%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC024+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 05:29:57 AM UTC 2025
% Result : Theorem 0.83s 1.01s
% Output : Proof 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC024+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 08:08:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.83/1.01 % SZS status Theorem
% 0.83/1.01 % SZS output start Proof
% 0.83/1.01 tff(frontsegP_type, type, (
% 0.83/1.01 frontsegP: ( $i * $i ) > $o)).
% 0.83/1.01 tff(tptp_fun_U_45_type, type, (
% 0.83/1.01 tptp_fun_U_45: $i)).
% 0.83/1.01 tff(app_type, type, (
% 0.83/1.01 app: ( $i * $i ) > $i)).
% 0.83/1.01 tff(tptp_fun_Z_47_type, type, (
% 0.83/1.01 tptp_fun_Z_47: $i)).
% 0.83/1.01 tff(tptp_fun_V_46_type, type, (
% 0.83/1.01 tptp_fun_V_46: $i)).
% 0.83/1.01 tff(neq_type, type, (
% 0.83/1.01 neq: ( $i * $i ) > $o)).
% 0.83/1.01 tff(nil_type, type, (
% 0.83/1.01 nil: $i)).
% 0.83/1.01 tff(ssList_type, type, (
% 0.83/1.01 ssList: $i > $o)).
% 0.83/1.01 tff(cons_type, type, (
% 0.83/1.01 cons: ( $i * $i ) > $i)).
% 0.83/1.01 tff(ssItem_type, type, (
% 0.83/1.01 ssItem: $i > $o)).
% 0.83/1.01 tff(equalelemsP_type, type, (
% 0.83/1.01 equalelemsP: $i > $o)).
% 0.83/1.01 tff(segmentP_type, type, (
% 0.83/1.01 segmentP: ( $i * $i ) > $o)).
% 0.83/1.01 tff(1,plain,
% 0.83/1.01 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45))))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))) <=> (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45))))) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(2,plain,
% 0.83/1.01 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45)))))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45))))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(3,plain,
% 0.83/1.01 ((equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45)))))) <=> (equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45))))))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(4,plain,
% 0.83/1.01 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45)))))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45)))))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))),
% 0.83/1.01 inference(monotonicity,[status(thm)],[3])).
% 0.83/1.01 tff(5,plain,
% 0.83/1.01 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45)))))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45))))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))),
% 0.83/1.01 inference(transitivity,[status(thm)],[4, 2])).
% 0.83/1.01 tff(6,plain,
% 0.83/1.01 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45)))))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))) <=> (ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45))))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)))))),
% 0.83/1.01 inference(monotonicity,[status(thm)],[5])).
% 0.83/1.01 tff(7,plain,
% 0.83/1.01 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45)))))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))) <=> (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45))))) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))),
% 0.83/1.01 inference(transitivity,[status(thm)],[6, 1])).
% 0.83/1.01 tff(8,plain,
% 0.83/1.01 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Z: $i] : ((~equalelemsP(U)) | (~(app(U, Z) = V)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X1, nil)) = U))))) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Z: $i] : ((~equalelemsP(U)) | (~(app(U, Z) = V)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X1, nil)) = U))))) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)))))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(9,plain,
% 0.83/1.01 ((~![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) => (((~(app(W, Z) = X)) | (~equalelemsP(W))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (app(cons(X1, nil), X2) = Z)) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X1, nil)) = W))))))) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Z: $i] : ((~equalelemsP(U)) | (~(app(U, Z) = V)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X1, nil)) = U))))) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)))))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(10,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) => (((~(app(W, Z) = X)) | (~equalelemsP(W))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (app(cons(X1, nil), X2) = Z)) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X1, nil)) = W))))))) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.83/1.01 tff(11,plain,
% 0.83/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Z: $i] : ((~equalelemsP(U)) | (~(app(U, Z) = V)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X1, nil)) = U))))) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.83/1.01 tff(12,plain,
% 0.83/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Z: $i] : ((~equalelemsP(U)) | (~(app(U, Z) = V)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X1, nil)) = U))))) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.83/1.01 tff(13,plain,
% 0.83/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Z: $i] : ((~equalelemsP(U)) | (~(app(U, Z) = V)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X1, nil)) = U))))) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.83/1.01 tff(14,plain,
% 0.83/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Z: $i] : ((~equalelemsP(U)) | (~(app(U, Z) = V)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X1, nil)) = U))))) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.83/1.01 tff(15,plain,
% 0.83/1.01 (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & equalelemsP(U!45) & (app(U!45, Z!47) = V!46) & ssList(Z!47) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!47)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X1, nil)) = U!45))))) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.83/1.01 tff(16,plain,
% 0.83/1.01 (app(U!45, Z!47) = V!46),
% 0.83/1.01 inference(and_elim,[status(thm)],[15])).
% 0.83/1.01 tff(17,plain,
% 0.83/1.01 (frontsegP(app(U!45, Z!47), U!45) <=> frontsegP(V!46, U!45)),
% 0.83/1.01 inference(monotonicity,[status(thm)],[16])).
% 0.83/1.01 tff(18,plain,
% 0.83/1.01 (frontsegP(V!46, U!45) <=> frontsegP(app(U!45, Z!47), U!45)),
% 0.83/1.01 inference(symmetry,[status(thm)],[17])).
% 0.83/1.01 tff(19,plain,
% 0.83/1.01 ((~frontsegP(V!46, U!45)) <=> (~frontsegP(app(U!45, Z!47), U!45))),
% 0.83/1.01 inference(monotonicity,[status(thm)],[18])).
% 0.83/1.01 tff(20,plain,
% 0.83/1.01 (ssList(U!45)),
% 0.83/1.01 inference(and_elim,[status(thm)],[15])).
% 0.83/1.01 tff(21,plain,
% 0.83/1.01 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 0.83/1.01 inference(bind,[status(th)],[])).
% 0.83/1.01 tff(22,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.83/1.01 inference(quant_intro,[status(thm)],[21])).
% 0.83/1.01 tff(23,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(24,plain,
% 0.83/1.01 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 0.83/1.01 inference(bind,[status(th)],[])).
% 0.83/1.01 tff(25,plain,
% 0.83/1.01 (![U: $i] : (ssList(U) => frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.83/1.01 inference(quant_intro,[status(thm)],[24])).
% 0.83/1.01 tff(26,axiom,(![U: $i] : (ssList(U) => frontsegP(U, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax42')).
% 0.83/1.01 tff(27,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.83/1.01 tff(28,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.83/1.01 tff(29,plain,(
% 0.83/1.01 ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.83/1.01 inference(skolemize,[status(sab)],[28])).
% 0.83/1.01 tff(30,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.83/1.01 tff(31,plain,
% 0.83/1.01 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(U!45)) | frontsegP(U!45, U!45))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(U!45)) | frontsegP(U!45, U!45))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(32,plain,
% 0.83/1.01 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(U!45)) | frontsegP(U!45, U!45))),
% 0.83/1.01 inference(quant_inst,[status(thm)],[])).
% 0.83/1.01 tff(33,plain,
% 0.83/1.01 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(U!45)) | frontsegP(U!45, U!45)),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.83/1.01 tff(34,plain,
% 0.83/1.01 (frontsegP(U!45, U!45)),
% 0.83/1.01 inference(unit_resolution,[status(thm)],[33, 30, 20])).
% 0.83/1.01 tff(35,plain,
% 0.83/1.01 (^[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))))))),
% 0.83/1.01 inference(bind,[status(th)],[])).
% 0.83/1.01 tff(36,plain,
% 0.83/1.01 (![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)))))),
% 0.83/1.01 inference(quant_intro,[status(thm)],[35])).
% 0.83/1.01 tff(37,plain,
% 0.83/1.01 (^[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))))))),
% 0.83/1.01 inference(bind,[status(th)],[])).
% 0.83/1.01 tff(38,plain,
% 0.83/1.01 (![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)))))),
% 0.83/1.01 inference(quant_intro,[status(thm)],[37])).
% 0.83/1.01 tff(39,plain,
% 0.83/1.01 (![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)))))),
% 0.83/1.01 inference(transitivity,[status(thm)],[38, 36])).
% 0.83/1.01 tff(40,plain,
% 0.83/1.01 (![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)))))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(41,plain,
% 0.83/1.01 (^[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)))))))),
% 0.83/1.01 inference(bind,[status(th)],[])).
% 0.83/1.01 tff(42,plain,
% 0.83/1.01 (![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)))))),
% 0.83/1.01 inference(quant_intro,[status(thm)],[41])).
% 0.83/1.01 tff(43,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.83/1.01 tff(44,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.83/1.01 tff(45,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.83/1.01 tff(46,plain,(
% 0.83/1.01 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.83/1.01 inference(skolemize,[status(sab)],[45])).
% 0.83/1.01 tff(47,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.83/1.01 tff(48,plain,
% 0.83/1.01 (((~![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)))))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(49,plain,
% 0.83/1.01 ((~![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)))))),
% 0.83/1.01 inference(quant_inst,[status(thm)],[])).
% 0.83/1.01 tff(50,plain,
% 0.83/1.01 ((~![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))))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.83/1.01 tff(51,plain,
% 0.83/1.01 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.83/1.01 inference(unit_resolution,[status(thm)],[50, 47, 20])).
% 0.83/1.01 tff(52,plain,
% 0.83/1.01 (ssList(nil) <=> ssList(nil)),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(53,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.83/1.01 tff(54,plain,
% 0.83/1.01 (ssList(nil)),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.83/1.01 tff(55,plain,
% 0.83/1.01 (((~![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))))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(56,plain,
% 0.83/1.01 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.83/1.01 inference(quant_inst,[status(thm)],[])).
% 0.83/1.01 tff(57,plain,
% 0.83/1.01 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.83/1.01 tff(58,plain,
% 0.83/1.01 (~((U!45 = nil) <=> neq(U!45, nil))),
% 0.83/1.01 inference(unit_resolution,[status(thm)],[57, 54, 51])).
% 0.83/1.01 tff(59,plain,
% 0.83/1.01 ((U!45 = nil) <=> (nil = U!45)),
% 0.83/1.01 inference(commutativity,[status(thm)],[])).
% 0.83/1.01 tff(60,plain,
% 0.83/1.01 ((nil = U!45) <=> (U!45 = nil)),
% 0.83/1.01 inference(symmetry,[status(thm)],[59])).
% 0.83/1.01 tff(61,plain,
% 0.83/1.01 ((~(nil = U!45)) <=> (~(U!45 = nil))),
% 0.83/1.01 inference(monotonicity,[status(thm)],[60])).
% 0.83/1.01 tff(62,plain,
% 0.83/1.01 (ssList(V!46)),
% 0.83/1.01 inference(and_elim,[status(thm)],[15])).
% 0.83/1.01 tff(63,plain,
% 0.83/1.01 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.83/1.01 inference(bind,[status(th)],[])).
% 0.83/1.01 tff(64,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.83/1.01 inference(quant_intro,[status(thm)],[63])).
% 0.83/1.01 tff(65,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(66,plain,
% 0.83/1.01 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.83/1.01 inference(bind,[status(th)],[])).
% 0.83/1.01 tff(67,plain,
% 0.83/1.01 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.83/1.01 inference(quant_intro,[status(thm)],[66])).
% 0.83/1.01 tff(68,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.83/1.01 tff(69,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.83/1.01 tff(70,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.83/1.01 tff(71,plain,(
% 0.83/1.01 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.83/1.01 inference(skolemize,[status(sab)],[70])).
% 0.83/1.01 tff(72,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.83/1.01 tff(73,plain,
% 0.83/1.01 (((~![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)))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(74,plain,
% 0.83/1.01 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 0.83/1.01 inference(quant_inst,[status(thm)],[])).
% 0.83/1.01 tff(75,plain,
% 0.83/1.01 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.83/1.01 tff(76,plain,
% 0.83/1.01 (segmentP(nil, V!46) <=> (nil = V!46)),
% 0.83/1.01 inference(unit_resolution,[status(thm)],[75, 72, 62])).
% 0.83/1.01 tff(77,plain,
% 0.83/1.01 (((~![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)))))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(78,plain,
% 0.83/1.01 ((~![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)))))),
% 0.83/1.01 inference(quant_inst,[status(thm)],[])).
% 0.83/1.01 tff(79,plain,
% 0.83/1.01 ((~![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))))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.83/1.01 tff(80,plain,
% 0.83/1.01 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.83/1.01 inference(unit_resolution,[status(thm)],[79, 47, 62])).
% 0.83/1.01 tff(81,plain,
% 0.83/1.01 (((~![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))))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(82,plain,
% 0.83/1.01 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.83/1.01 inference(quant_inst,[status(thm)],[])).
% 0.83/1.01 tff(83,plain,
% 0.83/1.01 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.83/1.01 tff(84,plain,
% 0.83/1.01 (~((V!46 = nil) <=> neq(V!46, nil))),
% 0.83/1.01 inference(unit_resolution,[status(thm)],[83, 54, 80])).
% 0.83/1.01 tff(85,plain,
% 0.83/1.01 (neq(V!46, nil)),
% 0.83/1.01 inference(and_elim,[status(thm)],[15])).
% 0.83/1.01 tff(86,plain,
% 0.83/1.01 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 0.83/1.01 inference(tautology,[status(thm)],[])).
% 0.83/1.01 tff(87,plain,
% 0.83/1.01 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 0.83/1.01 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.83/1.01 tff(88,plain,
% 0.83/1.01 (~(V!46 = nil)),
% 0.83/1.01 inference(unit_resolution,[status(thm)],[87, 84])).
% 0.83/1.01 tff(89,plain,
% 0.83/1.01 (^[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)))))),
% 0.83/1.01 inference(bind,[status(th)],[])).
% 0.83/1.01 tff(90,plain,
% 0.83/1.01 (![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))))),
% 0.83/1.01 inference(quant_intro,[status(thm)],[89])).
% 0.83/1.01 tff(91,plain,
% 0.83/1.01 (^[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)))))),
% 0.83/1.01 inference(bind,[status(th)],[])).
% 0.83/1.01 tff(92,plain,
% 0.83/1.01 (![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))))),
% 0.83/1.01 inference(quant_intro,[status(thm)],[91])).
% 0.83/1.01 tff(93,plain,
% 0.83/1.01 (![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))))),
% 0.83/1.01 inference(transitivity,[status(thm)],[92, 90])).
% 0.83/1.01 tff(94,plain,
% 0.83/1.01 (^[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)))))),
% 0.83/1.01 inference(bind,[status(th)],[])).
% 0.83/1.01 tff(95,plain,
% 0.83/1.01 (![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))))),
% 0.83/1.01 inference(quant_intro,[status(thm)],[94])).
% 0.83/1.01 tff(96,plain,
% 0.83/1.01 (![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)))))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(97,plain,
% 0.83/1.01 (^[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)))))))),
% 0.83/1.01 inference(bind,[status(th)],[])).
% 0.83/1.01 tff(98,plain,
% 0.83/1.01 (![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)))))),
% 0.83/1.01 inference(quant_intro,[status(thm)],[97])).
% 0.83/1.01 tff(99,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')).
% 0.83/1.01 tff(100,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.83/1.01 tff(101,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.83/1.01 tff(102,plain,(
% 0.83/1.01 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.83/1.01 inference(skolemize,[status(sab)],[101])).
% 0.83/1.01 tff(103,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.83/1.01 tff(104,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[103, 93])).
% 0.83/1.01 tff(105,plain,
% 0.83/1.01 (((~![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))))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(106,plain,
% 0.83/1.01 (((~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))))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(107,plain,
% 0.83/1.01 (((~![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)))))),
% 0.83/1.01 inference(monotonicity,[status(thm)],[106])).
% 0.83/1.01 tff(108,plain,
% 0.83/1.01 (((~![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))))),
% 0.83/1.01 inference(transitivity,[status(thm)],[107, 105])).
% 0.83/1.01 tff(109,plain,
% 0.83/1.01 ((~![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))))),
% 0.83/1.01 inference(quant_inst,[status(thm)],[])).
% 0.83/1.01 tff(110,plain,
% 0.83/1.01 ((~![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)))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.83/1.01 tff(111,plain,
% 0.83/1.01 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 0.83/1.01 inference(unit_resolution,[status(thm)],[110, 104, 62])).
% 0.83/1.01 tff(112,plain,
% 0.83/1.01 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.83/1.01 inference(bind,[status(th)],[])).
% 0.83/1.01 tff(113,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.83/1.01 inference(quant_intro,[status(thm)],[112])).
% 0.83/1.01 tff(114,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(115,plain,
% 0.83/1.01 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.83/1.01 inference(bind,[status(th)],[])).
% 0.83/1.01 tff(116,plain,
% 0.83/1.01 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.83/1.01 inference(quant_intro,[status(thm)],[115])).
% 0.83/1.01 tff(117,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.83/1.01 tff(118,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.83/1.01 tff(119,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.83/1.01 tff(120,plain,(
% 0.83/1.01 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.83/1.01 inference(skolemize,[status(sab)],[119])).
% 0.83/1.01 tff(121,plain,
% 0.83/1.01 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.83/1.01 tff(122,plain,
% 0.83/1.01 (((~![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))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(123,plain,
% 0.83/1.01 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 0.83/1.01 inference(quant_inst,[status(thm)],[])).
% 0.83/1.01 tff(124,plain,
% 0.83/1.01 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.83/1.01 tff(125,plain,
% 0.83/1.01 (segmentP(V!46, nil)),
% 0.83/1.01 inference(unit_resolution,[status(thm)],[124, 121, 62])).
% 0.83/1.01 tff(126,plain,
% 0.83/1.01 (((~![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)))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(127,plain,
% 0.83/1.01 (((~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)))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(128,plain,
% 0.83/1.01 (((~![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))))),
% 0.83/1.01 inference(monotonicity,[status(thm)],[127])).
% 0.83/1.01 tff(129,plain,
% 0.83/1.01 (((~![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)))),
% 0.83/1.01 inference(transitivity,[status(thm)],[128, 126])).
% 0.83/1.01 tff(130,plain,
% 0.83/1.01 ((~![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)))),
% 0.83/1.01 inference(quant_inst,[status(thm)],[])).
% 0.83/1.01 tff(131,plain,
% 0.83/1.01 ((~![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))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.83/1.01 tff(132,plain,
% 0.83/1.01 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 0.83/1.01 inference(unit_resolution,[status(thm)],[131, 54, 125, 111])).
% 0.83/1.01 tff(133,plain,
% 0.83/1.01 (~segmentP(nil, V!46)),
% 0.83/1.01 inference(unit_resolution,[status(thm)],[132, 88])).
% 0.83/1.01 tff(134,plain,
% 0.83/1.01 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 0.83/1.01 inference(tautology,[status(thm)],[])).
% 0.83/1.01 tff(135,plain,
% 0.83/1.01 (~(nil = V!46)),
% 0.83/1.01 inference(unit_resolution,[status(thm)],[134, 133, 76])).
% 0.83/1.01 tff(136,plain,
% 0.83/1.01 ((~(~((nil = V!46) | (~(nil = U!45))))) <=> ((nil = V!46) | (~(nil = U!45)))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(137,plain,
% 0.83/1.01 (((~(nil = V!46)) & (nil = U!45)) <=> (~((nil = V!46) | (~(nil = U!45))))),
% 0.83/1.01 inference(rewrite,[status(thm)],[])).
% 0.83/1.01 tff(138,plain,
% 0.83/1.02 ((~((~(nil = V!46)) & (nil = U!45))) <=> (~(~((nil = V!46) | (~(nil = U!45)))))),
% 0.83/1.02 inference(monotonicity,[status(thm)],[137])).
% 0.83/1.02 tff(139,plain,
% 0.83/1.02 ((~((~(nil = V!46)) & (nil = U!45))) <=> ((nil = V!46) | (~(nil = U!45)))),
% 0.83/1.02 inference(transitivity,[status(thm)],[138, 136])).
% 0.83/1.02 tff(140,plain,
% 0.83/1.02 (~((~(nil = V!46)) & (nil = U!45))),
% 0.83/1.02 inference(and_elim,[status(thm)],[15])).
% 0.83/1.02 tff(141,plain,
% 0.83/1.02 ((nil = V!46) | (~(nil = U!45))),
% 0.83/1.02 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.83/1.02 tff(142,plain,
% 0.83/1.02 (~(nil = U!45)),
% 0.83/1.02 inference(unit_resolution,[status(thm)],[141, 135])).
% 0.83/1.02 tff(143,plain,
% 0.83/1.02 (~(U!45 = nil)),
% 0.83/1.02 inference(modus_ponens,[status(thm)],[142, 61])).
% 0.83/1.02 tff(144,plain,
% 0.83/1.02 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 0.83/1.02 inference(tautology,[status(thm)],[])).
% 0.83/1.02 tff(145,plain,
% 0.83/1.02 (neq(U!45, nil)),
% 0.83/1.02 inference(unit_resolution,[status(thm)],[144, 143, 58])).
% 0.83/1.02 tff(146,plain,
% 0.83/1.02 (^[Y: $i] : refl(((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y))))),
% 0.83/1.02 inference(bind,[status(th)],[])).
% 0.83/1.02 tff(147,plain,
% 0.83/1.02 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))),
% 0.83/1.02 inference(quant_intro,[status(thm)],[146])).
% 0.83/1.02 tff(148,plain,
% 0.83/1.02 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)) <=> (~((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y))))), ((~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))) <=> (~(~((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y))))))), rewrite((~(~((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y))))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))), ((~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))))),
% 0.83/1.02 inference(bind,[status(th)],[])).
% 0.83/1.02 tff(149,plain,
% 0.83/1.02 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))),
% 0.83/1.02 inference(quant_intro,[status(thm)],[148])).
% 0.83/1.02 tff(150,plain,
% 0.83/1.02 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)))),
% 0.83/1.02 inference(and_elim,[status(thm)],[15])).
% 0.83/1.02 tff(151,plain,
% 0.83/1.02 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))),
% 0.83/1.02 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.83/1.02 tff(152,plain,
% 0.83/1.02 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))),
% 0.83/1.02 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.83/1.02 tff(153,plain,
% 0.83/1.02 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))) | ((~ssList(U!45)) | (~neq(U!45, nil)) | (~frontsegP(V!46, U!45)) | (~frontsegP(U!45, U!45)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))) | (~ssList(U!45)) | (~neq(U!45, nil)) | (~frontsegP(V!46, U!45)) | (~frontsegP(U!45, U!45)))),
% 0.83/1.02 inference(rewrite,[status(thm)],[])).
% 0.83/1.02 tff(154,plain,
% 0.83/1.02 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))) | ((~ssList(U!45)) | (~neq(U!45, nil)) | (~frontsegP(V!46, U!45)) | (~frontsegP(U!45, U!45)))),
% 0.83/1.02 inference(quant_inst,[status(thm)],[])).
% 0.83/1.02 tff(155,plain,
% 0.83/1.02 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))) | (~ssList(U!45)) | (~neq(U!45, nil)) | (~frontsegP(V!46, U!45)) | (~frontsegP(U!45, U!45))),
% 0.83/1.02 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.83/1.02 tff(156,plain,
% 0.83/1.02 ((~neq(U!45, nil)) | (~frontsegP(V!46, U!45)) | (~frontsegP(U!45, U!45))),
% 0.83/1.02 inference(unit_resolution,[status(thm)],[155, 20, 152])).
% 0.83/1.02 tff(157,plain,
% 0.83/1.02 (~frontsegP(V!46, U!45)),
% 0.83/1.02 inference(unit_resolution,[status(thm)],[156, 145, 34])).
% 0.83/1.02 tff(158,plain,
% 0.83/1.02 (~frontsegP(app(U!45, Z!47), U!45)),
% 0.83/1.02 inference(modus_ponens,[status(thm)],[157, 19])).
% 0.83/1.02 tff(159,plain,
% 0.83/1.02 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))),
% 0.83/1.02 inference(bind,[status(th)],[])).
% 0.83/1.02 tff(160,plain,
% 0.83/1.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 0.83/1.02 inference(quant_intro,[status(thm)],[159])).
% 0.83/1.02 tff(161,plain,
% 0.83/1.02 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))),
% 0.83/1.02 inference(bind,[status(th)],[])).
% 0.83/1.02 tff(162,plain,
% 0.83/1.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 0.83/1.02 inference(quant_intro,[status(thm)],[161])).
% 0.83/1.02 tff(163,plain,
% 0.83/1.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 0.83/1.02 inference(transitivity,[status(thm)],[162, 160])).
% 0.83/1.02 tff(164,plain,
% 0.83/1.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 0.83/1.02 inference(rewrite,[status(thm)],[])).
% 0.83/1.02 tff(165,plain,
% 0.83/1.02 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite((frontsegP(U, V) => frontsegP(app(U, W), V)) <=> ((~frontsegP(U, V)) | frontsegP(app(U, W), V))), ((ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> (ssList(W) => ((~frontsegP(U, V)) | frontsegP(app(U, W), V))))), rewrite((ssList(W) => ((~frontsegP(U, V)) | frontsegP(app(U, W), V))) <=> (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))), ((ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), (![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))), ((ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> (ssList(V) => ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), rewrite((ssList(V) => ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))) <=> ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))), ((ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))))),
% 0.83/1.02 inference(bind,[status(th)],[])).
% 0.83/1.02 tff(166,plain,
% 0.83/1.02 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 0.83/1.02 inference(quant_intro,[status(thm)],[165])).
% 0.83/1.02 tff(167,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax43')).
% 0.83/1.02 tff(168,plain,
% 0.83/1.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 0.83/1.02 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.83/1.02 tff(169,plain,
% 0.83/1.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 0.83/1.02 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.83/1.02 tff(170,plain,(
% 0.83/1.02 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 0.83/1.02 inference(skolemize,[status(sab)],[169])).
% 0.83/1.02 tff(171,plain,
% 0.83/1.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 0.83/1.02 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.83/1.02 tff(172,plain,
% 0.83/1.02 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V)))))),
% 0.83/1.02 inference(rewrite,[status(thm)],[])).
% 0.83/1.02 tff(173,plain,
% 0.83/1.02 (((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U!45, W), V) | (~ssList(W)) | (~frontsegP(U!45, V))))) <=> ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V)))))),
% 0.83/1.02 inference(rewrite,[status(thm)],[])).
% 0.83/1.02 tff(174,plain,
% 0.83/1.02 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U!45, W), V) | (~ssList(W)) | (~frontsegP(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))))),
% 0.83/1.02 inference(monotonicity,[status(thm)],[173])).
% 0.83/1.02 tff(175,plain,
% 0.83/1.02 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U!45, W), V) | (~ssList(W)) | (~frontsegP(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V)))))),
% 0.83/1.02 inference(transitivity,[status(thm)],[174, 172])).
% 0.83/1.02 tff(176,plain,
% 0.83/1.02 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U!45, W), V) | (~ssList(W)) | (~frontsegP(U!45, V)))))),
% 0.83/1.02 inference(quant_inst,[status(thm)],[])).
% 0.83/1.02 tff(177,plain,
% 0.83/1.02 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))),
% 0.83/1.02 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.83/1.02 tff(178,plain,
% 0.83/1.02 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))),
% 0.83/1.02 inference(unit_resolution,[status(thm)],[177, 171, 20])).
% 0.83/1.02 tff(179,plain,
% 0.83/1.02 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45)))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45)))),
% 0.83/1.02 inference(rewrite,[status(thm)],[])).
% 0.83/1.02 tff(180,plain,
% 0.83/1.02 (((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), U!45) | (~frontsegP(U!45, U!45)))) <=> ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45)))),
% 0.83/1.02 inference(rewrite,[status(thm)],[])).
% 0.83/1.02 tff(181,plain,
% 0.83/1.02 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), U!45) | (~frontsegP(U!45, U!45))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))))),
% 0.83/1.02 inference(monotonicity,[status(thm)],[180])).
% 0.83/1.02 tff(182,plain,
% 0.83/1.02 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), U!45) | (~frontsegP(U!45, U!45))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45)))),
% 0.83/1.02 inference(transitivity,[status(thm)],[181, 179])).
% 0.83/1.02 tff(183,plain,
% 0.83/1.02 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), U!45) | (~frontsegP(U!45, U!45))))),
% 0.83/1.02 inference(quant_inst,[status(thm)],[])).
% 0.83/1.02 tff(184,plain,
% 0.83/1.02 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))),
% 0.83/1.02 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.83/1.02 tff(185,plain,
% 0.83/1.02 (![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))),
% 0.83/1.02 inference(unit_resolution,[status(thm)],[184, 20, 178])).
% 0.83/1.02 tff(186,plain,
% 0.83/1.02 (ssList(Z!47)),
% 0.83/1.02 inference(and_elim,[status(thm)],[15])).
% 0.83/1.02 tff(187,plain,
% 0.83/1.02 (((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | ((~ssList(Z!47)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, Z!47), U!45))) <=> ((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | (~ssList(Z!47)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, Z!47), U!45))),
% 0.83/1.02 inference(rewrite,[status(thm)],[])).
% 0.83/1.02 tff(188,plain,
% 0.83/1.02 ((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | ((~ssList(Z!47)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, Z!47), U!45))),
% 0.83/1.02 inference(quant_inst,[status(thm)],[])).
% 0.83/1.02 tff(189,plain,
% 0.83/1.02 ((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | (~ssList(Z!47)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, Z!47), U!45)),
% 0.83/1.02 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.83/1.03 tff(190,plain,
% 0.83/1.03 (frontsegP(app(U!45, Z!47), U!45)),
% 0.83/1.03 inference(unit_resolution,[status(thm)],[189, 186, 34, 185])).
% 0.83/1.03 tff(191,plain,
% 0.83/1.03 ($false),
% 0.83/1.03 inference(unit_resolution,[status(thm)],[190, 158])).
% 0.83/1.03 % SZS output end Proof
% 0.83/1.03 % E exiting
%------------------------------------------------------------------------------