%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC023+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:29:57 AM UTC 2025
% Result : Theorem 0.60s 0.77s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC023+1 : TPTP v9.0.0. Released v2.4.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 08:02:22 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.60/0.77 % SZS status Theorem
% 0.60/0.77 % SZS output start Proof
% 0.60/0.77 tff(frontsegP_type, type, (
% 0.60/0.77 frontsegP: ( $i * $i ) > $o)).
% 0.60/0.77 tff(tptp_fun_V_46_type, type, (
% 0.60/0.77 tptp_fun_V_46: $i)).
% 0.60/0.77 tff(tptp_fun_U_45_type, type, (
% 0.60/0.77 tptp_fun_U_45: $i)).
% 0.60/0.77 tff(ssList_type, type, (
% 0.60/0.77 ssList: $i > $o)).
% 0.60/0.77 tff(neq_type, type, (
% 0.60/0.77 neq: ( $i * $i ) > $o)).
% 0.60/0.77 tff(nil_type, type, (
% 0.60/0.77 nil: $i)).
% 0.60/0.77 tff(tptp_fun_Z_47_type, type, (
% 0.60/0.77 tptp_fun_Z_47: $i)).
% 0.60/0.77 tff(segmentP_type, type, (
% 0.60/0.77 segmentP: ( $i * $i ) > $o)).
% 0.60/0.77 tff(1,plain,
% 0.60/0.77 (^[Y: $i] : refl(((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y))) <=> ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(2,plain,
% 0.60/0.77 (![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y))) <=> ![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[1])).
% 0.60/0.77 tff(3,plain,
% 0.60/0.77 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)) <=> (~((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y))))), ((~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))) <=> (~(~((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y))))))), rewrite((~(~((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y))))) <=> ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y)))), ((~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))) <=> ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(4,plain,
% 0.60/0.77 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))) <=> ![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[3])).
% 0.60/0.77 tff(5,plain,
% 0.60/0.77 ((ssList(U!45) & (neq(V!46, nil) & ssList(V!46) & ((~((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))) <=> (ssList(U!45) & neq(V!46, nil) & ssList(V!46) & ((~((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(6,plain,
% 0.60/0.77 ((neq(V!46, nil) & ssList(V!46) & ((~((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) | (~((~(nil = V!46)) | (~(nil = U!45))))) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)))) <=> (neq(V!46, nil) & ssList(V!46) & ((~((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(7,plain,
% 0.60/0.77 ((ssList(U!45) & (neq(V!46, nil) & ssList(V!46) & ((~((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) | (~((~(nil = V!46)) | (~(nil = U!45))))) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))) <=> (ssList(U!45) & (neq(V!46, nil) & ssList(V!46) & ((~((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[6])).
% 0.60/0.77 tff(8,plain,
% 0.60/0.77 ((ssList(U!45) & (neq(V!46, nil) & ssList(V!46) & ((~((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) | (~((~(nil = V!46)) | (~(nil = U!45))))) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))) <=> (ssList(U!45) & neq(V!46, nil) & ssList(V!46) & ((~((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))),
% 0.60/0.77 inference(transitivity,[status(thm)],[7, 5])).
% 0.60/0.77 tff(9,plain,
% 0.60/0.77 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~neq(V, nil)) | (~ssList(V)) | (![Z: $i] : ((~frontsegP(U, Z)) | (~frontsegP(V, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~neq(V, nil)) | (~ssList(V)) | (![Z: $i] : ((~frontsegP(U, Z)) | (~frontsegP(V, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(10,plain,
% 0.60/0.77 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ?[Y: $i] : (((ssList(Y) & neq(Y, nil)) & frontsegP(V, Y)) & frontsegP(U, Y))) | (![Z: $i] : (ssList(Z) => (((~neq(Z, nil)) | (~frontsegP(X, Z))) | (~frontsegP(W, Z)))) & ((~(nil = X)) | (~(nil = W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~neq(V, nil)) | (~ssList(V)) | (![Z: $i] : ((~frontsegP(U, Z)) | (~frontsegP(V, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(11,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ?[Y: $i] : (((ssList(Y) & neq(Y, nil)) & frontsegP(V, Y)) & frontsegP(U, Y))) | (![Z: $i] : (ssList(Z) => (((~neq(Z, nil)) | (~frontsegP(X, Z))) | (~frontsegP(W, Z)))) & ((~(nil = X)) | (~(nil = W)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.60/0.77 tff(12,plain,
% 0.60/0.77 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~neq(V, nil)) | (~ssList(V)) | (![Z: $i] : ((~frontsegP(U, Z)) | (~frontsegP(V, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.60/0.77 tff(13,plain,
% 0.60/0.77 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~neq(V, nil)) | (~ssList(V)) | (![Z: $i] : ((~frontsegP(U, Z)) | (~frontsegP(V, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.60/0.77 tff(14,plain,
% 0.60/0.77 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~neq(V, nil)) | (~ssList(V)) | (![Z: $i] : ((~frontsegP(U, Z)) | (~frontsegP(V, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.60/0.77 tff(15,plain,
% 0.60/0.77 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~neq(V, nil)) | (~ssList(V)) | (![Z: $i] : ((~frontsegP(U, Z)) | (~frontsegP(V, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.60/0.77 tff(16,plain,
% 0.60/0.77 (ssList(U!45) & neq(V!46, nil) & ssList(V!46) & ((~((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.60/0.77 tff(17,plain,
% 0.60/0.77 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)))),
% 0.60/0.77 inference(and_elim,[status(thm)],[16])).
% 0.60/0.77 tff(18,plain,
% 0.60/0.77 (![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[17, 4])).
% 0.60/0.77 tff(19,plain,
% 0.60/0.77 (![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.60/0.77 tff(20,plain,
% 0.60/0.77 (ssList(V!46)),
% 0.60/0.77 inference(and_elim,[status(thm)],[16])).
% 0.60/0.77 tff(21,plain,
% 0.60/0.77 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(22,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[21])).
% 0.60/0.77 tff(23,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(24,plain,
% 0.60/0.77 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(25,plain,
% 0.60/0.77 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[24])).
% 0.60/0.77 tff(26,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.60/0.77 tff(27,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.60/0.77 tff(28,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.60/0.77 tff(29,plain,(
% 0.60/0.77 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.60/0.77 inference(skolemize,[status(sab)],[28])).
% 0.60/0.77 tff(30,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.60/0.77 tff(31,plain,
% 0.60/0.77 (((~![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)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(32,plain,
% 0.60/0.77 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(33,plain,
% 0.60/0.77 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.60/0.77 tff(34,plain,
% 0.60/0.77 (segmentP(nil, V!46) <=> (nil = V!46)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[33, 30, 20])).
% 0.60/0.77 tff(35,plain,
% 0.60/0.77 (^[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))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(36,plain,
% 0.60/0.77 (![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)))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[35])).
% 0.60/0.77 tff(37,plain,
% 0.60/0.77 (^[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))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(38,plain,
% 0.60/0.77 (![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)))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[37])).
% 0.60/0.77 tff(39,plain,
% 0.60/0.77 (![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)))))),
% 0.60/0.77 inference(transitivity,[status(thm)],[38, 36])).
% 0.60/0.77 tff(40,plain,
% 0.60/0.77 (![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)))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(41,plain,
% 0.60/0.77 (^[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)))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(42,plain,
% 0.60/0.77 (![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)))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[41])).
% 0.60/0.77 tff(43,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.60/0.77 tff(44,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.60/0.77 tff(45,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.60/0.77 tff(46,plain,(
% 0.60/0.77 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.60/0.77 inference(skolemize,[status(sab)],[45])).
% 0.60/0.77 tff(47,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.60/0.77 tff(48,plain,
% 0.60/0.77 (((~![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)))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(49,plain,
% 0.60/0.77 ((~![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)))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(50,plain,
% 0.60/0.77 ((~![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))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.60/0.78 tff(51,plain,
% 0.60/0.78 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[50, 47, 20])).
% 0.60/0.78 tff(52,plain,
% 0.60/0.78 (ssList(nil) <=> ssList(nil)),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(53,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.60/0.78 tff(54,plain,
% 0.60/0.78 (ssList(nil)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.60/0.78 tff(55,plain,
% 0.60/0.78 (((~![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))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(56,plain,
% 0.60/0.78 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(57,plain,
% 0.60/0.78 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.60/0.78 tff(58,plain,
% 0.60/0.78 (~((V!46 = nil) <=> neq(V!46, nil))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[57, 54, 51])).
% 0.60/0.78 tff(59,plain,
% 0.60/0.78 (neq(V!46, nil)),
% 0.60/0.78 inference(and_elim,[status(thm)],[16])).
% 0.60/0.78 tff(60,plain,
% 0.60/0.78 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 0.60/0.78 inference(tautology,[status(thm)],[])).
% 0.60/0.78 tff(61,plain,
% 0.60/0.78 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.60/0.78 tff(62,plain,
% 0.60/0.78 (~(V!46 = nil)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.60/0.78 tff(63,plain,
% 0.60/0.78 (^[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)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(64,plain,
% 0.60/0.78 (![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))))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[63])).
% 0.60/0.78 tff(65,plain,
% 0.60/0.78 (^[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)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(66,plain,
% 0.60/0.78 (![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))))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[65])).
% 0.60/0.78 tff(67,plain,
% 0.60/0.78 (![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))))),
% 0.60/0.78 inference(transitivity,[status(thm)],[66, 64])).
% 0.60/0.78 tff(68,plain,
% 0.60/0.78 (^[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)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(69,plain,
% 0.60/0.78 (![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))))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[68])).
% 0.60/0.78 tff(70,plain,
% 0.60/0.78 (![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)))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(71,plain,
% 0.60/0.78 (^[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)))))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(72,plain,
% 0.60/0.78 (![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)))))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[71])).
% 0.60/0.78 tff(73,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax54')).
% 0.60/0.78 tff(74,plain,
% 0.60/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.60/0.78 tff(75,plain,
% 0.60/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.60/0.78 tff(76,plain,(
% 0.60/0.78 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.60/0.78 inference(skolemize,[status(sab)],[75])).
% 0.60/0.78 tff(77,plain,
% 0.60/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.60/0.78 tff(78,plain,
% 0.60/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.60/0.78 tff(79,plain,
% 0.60/0.78 (((~![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))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(80,plain,
% 0.60/0.78 (((~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))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(81,plain,
% 0.60/0.78 (((~![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)))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[80])).
% 0.60/0.78 tff(82,plain,
% 0.60/0.78 (((~![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))))),
% 0.60/0.78 inference(transitivity,[status(thm)],[81, 79])).
% 0.60/0.78 tff(83,plain,
% 0.60/0.78 ((~![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))))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(84,plain,
% 0.60/0.78 ((~![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)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.60/0.78 tff(85,plain,
% 0.60/0.78 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[84, 78, 20])).
% 0.60/0.78 tff(86,plain,
% 0.60/0.78 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(87,plain,
% 0.60/0.78 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[86])).
% 0.60/0.78 tff(88,plain,
% 0.60/0.78 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(89,plain,
% 0.60/0.78 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(90,plain,
% 0.60/0.78 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[89])).
% 0.60/0.78 tff(91,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.60/0.78 tff(92,plain,
% 0.60/0.78 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.60/0.78 tff(93,plain,
% 0.60/0.78 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.60/0.78 tff(94,plain,(
% 0.60/0.78 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.60/0.78 inference(skolemize,[status(sab)],[93])).
% 0.60/0.78 tff(95,plain,
% 0.60/0.78 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.60/0.78 tff(96,plain,
% 0.60/0.78 (((~![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))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(97,plain,
% 0.60/0.78 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(98,plain,
% 0.60/0.78 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.60/0.78 tff(99,plain,
% 0.60/0.78 (segmentP(V!46, nil)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[98, 95, 20])).
% 0.60/0.78 tff(100,plain,
% 0.60/0.78 (((~![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)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(101,plain,
% 0.60/0.78 (((~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)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(102,plain,
% 0.60/0.78 (((~![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))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[101])).
% 0.60/0.78 tff(103,plain,
% 0.60/0.78 (((~![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)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[102, 100])).
% 0.60/0.78 tff(104,plain,
% 0.60/0.78 ((~![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)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(105,plain,
% 0.60/0.78 ((~![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))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.60/0.78 tff(106,plain,
% 0.60/0.78 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[105, 54, 99, 85])).
% 0.60/0.78 tff(107,plain,
% 0.60/0.78 (~segmentP(nil, V!46)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[106, 62])).
% 0.60/0.78 tff(108,plain,
% 0.60/0.78 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 0.60/0.78 inference(tautology,[status(thm)],[])).
% 0.60/0.78 tff(109,plain,
% 0.60/0.78 (~(nil = V!46)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[108, 107, 34])).
% 0.60/0.78 tff(110,plain,
% 0.60/0.78 (((~(nil = U!45)) | (~(nil = V!46))) | (nil = V!46)),
% 0.60/0.78 inference(tautology,[status(thm)],[])).
% 0.60/0.78 tff(111,plain,
% 0.60/0.78 ((~(nil = U!45)) | (~(nil = V!46))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.60/0.78 tff(112,plain,
% 0.60/0.78 ((~((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))),
% 0.60/0.78 inference(and_elim,[status(thm)],[16])).
% 0.60/0.78 tff(113,plain,
% 0.60/0.78 (~((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.60/0.78 tff(114,plain,
% 0.60/0.78 (((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))) | ssList(Z!47)),
% 0.60/0.78 inference(tautology,[status(thm)],[])).
% 0.60/0.78 tff(115,plain,
% 0.60/0.78 (ssList(Z!47)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.60/0.78 tff(116,plain,
% 0.60/0.78 (((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))) | neq(Z!47, nil)),
% 0.60/0.78 inference(tautology,[status(thm)],[])).
% 0.60/0.78 tff(117,plain,
% 0.60/0.78 (neq(Z!47, nil)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[116, 113])).
% 0.60/0.78 tff(118,plain,
% 0.60/0.78 (((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))) | frontsegP(V!46, Z!47)),
% 0.60/0.78 inference(tautology,[status(thm)],[])).
% 0.60/0.78 tff(119,plain,
% 0.60/0.78 (frontsegP(V!46, Z!47)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[118, 113])).
% 0.60/0.78 tff(120,plain,
% 0.60/0.78 (((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))) | frontsegP(U!45, Z!47)),
% 0.60/0.78 inference(tautology,[status(thm)],[])).
% 0.60/0.78 tff(121,plain,
% 0.60/0.78 (frontsegP(U!45, Z!47)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[120, 113])).
% 0.60/0.78 tff(122,plain,
% 0.60/0.78 (((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y)))) | ((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) <=> ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y)))) | (~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(123,plain,
% 0.60/0.78 (((~neq(Z!47, nil)) | (~ssList(Z!47)) | (~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47))) <=> ((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(124,plain,
% 0.60/0.78 (((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y)))) | ((~neq(Z!47, nil)) | (~ssList(Z!47)) | (~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)))) <=> ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y)))) | ((~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[123])).
% 0.60/0.78 tff(125,plain,
% 0.60/0.78 (((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y)))) | ((~neq(Z!47, nil)) | (~ssList(Z!47)) | (~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)))) <=> ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y)))) | (~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[124, 122])).
% 0.60/0.78 tff(126,plain,
% 0.60/0.78 ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y)))) | ((~neq(Z!47, nil)) | (~ssList(Z!47)) | (~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(127,plain,
% 0.60/0.78 ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~frontsegP(U!45, Y)) | (~frontsegP(V!46, Y)))) | (~frontsegP(U!45, Z!47)) | (~frontsegP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.60/0.79 tff(128,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[127, 121, 119, 117, 115, 19])).
% 0.60/0.79 % SZS output end Proof
% 0.60/0.79 % E exiting
%------------------------------------------------------------------------------