%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC096+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 05:30:09 AM UTC 2025
% Result : Theorem 0.18s 0.48s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWC096+1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 08:17:50 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.48 % SZS status Theorem
% 0.18/0.48 % SZS output start Proof
% 0.18/0.48 tff(tptp_fun_V_46_type, type, (
% 0.18/0.48 tptp_fun_V_46: $i)).
% 0.18/0.48 tff(app_type, type, (
% 0.18/0.48 app: ( $i * $i ) > $i)).
% 0.18/0.48 tff(cons_type, type, (
% 0.18/0.48 cons: ( $i * $i ) > $i)).
% 0.18/0.48 tff(nil_type, type, (
% 0.18/0.48 nil: $i)).
% 0.18/0.48 tff(tptp_fun_X1_47_type, type, (
% 0.18/0.48 tptp_fun_X1_47: $i)).
% 0.18/0.48 tff(tptp_fun_U_45_type, type, (
% 0.18/0.48 tptp_fun_U_45: $i)).
% 0.18/0.48 tff(ssList_type, type, (
% 0.18/0.48 ssList: $i > $o)).
% 0.18/0.48 tff(ssItem_type, type, (
% 0.18/0.48 ssItem: $i > $o)).
% 0.18/0.48 tff(tptp_fun_X2_48_type, type, (
% 0.18/0.48 tptp_fun_X2_48: $i)).
% 0.18/0.48 tff(neq_type, type, (
% 0.18/0.48 neq: ( $i * $i ) > $o)).
% 0.18/0.48 tff(1,plain,
% 0.18/0.48 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (cons(Y, nil) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))))) <=> (ssList(U!45) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (cons(Y, nil) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(2,plain,
% 0.18/0.48 ((ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (cons(Y, nil) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & (ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))))) <=> (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (cons(Y, nil) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(3,plain,
% 0.18/0.48 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (cons(Y, nil) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & (ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46))))))) <=> (ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (cons(Y, nil) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[2])).
% 0.18/0.48 tff(4,plain,
% 0.18/0.48 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (cons(Y, nil) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & (ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46))))))) <=> (ssList(U!45) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (cons(Y, nil) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[3, 1])).
% 0.18/0.48 tff(5,plain,
% 0.18/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (cons(Y, nil) = U) & (app(Z, cons(Y, nil)) = V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(cons(X1, nil) = U)) | (~(app(X2, cons(X1, nil)) = V))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (cons(Y, nil) = U) & (app(Z, cons(Y, nil)) = V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(cons(X1, nil) = U)) | (~(app(X2, cons(X1, nil)) = V)))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(6,plain,
% 0.18/0.48 ((~![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) & (cons(Y, nil) = U)) & (app(Z, cons(Y, nil)) = V)))) | ![X1: $i] : (ssItem(X1) => ![X2: $i] : (((~ssList(X2)) | (~(cons(X1, nil) = W))) | (~(app(X2, cons(X1, nil)) = X))))) & ((~neq(V, nil)) | neq(X, nil)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (cons(Y, nil) = U) & (app(Z, cons(Y, nil)) = V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(cons(X1, nil) = U)) | (~(app(X2, cons(X1, nil)) = V)))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 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) & (cons(Y, nil) = U)) & (app(Z, cons(Y, nil)) = V)))) | ![X1: $i] : (ssItem(X1) => ![X2: $i] : (((~ssList(X2)) | (~(cons(X1, nil) = W))) | (~(app(X2, cons(X1, nil)) = X))))) & ((~neq(V, nil)) | neq(X, nil)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.18/0.48 tff(8,plain,
% 0.18/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (cons(Y, nil) = U) & (app(Z, cons(Y, nil)) = V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(cons(X1, nil) = U)) | (~(app(X2, cons(X1, nil)) = V))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.18/0.48 tff(9,plain,
% 0.18/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (cons(Y, nil) = U) & (app(Z, cons(Y, nil)) = V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(cons(X1, nil) = U)) | (~(app(X2, cons(X1, nil)) = V))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.18/0.48 tff(10,plain,
% 0.18/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (cons(Y, nil) = U) & (app(Z, cons(Y, nil)) = V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(cons(X1, nil) = U)) | (~(app(X2, cons(X1, nil)) = V))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.18/0.48 tff(11,plain,
% 0.18/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (cons(Y, nil) = U) & (app(Z, cons(Y, nil)) = V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(cons(X1, nil) = U)) | (~(app(X2, cons(X1, nil)) = V))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.18/0.48 tff(12,plain,
% 0.18/0.48 (ssList(U!45) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (cons(Y, nil) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.18/0.48 tff(13,plain,
% 0.18/0.48 (ssItem(X1!47)),
% 0.18/0.48 inference(and_elim,[status(thm)],[12])).
% 0.18/0.48 tff(14,plain,
% 0.18/0.48 (^[Y: $i] : refl(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(15,plain,
% 0.18/0.48 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[14])).
% 0.18/0.48 tff(16,plain,
% 0.18/0.48 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(17,plain,
% 0.18/0.48 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.48 tff(18,plain,
% 0.18/0.48 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[17, 15])).
% 0.18/0.48 tff(19,plain,
% 0.18/0.48 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (cons(Y, nil) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(20,plain,
% 0.18/0.48 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (cons(Y, nil) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.48 tff(21,plain,
% 0.18/0.48 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (cons(Y, nil) = U!45) & (app(Z, cons(Y, nil)) = V!46))))),
% 0.18/0.48 inference(and_elim,[status(thm)],[12])).
% 0.18/0.48 tff(22,plain,
% 0.18/0.48 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.48 tff(23,plain,
% 0.18/0.48 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.18/0.48 tff(24,plain,
% 0.18/0.48 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))) | ((~ssItem(X1!47)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(X1!47, nil) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))) | (~ssItem(X1!47)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(X1!47, nil) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(25,plain,
% 0.18/0.48 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))) | ((~ssItem(X1!47)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(X1!47, nil) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(26,plain,
% 0.18/0.48 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))) | (~ssItem(X1!47)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(X1!47, nil) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.18/0.48 tff(27,plain,
% 0.18/0.48 (![Z: $i] : ((~ssList(Z)) | (~(cons(X1!47, nil) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 0.18/0.48 tff(28,plain,
% 0.18/0.48 (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))),
% 0.18/0.48 inference(and_elim,[status(thm)],[12])).
% 0.18/0.48 tff(29,plain,
% 0.18/0.48 (app(X2!48, cons(X1!47, nil)) = V!46),
% 0.18/0.48 inference(or_elim,[status(thm)],[28])).
% 0.18/0.48 tff(30,plain,
% 0.18/0.48 (cons(X1!47, nil) = U!45),
% 0.18/0.48 inference(or_elim,[status(thm)],[28])).
% 0.18/0.48 tff(31,plain,
% 0.18/0.48 (ssList(X2!48)),
% 0.18/0.48 inference(or_elim,[status(thm)],[28])).
% 0.18/0.48 tff(32,plain,
% 0.18/0.48 (((~![Z: $i] : ((~ssList(Z)) | (~(cons(X1!47, nil) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46)))) | ((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))) <=> ((~![Z: $i] : ((~ssList(Z)) | (~(cons(X1!47, nil) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46)))) | (~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(33,plain,
% 0.18/0.48 ((~![Z: $i] : ((~ssList(Z)) | (~(cons(X1!47, nil) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46)))) | ((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(34,plain,
% 0.18/0.48 ((~![Z: $i] : ((~ssList(Z)) | (~(cons(X1!47, nil) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46)))) | (~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.18/0.49 tff(35,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[34, 31, 30, 29, 27])).
% 0.18/0.49 % SZS output end Proof
% 0.18/0.49 % E exiting
%------------------------------------------------------------------------------