C!18, A!17)) | (~((~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))))) | ((~transfinite_sequence_of(C!18, A!17)) | (~((~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : ((~transfinite_sequence_of(B, A)) | (~((~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))))) | (~transfinite_sequence_of(C!18, A!17)) | (~((~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (~((~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[25, 22, 9])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (((~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18))) | relation(C!18)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (relation(C!18)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (((~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18))) | transfinite_sequence(C!18)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (transfinite_sequence(C!18)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[29, 26])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (((~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18))) | function(C!18)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (function(C!18)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[31, 26])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (^[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))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (![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] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.38 tff(40,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/sandbox2/benchmark/theBenchmark.p','d8_ordinal1')).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~(relation(B) & function(B) & transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~(relation(B) & function(B) & transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.19/0.38 tff(43,plain,(
% 0.19/0.38 ![A: $i, B: $i] : ((~(relation(B) & function(B) & transfinite_sequence(B))) | (transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[42])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | ((~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)) | (transfinite_sequence_of(C!18, B!16) <=> subset(relation_rng(C!18), B!16)))) <=> ((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | (~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)) | (transfinite_sequence_of(C!18, B!16) <=> subset(relation_rng(C!18), B!16)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (((transfinite_sequence_of(C!18, B!16) <=> subset(relation_rng(C!18), B!16)) | (~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18))) <=> ((~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)) | (transfinite_sequence_of(C!18, B!16) <=> subset(relation_rng(C!18), B!16)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | ((transfinite_sequence_of(C!18, B!16) <=> subset(relation_rng(C!18), B!16)) | (~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)))) <=> ((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | ((~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)) | (transfinite_sequence_of(C!18, B!16) <=> subset(relation_rng(C!18), B!16))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | ((transfinite_sequence_of(C!18, B!16) <=> subset(relation_rng(C!18), B!16)) | (~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)))) <=> ((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | (~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)) | (transfinite_sequence_of(C!18, B!16) <=> subset(relation_rng(C!18), B!16)))),
% 0.19/0.38 inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | ((transfinite_sequence_of(C!18, B!16) <=> subset(relation_rng(C!18), B!16)) | (~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | (~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)) | (transfinite_sequence_of(C!18, B!16) <=> subset(relation_rng(C!18), B!16))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 ((~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)) | (transfinite_sequence_of(C!18, B!16) <=> subset(relation_rng(C!18), B!16))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[51, 45])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (transfinite_sequence_of(C!18, B!16) <=> subset(relation_rng(C!18), B!16)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[52, 32, 30, 28])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 (~transfinite_sequence_of(C!18, B!16)),
% 0.19/0.38 inference(or_elim,[status(thm)],[8])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 ((~(transfinite_sequence_of(C!18, B!16) <=> subset(relation_rng(C!18), B!16))) | transfinite_sequence_of(C!18, B!16) | (~subset(relation_rng(C!18), B!16))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 ((~(transfinite_sequence_of(C!18, B!16) <=> subset(relation_rng(C!18), B!16))) | (~subset(relation_rng(C!18), B!16))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (~subset(relation_rng(C!18), B!16)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | ((transfinite_sequence_of(C!18, A!17) <=> subset(relation_rng(C!18), A!17)) | (~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)))) <=> ((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | (transfinite_sequence_of(C!18, A!17) <=> subset(relation_rng(C!18), A!17)) | (~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | ((transfinite_sequence_of(C!18, A!17) <=> subset(relation_rng(C!18), A!17)) | (~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : ((transfinite_sequence_of(B, A) <=> subset(relation_rng(B), A)) | (~relation(B)) | (~function(B)) | (~transfinite_sequence(B)))) | (transfinite_sequence_of(C!18, A!17) <=> subset(relation_rng(C!18), A!17)) | (~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 ((transfinite_sequence_of(C!18, A!17) <=> subset(relation_rng(C!18), A!17)) | (~relation(C!18)) | (~function(C!18)) | (~transfinite_sequence(C!18))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[60, 45])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 (transfinite_sequence_of(C!18, A!17) <=> subset(relation_rng(C!18), A!17)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[61, 28, 32, 30])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 ((~(transfinite_sequence_of(C!18, A!17) <=> subset(relation_rng(C!18), A!17))) | (~transfinite_sequence_of(C!18, A!17)) | subset(relation_rng(C!18), A!17)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 ((~(transfinite_sequence_of(C!18, A!17) <=> subset(relation_rng(C!18), A!17))) | subset(relation_rng(C!18), A!17)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[63, 9])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 (subset(relation_rng(C!18), A!17)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[64, 62])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 (subset(A!17, B!16)),
% 0.19/0.38 inference(and_elim,[status(thm)],[7])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(B, C)) <=> (~((~subset(B, C)) | (~subset(A, B))))), ((~(subset(A, B) & subset(B, C))) <=> (~(~((~subset(B, C)) | (~subset(A, B))))))), rewrite((~(~((~subset(B, C)) | (~subset(A, B))))) <=> ((~subset(B, C)) | (~subset(A, B)))), ((~(subset(A, B) & subset(B, C))) <=> ((~subset(B, C)) | (~subset(A, B))))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (((~subset(B, C)) | (~subset(A, B))) | subset(A, C)))), rewrite((((~subset(B, C)) | (~subset(A, B))) | subset(A, C)) <=> (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(69,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.38 tff(70,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(71,plain,
% 0.19/0.38 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ((~(subset(A, B) & subset(B, C))) | subset(A, C)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(72,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.38 tff(73,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_xboole_1')).
% 0.19/0.38 tff(74,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.38 tff(75,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.19/0.38 tff(76,plain,(
% 0.19/0.38 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.19/0.38 inference(skolemize,[status(sab)],[75])).
% 0.19/0.38 tff(77,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.19/0.38 tff(78,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.19/0.38 tff(79,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | ((~subset(A!17, B!16)) | (~subset(relation_rng(C!18), A!17)) | subset(relation_rng(C!18), B!16))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(A!17, B!16)) | (~subset(relation_rng(C!18), A!17)) | subset(relation_rng(C!18), B!16))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(80,plain,
% 0.19/0.38 ((subset(relation_rng(C!18), B!16) | (~subset(A!17, B!16)) | (~subset(relation_rng(C!18), A!17))) <=> ((~subset(A!17, B!16)) | (~subset(relation_rng(C!18), A!17)) | subset(relation_rng(C!18), B!16))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(81,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(relation_rng(C!18), B!16) | (~subset(A!17, B!16)) | (~subset(relation_rng(C!18), A!17)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | ((~subset(A!17, B!16)) | (~subset(relation_rng(C!18), A!17)) | subset(relation_rng(C!18), B!16)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[80])).
% 0.19/0.38 tff(82,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(relation_rng(C!18), B!16) | (~subset(A!17, B!16)) | (~subset(relation_rng(C!18), A!17)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(A!17, B!16)) | (~subset(relation_rng(C!18), A!17)) | subset(relation_rng(C!18), B!16))),
% 0.19/0.38 inference(transitivity,[status(thm)],[81, 79])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(relation_rng(C!18), B!16) | (~subset(A!17, B!16)) | (~subset(relation_rng(C!18), A!17)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(A!17, B!16)) | (~subset(relation_rng(C!18), A!17)) | subset(relation_rng(C!18), B!16)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[84, 78, 66, 65, 57])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------