%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC207+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:30:31 AM UTC 2025
% Result : Theorem 0.50s 0.68s
% Output : Proof 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC207+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 08:41:50 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.50/0.68 % SZS status Theorem
% 0.50/0.68 % SZS output start Proof
% 0.50/0.68 tff(nil_type, type, (
% 0.50/0.68 nil: $i)).
% 0.50/0.68 tff(cons_type, type, (
% 0.50/0.68 cons: ( $i * $i ) > $i)).
% 0.50/0.68 tff(tptp_fun_Y_47_type, type, (
% 0.50/0.68 tptp_fun_Y_47: $i)).
% 0.50/0.68 tff(tptp_fun_U_45_type, type, (
% 0.50/0.68 tptp_fun_U_45: $i)).
% 0.50/0.68 tff(neq_type, type, (
% 0.50/0.68 neq: ( $i * $i ) > $o)).
% 0.50/0.68 tff(ssList_type, type, (
% 0.50/0.68 ssList: $i > $o)).
% 0.50/0.68 tff(tptp_fun_V_46_type, type, (
% 0.50/0.68 tptp_fun_V_46: $i)).
% 0.50/0.68 tff(leq_type, type, (
% 0.50/0.68 leq: ( $i * $i ) > $o)).
% 0.50/0.68 tff(memberP_type, type, (
% 0.50/0.68 memberP: ( $i * $i ) > $o)).
% 0.50/0.68 tff(ssItem_type, type, (
% 0.50/0.68 ssItem: $i > $o)).
% 0.50/0.68 tff(segmentP_type, type, (
% 0.50/0.68 segmentP: ( $i * $i ) > $o)).
% 0.50/0.68 tff(1,plain,
% 0.50/0.68 ((ssList(U!45) & (ssList(V!46) & (((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))) <=> (ssList(U!45) & ssList(V!46) & (((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & (~neq(U!45, nil)) & neq(V!46, nil))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(2,plain,
% 0.50/0.68 ((ssList(V!46) & (((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)))) | (~((~(nil = V!46)) | (~(nil = U!45))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil)) <=> (ssList(V!46) & (((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(3,plain,
% 0.50/0.68 ((ssList(U!45) & (ssList(V!46) & (((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)))) | (~((~(nil = V!46)) | (~(nil = U!45))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))) <=> (ssList(U!45) & (ssList(V!46) & (((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil)))),
% 0.50/0.68 inference(monotonicity,[status(thm)],[2])).
% 0.50/0.68 tff(4,plain,
% 0.50/0.68 ((ssList(U!45) & (ssList(V!46) & (((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)))) | (~((~(nil = V!46)) | (~(nil = U!45))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))) <=> (ssList(U!45) & ssList(V!46) & (((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & (~neq(U!45, nil)) & neq(V!46, nil))),
% 0.50/0.68 inference(transitivity,[status(thm)],[3, 1])).
% 0.50/0.68 tff(5,plain,
% 0.50/0.68 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(V, Z) & leq(Y, Z))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(V, Z) & leq(Y, Z))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil)))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(6,plain,
% 0.50/0.68 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | neq(U, nil)) | (![Y: $i] : (ssItem(Y) => (((~(cons(Y, nil) = W)) | (~memberP(X, Y))) | ?[Z: $i] : (((ssItem(Z) & (~(Y = Z))) & memberP(X, Z)) & leq(Y, Z)))) & ((~(nil = X)) | (~(nil = W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(V, Z) & leq(Y, Z))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil)))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(7,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | neq(U, nil)) | (![Y: $i] : (ssItem(Y) => (((~(cons(Y, nil) = W)) | (~memberP(X, Y))) | ?[Z: $i] : (((ssItem(Z) & (~(Y = Z))) & memberP(X, Z)) & leq(Y, Z)))) & ((~(nil = X)) | (~(nil = W)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.50/0.68 tff(8,plain,
% 0.50/0.68 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(V, Z) & leq(Y, Z))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.50/0.68 tff(9,plain,
% 0.50/0.68 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(V, Z) & leq(Y, Z))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.50/0.68 tff(10,plain,
% 0.50/0.68 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(V, Z) & leq(Y, Z))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.50/0.68 tff(11,plain,
% 0.50/0.68 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y)) | ?[Z: $i] : (ssItem(Z) & (~(Y = Z)) & memberP(V, Z) & leq(Y, Z))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.50/0.68 tff(12,plain,
% 0.50/0.68 (ssList(U!45) & ssList(V!46) & (((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & (~neq(U!45, nil)) & neq(V!46, nil)),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.50/0.68 tff(13,plain,
% 0.50/0.68 (ssList(U!45)),
% 0.50/0.68 inference(and_elim,[status(thm)],[12])).
% 0.50/0.68 tff(14,plain,
% 0.50/0.68 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(15,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[14])).
% 0.50/0.68 tff(16,plain,
% 0.50/0.68 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(17,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[16])).
% 0.50/0.68 tff(18,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.50/0.68 inference(transitivity,[status(thm)],[17, 15])).
% 0.50/0.68 tff(19,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(20,plain,
% 0.50/0.68 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(trans(rewrite((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V)))), rewrite((~((U = V) <=> neq(U, V))) <=> (~((U = V) <=> neq(U, V)))), ((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> (ssList(V) => (~((U = V) <=> neq(U, V)))))), rewrite((ssList(V) => (~((U = V) <=> neq(U, V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), (![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(21,plain,
% 0.50/0.68 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[20])).
% 0.50/0.68 tff(22,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.50/0.68 tff(23,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.50/0.68 tff(24,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.50/0.68 tff(25,plain,(
% 0.50/0.68 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.50/0.68 inference(skolemize,[status(sab)],[24])).
% 0.50/0.68 tff(26,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.50/0.68 tff(27,plain,
% 0.50/0.68 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(28,plain,
% 0.50/0.68 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(29,plain,
% 0.50/0.68 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.50/0.68 tff(30,plain,
% 0.50/0.68 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[29, 26, 13])).
% 0.50/0.68 tff(31,plain,
% 0.50/0.68 (ssList(nil) <=> ssList(nil)),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(32,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.50/0.68 tff(33,plain,
% 0.50/0.68 (ssList(nil)),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.50/0.68 tff(34,plain,
% 0.50/0.68 (((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(35,plain,
% 0.50/0.68 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(36,plain,
% 0.50/0.68 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.50/0.68 tff(37,plain,
% 0.50/0.68 (~((U!45 = nil) <=> neq(U!45, nil))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[36, 33, 30])).
% 0.50/0.68 tff(38,plain,
% 0.50/0.68 (~neq(U!45, nil)),
% 0.50/0.68 inference(and_elim,[status(thm)],[12])).
% 0.50/0.68 tff(39,plain,
% 0.50/0.68 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 0.50/0.68 inference(tautology,[status(thm)],[])).
% 0.50/0.68 tff(40,plain,
% 0.50/0.68 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil)),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.50/0.68 tff(41,plain,
% 0.50/0.68 (U!45 = nil),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.50/0.68 tff(42,plain,
% 0.50/0.68 (ssList(V!46)),
% 0.50/0.68 inference(and_elim,[status(thm)],[12])).
% 0.50/0.68 tff(43,plain,
% 0.50/0.68 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(44,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[43])).
% 0.50/0.68 tff(45,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(46,plain,
% 0.50/0.68 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(47,plain,
% 0.50/0.68 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[46])).
% 0.50/0.68 tff(48,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.50/0.68 tff(49,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.50/0.68 tff(50,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.50/0.68 tff(51,plain,(
% 0.50/0.68 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.50/0.68 inference(skolemize,[status(sab)],[50])).
% 0.50/0.68 tff(52,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.50/0.68 tff(53,plain,
% 0.50/0.68 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(54,plain,
% 0.50/0.68 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(55,plain,
% 0.50/0.68 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.50/0.68 tff(56,plain,
% 0.50/0.68 (segmentP(nil, V!46) <=> (nil = V!46)),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[55, 52, 42])).
% 0.50/0.68 tff(57,plain,
% 0.50/0.68 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(58,plain,
% 0.50/0.68 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(59,plain,
% 0.50/0.68 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.50/0.68 tff(60,plain,
% 0.50/0.68 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[59, 26, 42])).
% 0.50/0.68 tff(61,plain,
% 0.50/0.68 (((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(62,plain,
% 0.50/0.68 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(63,plain,
% 0.50/0.68 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.50/0.68 tff(64,plain,
% 0.50/0.68 (~((V!46 = nil) <=> neq(V!46, nil))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[63, 33, 60])).
% 0.50/0.68 tff(65,plain,
% 0.50/0.68 (neq(V!46, nil)),
% 0.50/0.68 inference(and_elim,[status(thm)],[12])).
% 0.50/0.68 tff(66,plain,
% 0.50/0.68 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 0.50/0.68 inference(tautology,[status(thm)],[])).
% 0.50/0.68 tff(67,plain,
% 0.50/0.68 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.50/0.68 tff(68,plain,
% 0.50/0.68 (~(V!46 = nil)),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[67, 64])).
% 0.50/0.68 tff(69,plain,
% 0.50/0.68 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(70,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[69])).
% 0.50/0.68 tff(71,plain,
% 0.50/0.68 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(72,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[71])).
% 0.50/0.68 tff(73,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.50/0.68 inference(transitivity,[status(thm)],[72, 70])).
% 0.50/0.68 tff(74,plain,
% 0.50/0.68 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(75,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[74])).
% 0.50/0.68 tff(76,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(77,plain,
% 0.50/0.68 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((segmentP(U, V) & segmentP(V, U)) => (U = V)) <=> ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> (ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))))), rewrite((ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), (![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> (ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(78,plain,
% 0.50/0.68 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[77])).
% 0.50/0.68 tff(79,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax54')).
% 0.50/0.68 tff(80,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.50/0.68 tff(81,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.50/0.68 tff(82,plain,(
% 0.50/0.68 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.50/0.68 inference(skolemize,[status(sab)],[81])).
% 0.50/0.68 tff(83,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.50/0.68 tff(84,plain,
% 0.50/0.68 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.50/0.68 tff(85,plain,
% 0.50/0.68 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(86,plain,
% 0.50/0.68 (((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) <=> ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(87,plain,
% 0.50/0.68 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))))),
% 0.50/0.68 inference(monotonicity,[status(thm)],[86])).
% 0.50/0.68 tff(88,plain,
% 0.50/0.68 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.50/0.68 inference(transitivity,[status(thm)],[87, 85])).
% 0.50/0.68 tff(89,plain,
% 0.50/0.68 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(90,plain,
% 0.50/0.68 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.50/0.69 tff(91,plain,
% 0.50/0.69 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[90, 84, 42])).
% 0.50/0.69 tff(92,plain,
% 0.50/0.69 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(93,plain,
% 0.50/0.69 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[92])).
% 0.50/0.69 tff(94,plain,
% 0.50/0.69 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(95,plain,
% 0.50/0.69 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(96,plain,
% 0.50/0.69 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[95])).
% 0.50/0.69 tff(97,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.50/0.69 tff(98,plain,
% 0.50/0.69 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.50/0.69 tff(99,plain,
% 0.50/0.69 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.50/0.69 tff(100,plain,(
% 0.50/0.69 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.50/0.69 inference(skolemize,[status(sab)],[99])).
% 0.50/0.69 tff(101,plain,
% 0.50/0.69 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.50/0.69 tff(102,plain,
% 0.50/0.69 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(103,plain,
% 0.50/0.69 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(104,plain,
% 0.50/0.69 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.50/0.69 tff(105,plain,
% 0.50/0.69 (segmentP(V!46, nil)),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[104, 101, 42])).
% 0.50/0.69 tff(106,plain,
% 0.50/0.69 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(107,plain,
% 0.50/0.69 (((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46))) <=> ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(108,plain,
% 0.50/0.69 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil))))),
% 0.50/0.69 inference(monotonicity,[status(thm)],[107])).
% 0.50/0.69 tff(109,plain,
% 0.50/0.69 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 0.50/0.69 inference(transitivity,[status(thm)],[108, 106])).
% 0.50/0.69 tff(110,plain,
% 0.50/0.69 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(111,plain,
% 0.50/0.69 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.50/0.69 tff(112,plain,
% 0.50/0.69 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[111, 33, 105, 91])).
% 0.50/0.69 tff(113,plain,
% 0.50/0.69 (~segmentP(nil, V!46)),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[112, 68])).
% 0.50/0.69 tff(114,plain,
% 0.50/0.69 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 0.50/0.69 inference(tautology,[status(thm)],[])).
% 0.50/0.69 tff(115,plain,
% 0.50/0.69 (~(nil = V!46)),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[114, 113, 56])).
% 0.50/0.69 tff(116,plain,
% 0.50/0.69 (((~(nil = U!45)) | (~(nil = V!46))) | (nil = V!46)),
% 0.50/0.69 inference(tautology,[status(thm)],[])).
% 0.50/0.69 tff(117,plain,
% 0.50/0.69 ((~(nil = U!45)) | (~(nil = V!46))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.50/0.69 tff(118,plain,
% 0.50/0.69 (((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~ssItem(Y!47)) | (~memberP(V!46, Y!47)) | (~(cons(Y!47, nil) = U!45)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z))))))) <=> ((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~ssItem(Y!47)) | (~memberP(V!46, Y!47)) | (~(cons(Y!47, nil) = U!45)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z)))))))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(119,plain,
% 0.50/0.69 (((~((~ssItem(Y!47)) | (~memberP(V!46, Y!47)) | (~(cons(Y!47, nil) = U!45)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z)))))) | (~((~(nil = U!45)) | (~(nil = V!46))))) <=> ((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~ssItem(Y!47)) | (~memberP(V!46, Y!47)) | (~(cons(Y!47, nil) = U!45)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z)))))))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(120,plain,
% 0.50/0.69 (((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z)))) <=> (~((~ssItem(Y!47)) | (~memberP(V!46, Y!47)) | (~(cons(Y!47, nil) = U!45)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z))))))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(121,plain,
% 0.50/0.69 (^[Z: $i] : trans(monotonicity(rewrite((ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)) <=> (~((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z))))), ((~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z))) <=> (~(~((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z))))))), rewrite((~(~((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z))))) <=> ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z)))), ((~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z))) <=> ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z)))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(122,plain,
% 0.50/0.69 (![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z))) <=> ![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z)))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[121])).
% 0.50/0.69 tff(123,plain,
% 0.50/0.69 (((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)))) <=> ((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z))))),
% 0.50/0.69 inference(monotonicity,[status(thm)],[122])).
% 0.50/0.69 tff(124,plain,
% 0.50/0.69 (((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)))) <=> (~((~ssItem(Y!47)) | (~memberP(V!46, Y!47)) | (~(cons(Y!47, nil) = U!45)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z))))))),
% 0.50/0.69 inference(transitivity,[status(thm)],[123, 120])).
% 0.50/0.69 tff(125,plain,
% 0.50/0.69 ((((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) <=> ((~((~ssItem(Y!47)) | (~memberP(V!46, Y!47)) | (~(cons(Y!47, nil) = U!45)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z)))))) | (~((~(nil = U!45)) | (~(nil = V!46)))))),
% 0.50/0.69 inference(monotonicity,[status(thm)],[124])).
% 0.50/0.69 tff(126,plain,
% 0.50/0.69 ((((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) <=> ((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~ssItem(Y!47)) | (~memberP(V!46, Y!47)) | (~(cons(Y!47, nil) = U!45)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z)))))))),
% 0.50/0.69 inference(transitivity,[status(thm)],[125, 119])).
% 0.50/0.69 tff(127,plain,
% 0.50/0.69 (((cons(Y!47, nil) = U!45) & memberP(V!46, Y!47) & ssItem(Y!47) & ![Z: $i] : (~(ssItem(Z) & (~(Y!47 = Z)) & memberP(V!46, Z) & leq(Y!47, Z)))) | (~((~(nil = U!45)) | (~(nil = V!46))))),
% 0.50/0.69 inference(and_elim,[status(thm)],[12])).
% 0.50/0.69 tff(128,plain,
% 0.50/0.69 ((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~ssItem(Y!47)) | (~memberP(V!46, Y!47)) | (~(cons(Y!47, nil) = U!45)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z))))))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.50/0.69 tff(129,plain,
% 0.50/0.69 ((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~ssItem(Y!47)) | (~memberP(V!46, Y!47)) | (~(cons(Y!47, nil) = U!45)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z))))))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[128, 118])).
% 0.50/0.69 tff(130,plain,
% 0.50/0.69 (~((~ssItem(Y!47)) | (~memberP(V!46, Y!47)) | (~(cons(Y!47, nil) = U!45)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z)))))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[129, 117])).
% 0.50/0.69 tff(131,plain,
% 0.50/0.69 (((~ssItem(Y!47)) | (~memberP(V!46, Y!47)) | (~(cons(Y!47, nil) = U!45)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z))))) | (cons(Y!47, nil) = U!45)),
% 0.50/0.69 inference(tautology,[status(thm)],[])).
% 0.50/0.69 tff(132,plain,
% 0.50/0.69 (cons(Y!47, nil) = U!45),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.50/0.69 tff(133,plain,
% 0.50/0.69 (cons(Y!47, nil) = nil),
% 0.50/0.69 inference(transitivity,[status(thm)],[132, 41])).
% 0.50/0.69 tff(134,plain,
% 0.50/0.69 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(135,plain,
% 0.50/0.69 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[134])).
% 0.50/0.69 tff(136,plain,
% 0.50/0.69 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(137,plain,
% 0.50/0.69 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[136])).
% 0.50/0.69 tff(138,plain,
% 0.50/0.69 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.50/0.69 inference(transitivity,[status(thm)],[137, 135])).
% 0.50/0.69 tff(139,plain,
% 0.50/0.69 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(140,plain,
% 0.50/0.69 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (~(cons(V, U) = U))) <=> ((~ssItem(V)) | (~(cons(V, U) = U))))), (![V: $i] : (ssItem(V) => (~(cons(V, U) = U))) <=> ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(141,plain,
% 0.50/0.70 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[140])).
% 0.50/0.70 tff(142,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax18')).
% 0.50/0.70 tff(143,plain,
% 0.50/0.70 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.50/0.70 tff(144,plain,
% 0.50/0.70 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.50/0.70 tff(145,plain,(
% 0.50/0.70 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.50/0.70 inference(skolemize,[status(sab)],[144])).
% 0.50/0.70 tff(146,plain,
% 0.50/0.70 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.50/0.70 tff(147,plain,
% 0.50/0.70 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(148,plain,
% 0.50/0.70 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(149,plain,
% 0.50/0.70 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.50/0.70 tff(150,plain,
% 0.50/0.70 (![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[149, 33, 146])).
% 0.50/0.70 tff(151,plain,
% 0.50/0.70 (((~ssItem(Y!47)) | (~memberP(V!46, Y!47)) | (~(cons(Y!47, nil) = U!45)) | (~![Z: $i] : ((~ssItem(Z)) | (~memberP(V!46, Z)) | (Y!47 = Z) | (~leq(Y!47, Z))))) | ssItem(Y!47)),
% 0.50/0.70 inference(tautology,[status(thm)],[])).
% 0.50/0.70 tff(152,plain,
% 0.50/0.70 (ssItem(Y!47)),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[151, 130])).
% 0.50/0.70 tff(153,plain,
% 0.50/0.70 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(154,plain,
% 0.50/0.70 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil)))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(155,plain,
% 0.50/0.70 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.50/0.70 tff(156,plain,
% 0.50/0.70 ($false),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[155, 152, 150, 133])).
% 0.50/0.70 % SZS output end Proof
% 0.50/0.70 % E exiting
%------------------------------------------------------------------------------