%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC012+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:29:55 AM UTC 2025
% Result : Theorem 0.71s 0.93s
% Output : Proof 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC012+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 08:00:20 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.71/0.93 % SZS status Theorem
% 0.71/0.93 % SZS output start Proof
% 0.71/0.93 tff(tptp_fun_V_46_type, type, (
% 0.71/0.93 tptp_fun_V_46: $i)).
% 0.71/0.93 tff(app_type, type, (
% 0.71/0.93 app: ( $i * $i ) > $i)).
% 0.71/0.93 tff(nil_type, type, (
% 0.71/0.93 nil: $i)).
% 0.71/0.93 tff(cons_type, type, (
% 0.71/0.93 cons: ( $i * $i ) > $i)).
% 0.71/0.93 tff(tptp_fun_X2_47_type, type, (
% 0.71/0.93 tptp_fun_X2_47: $i)).
% 0.71/0.93 tff(tptp_fun_U_45_type, type, (
% 0.71/0.93 tptp_fun_U_45: $i)).
% 0.71/0.93 tff(ssList_type, type, (
% 0.71/0.93 ssList: $i > $o)).
% 0.71/0.93 tff(neq_type, type, (
% 0.71/0.93 neq: ( $i * $i ) > $o)).
% 0.71/0.93 tff(ssItem_type, type, (
% 0.71/0.93 ssItem: $i > $o)).
% 0.71/0.93 tff(1,plain,
% 0.71/0.93 ((ssList(U!45) & (ssList(V!46) & (~((~ssItem(X2!47)) | (~(app(U!45, cons(X2!47, nil)) = V!46)))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(Z, X1) = U!45))))) & neq(V!46, nil))) <=> (ssList(U!45) & ssList(V!46) & (~((~ssItem(X2!47)) | (~(app(U!45, cons(X2!47, nil)) = V!46)))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(Z, X1) = U!45))))) & neq(V!46, nil))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(2,plain,
% 0.71/0.93 ((ssList(V!46) & (~((~ssItem(X2!47)) | (~(app(U!45, cons(X2!47, nil)) = V!46)))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(Z, X1) = U!45))))) & neq(V!46, nil)) <=> (ssList(V!46) & (~((~ssItem(X2!47)) | (~(app(U!45, cons(X2!47, nil)) = V!46)))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(Z, X1) = U!45))))) & neq(V!46, nil))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(3,plain,
% 0.71/0.93 ((ssList(U!45) & (ssList(V!46) & (~((~ssItem(X2!47)) | (~(app(U!45, cons(X2!47, nil)) = V!46)))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(Z, X1) = U!45))))) & neq(V!46, nil))) <=> (ssList(U!45) & (ssList(V!46) & (~((~ssItem(X2!47)) | (~(app(U!45, cons(X2!47, nil)) = V!46)))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(Z, X1) = U!45))))) & neq(V!46, nil)))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[2])).
% 0.71/0.93 tff(4,plain,
% 0.71/0.93 ((ssList(U!45) & (ssList(V!46) & (~((~ssItem(X2!47)) | (~(app(U!45, cons(X2!47, nil)) = V!46)))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(Z, X1) = U!45))))) & neq(V!46, nil))) <=> (ssList(U!45) & ssList(V!46) & (~((~ssItem(X2!47)) | (~(app(U!45, cons(X2!47, nil)) = V!46)))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(Z, X1) = U!45))))) & neq(V!46, nil))),
% 0.71/0.93 inference(transitivity,[status(thm)],[3, 1])).
% 0.71/0.93 tff(5,plain,
% 0.71/0.93 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![X2: $i] : ((~ssItem(X2)) | (~(app(U, cons(X2, nil)) = V))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(Z, X1) = U)))) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![X2: $i] : ((~ssItem(X2)) | (~(app(U, cons(X2, nil)) = V))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(Z, X1) = U)))) | (~neq(V, nil)))))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(6,plain,
% 0.71/0.93 ((~![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] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V)) & (app(Z, X1) = U))))) | ![X2: $i] : (ssItem(X2) => (~(app(W, cons(X2, nil)) = X)))) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![X2: $i] : ((~ssItem(X2)) | (~(app(U, cons(X2, nil)) = V))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(Z, X1) = U)))) | (~neq(V, nil)))))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(7,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V)) & (app(Z, X1) = U))))) | ![X2: $i] : (ssItem(X2) => (~(app(W, cons(X2, nil)) = X)))) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.71/0.93 tff(8,plain,
% 0.71/0.93 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![X2: $i] : ((~ssItem(X2)) | (~(app(U, cons(X2, nil)) = V))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(Z, X1) = U)))) | (~neq(V, nil))))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.71/0.93 tff(9,plain,
% 0.71/0.93 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![X2: $i] : ((~ssItem(X2)) | (~(app(U, cons(X2, nil)) = V))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(Z, X1) = U)))) | (~neq(V, nil))))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.71/0.93 tff(10,plain,
% 0.71/0.93 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![X2: $i] : ((~ssItem(X2)) | (~(app(U, cons(X2, nil)) = V))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(Z, X1) = U)))) | (~neq(V, nil))))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.71/0.93 tff(11,plain,
% 0.71/0.93 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![X2: $i] : ((~ssItem(X2)) | (~(app(U, cons(X2, nil)) = V))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(Z, X1) = U)))) | (~neq(V, nil))))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.71/0.93 tff(12,plain,
% 0.71/0.93 (ssList(U!45) & ssList(V!46) & (~((~ssItem(X2!47)) | (~(app(U!45, cons(X2!47, nil)) = V!46)))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(Z, X1) = U!45))))) & neq(V!46, nil)),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.71/0.93 tff(13,plain,
% 0.71/0.93 (ssList(V!46)),
% 0.71/0.93 inference(and_elim,[status(thm)],[12])).
% 0.71/0.93 tff(14,plain,
% 0.71/0.93 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 0.71/0.93 inference(bind,[status(th)],[])).
% 0.71/0.93 tff(15,plain,
% 0.71/0.93 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.71/0.93 inference(quant_intro,[status(thm)],[14])).
% 0.71/0.93 tff(16,plain,
% 0.71/0.93 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(17,plain,
% 0.71/0.93 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 0.71/0.93 inference(bind,[status(th)],[])).
% 0.71/0.93 tff(18,plain,
% 0.71/0.93 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.71/0.93 inference(quant_intro,[status(thm)],[17])).
% 0.71/0.93 tff(19,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax84')).
% 0.71/0.93 tff(20,plain,
% 0.71/0.93 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.71/0.93 tff(21,plain,
% 0.71/0.93 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.71/0.93 tff(22,plain,(
% 0.71/0.93 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.71/0.93 inference(skolemize,[status(sab)],[21])).
% 0.71/0.93 tff(23,plain,
% 0.71/0.93 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.71/0.93 tff(24,plain,
% 0.71/0.93 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(25,plain,
% 0.77/0.93 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(26,plain,
% 0.77/0.93 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.77/0.93 tff(27,plain,
% 0.77/0.93 (app(V!46, nil) = V!46),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 0.77/0.93 tff(28,plain,
% 0.77/0.93 (~((~ssItem(X2!47)) | (~(app(U!45, cons(X2!47, nil)) = V!46)))),
% 0.77/0.93 inference(and_elim,[status(thm)],[12])).
% 0.77/0.93 tff(29,plain,
% 0.77/0.93 (app(U!45, cons(X2!47, nil)) = V!46),
% 0.77/0.93 inference(or_elim,[status(thm)],[28])).
% 0.77/0.93 tff(30,plain,
% 0.77/0.93 (app(app(U!45, cons(X2!47, nil)), nil) = app(V!46, nil)),
% 0.77/0.93 inference(monotonicity,[status(thm)],[29])).
% 0.77/0.93 tff(31,plain,
% 0.77/0.93 (app(app(U!45, cons(X2!47, nil)), nil) = V!46),
% 0.77/0.93 inference(transitivity,[status(thm)],[30, 27])).
% 0.77/0.93 tff(32,plain,
% 0.77/0.93 (^[Y: $i] : refl(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45))))))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(33,plain,
% 0.77/0.93 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[32])).
% 0.77/0.93 tff(34,plain,
% 0.77/0.93 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45))))))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(35,plain,
% 0.77/0.93 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[34])).
% 0.77/0.93 tff(36,plain,
% 0.77/0.93 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))),
% 0.77/0.93 inference(transitivity,[status(thm)],[35, 33])).
% 0.77/0.93 tff(37,plain,
% 0.77/0.93 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(Z, X1) = U!45))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45))))))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(38,plain,
% 0.77/0.93 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(Z, X1) = U!45))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[37])).
% 0.77/0.93 tff(39,plain,
% 0.77/0.93 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(Z, X1) = U!45)))))),
% 0.77/0.93 inference(and_elim,[status(thm)],[12])).
% 0.77/0.93 tff(40,plain,
% 0.77/0.93 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.77/0.93 tff(41,plain,
% 0.77/0.93 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.77/0.93 tff(42,plain,
% 0.77/0.93 (ssItem(X2!47)),
% 0.77/0.93 inference(or_elim,[status(thm)],[28])).
% 0.77/0.93 tff(43,plain,
% 0.77/0.93 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))) | ((~ssItem(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Z, X1) = U!45)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))) | (~ssItem(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Z, X1) = U!45)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)))))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(44,plain,
% 0.77/0.93 (((~ssItem(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45))))) <=> ((~ssItem(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Z, X1) = U!45)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)))))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(45,plain,
% 0.77/0.93 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))) | ((~ssItem(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))) | ((~ssItem(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Z, X1) = U!45)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46))))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[44])).
% 0.77/0.93 tff(46,plain,
% 0.77/0.93 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))) | ((~ssItem(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))) | (~ssItem(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Z, X1) = U!45)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)))))),
% 0.77/0.93 inference(transitivity,[status(thm)],[45, 43])).
% 0.77/0.93 tff(47,plain,
% 0.77/0.93 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))) | ((~ssItem(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(48,plain,
% 0.77/0.93 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(Z, X1) = U!45)))))) | (~ssItem(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Z, X1) = U!45)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46))))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.77/0.93 tff(49,plain,
% 0.77/0.93 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Z, X1) = U!45)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46))))),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[48, 42, 41])).
% 0.77/0.93 tff(50,plain,
% 0.77/0.93 (ssList(U!45)),
% 0.77/0.93 inference(and_elim,[status(thm)],[12])).
% 0.77/0.93 tff(51,plain,
% 0.77/0.93 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Z, X1) = U!45)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46))))) | ((~ssList(U!45)) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, cons(X2!47, nil)), X1) = V!46))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Z, X1) = U!45)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46))))) | (~ssList(U!45)) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, cons(X2!47, nil)), X1) = V!46))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(52,plain,
% 0.77/0.94 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Z, X1) = U!45)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46))))) | ((~ssList(U!45)) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, cons(X2!47, nil)), X1) = V!46))))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(53,plain,
% 0.77/0.94 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Z, X1) = U!45)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46))))) | (~ssList(U!45)) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, cons(X2!47, nil)), X1) = V!46)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.77/0.94 tff(54,plain,
% 0.77/0.94 (![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, cons(X2!47, nil)), X1) = V!46)))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[53, 50, 49])).
% 0.77/0.94 tff(55,plain,
% 0.77/0.94 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(U!45)) | (app(U!45, nil) = U!45))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(U!45)) | (app(U!45, nil) = U!45))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(56,plain,
% 0.77/0.94 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(U!45)) | (app(U!45, nil) = U!45))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(57,plain,
% 0.77/0.94 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(U!45)) | (app(U!45, nil) = U!45)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.77/0.94 tff(58,plain,
% 0.77/0.94 (app(U!45, nil) = U!45),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[57, 23, 50])).
% 0.77/0.94 tff(59,plain,
% 0.77/0.94 (ssList(nil) <=> ssList(nil)),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(60,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.77/0.94 tff(61,plain,
% 0.77/0.94 (ssList(nil)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.77/0.94 tff(62,plain,
% 0.77/0.94 (((~![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, cons(X2!47, nil)), X1) = V!46)))) | ((~ssList(nil)) | (~(app(U!45, nil) = U!45)) | (~(app(app(U!45, cons(X2!47, nil)), nil) = V!46)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, cons(X2!47, nil)), X1) = V!46)))) | (~ssList(nil)) | (~(app(U!45, nil) = U!45)) | (~(app(app(U!45, cons(X2!47, nil)), nil) = V!46)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(63,plain,
% 0.77/0.94 ((~![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, cons(X2!47, nil)), X1) = V!46)))) | ((~ssList(nil)) | (~(app(U!45, nil) = U!45)) | (~(app(app(U!45, cons(X2!47, nil)), nil) = V!46)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(64,plain,
% 0.77/0.94 ((~![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, cons(X2!47, nil)), X1) = V!46)))) | (~ssList(nil)) | (~(app(U!45, nil) = U!45)) | (~(app(app(U!45, cons(X2!47, nil)), nil) = V!46))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.77/0.94 tff(65,plain,
% 0.77/0.94 (~(app(app(U!45, cons(X2!47, nil)), nil) = V!46)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[64, 61, 58, 54])).
% 0.77/0.94 tff(66,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[65, 31])).
% 0.77/0.94 % SZS output end Proof
% 0.77/0.94 % E exiting
%------------------------------------------------------------------------------