%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC405+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:31:09 AM UTC 2025
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC405+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 09:15:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(memberP_type, type, (
% 0.19/0.44 memberP: ( $i * $i ) > $o)).
% 0.19/0.44 tff(tptp_fun_Z_47_type, type, (
% 0.19/0.44 tptp_fun_Z_47: $i)).
% 0.19/0.44 tff(tptp_fun_V_46_type, type, (
% 0.19/0.44 tptp_fun_V_46: $i)).
% 0.19/0.44 tff(tptp_fun_U_45_type, type, (
% 0.19/0.44 tptp_fun_U_45: $i)).
% 0.19/0.44 tff(ssItem_type, type, (
% 0.19/0.44 ssItem: $i > $o)).
% 0.19/0.44 tff(ssList_type, type, (
% 0.19/0.44 ssList: $i > $o)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 ((ssList(U!45) & (![Y: $i] : (~(ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y))))) & ssList(V!46) & ssList(U!45) & (~(memberP(V!46, Z!47) | (~memberP(U!45, Z!47)) | (~ssItem(Z!47)))))) <=> (ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y))))) & ssList(V!46) & (~(memberP(V!46, Z!47) | (~memberP(U!45, Z!47)) | (~ssItem(Z!47)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 ((![Y: $i] : (~(ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y))))) & ssList(V!46) & ssList(U!45) & (~(memberP(V!46, Z!47) | (~memberP(U!45, Z!47)) | (~ssItem(Z!47))))) <=> (![Y: $i] : (~(ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y))))) & ssList(V!46) & ssList(U!45) & (~(memberP(V!46, Z!47) | (~memberP(U!45, Z!47)) | (~ssItem(Z!47)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 ((ssList(U!45) & (![Y: $i] : (~(ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y))))) & ssList(V!46) & ssList(U!45) & (~(memberP(V!46, Z!47) | (~memberP(U!45, Z!47)) | (~ssItem(Z!47)))))) <=> (ssList(U!45) & (![Y: $i] : (~(ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y))))) & ssList(V!46) & ssList(U!45) & (~(memberP(V!46, Z!47) | (~memberP(U!45, Z!47)) | (~ssItem(Z!47))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[2])).
% 0.19/0.44 tff(4,plain,
% 0.19/0.44 ((ssList(U!45) & (![Y: $i] : (~(ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y))))) & ssList(V!46) & ssList(U!45) & (~(memberP(V!46, Z!47) | (~memberP(U!45, Z!47)) | (~ssItem(Z!47)))))) <=> (ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y))))) & ssList(V!46) & (~(memberP(V!46, Z!47) | (~memberP(U!45, Z!47)) | (~ssItem(Z!47)))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[3, 1])).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (?[Y: $i] : (ssItem(Y) & (((~memberP(V, Y)) & memberP(U, Y)) | ((~memberP(U, Y)) & memberP(V, Y)))) | (~ssList(V)) | (~ssList(U)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z)))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (?[Y: $i] : (ssItem(Y) & (((~memberP(V, Y)) & memberP(U, Y)) | ((~memberP(U, Y)) & memberP(V, Y)))) | (~ssList(V)) | (~ssList(U)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(6,plain,
% 0.19/0.44 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | ?[Y: $i] : (ssItem(Y) & (((~memberP(X, Y)) & memberP(W, Y)) | ((~memberP(W, Y)) & memberP(X, Y))))) | ![Z: $i] : (ssItem(Z) => ((~memberP(U, Z)) | memberP(V, Z))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (?[Y: $i] : (ssItem(Y) & (((~memberP(V, Y)) & memberP(U, Y)) | ((~memberP(U, Y)) & memberP(V, Y)))) | (~ssList(V)) | (~ssList(U)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(7,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | ?[Y: $i] : (ssItem(Y) & (((~memberP(X, Y)) & memberP(W, Y)) | ((~memberP(W, Y)) & memberP(X, Y))))) | ![Z: $i] : (ssItem(Z) => ((~memberP(U, Z)) | memberP(V, Z))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.19/0.44 tff(8,plain,
% 0.19/0.44 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (?[Y: $i] : (ssItem(Y) & (((~memberP(V, Y)) & memberP(U, Y)) | ((~memberP(U, Y)) & memberP(V, Y)))) | (~ssList(V)) | (~ssList(U)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (?[Y: $i] : (ssItem(Y) & (((~memberP(V, Y)) & memberP(U, Y)) | ((~memberP(U, Y)) & memberP(V, Y)))) | (~ssList(V)) | (~ssList(U)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.19/0.44 tff(10,plain,
% 0.19/0.44 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (?[Y: $i] : (ssItem(Y) & (((~memberP(V, Y)) & memberP(U, Y)) | ((~memberP(U, Y)) & memberP(V, Y)))) | (~ssList(V)) | (~ssList(U)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.44 tff(11,plain,
% 0.19/0.44 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (?[Y: $i] : (ssItem(Y) & (((~memberP(V, Y)) & memberP(U, Y)) | ((~memberP(U, Y)) & memberP(V, Y)))) | (~ssList(V)) | (~ssList(U)) | ![Z: $i] : (memberP(V, Z) | (~memberP(U, Z)) | (~ssItem(Z)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.19/0.44 tff(12,plain,
% 0.19/0.44 (ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y))))) & ssList(V!46) & (~(memberP(V!46, Z!47) | (~memberP(U!45, Z!47)) | (~ssItem(Z!47))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.44 tff(13,plain,
% 0.19/0.44 (~(memberP(V!46, Z!47) | (~memberP(U!45, Z!47)) | (~ssItem(Z!47)))),
% 0.19/0.44 inference(and_elim,[status(thm)],[12])).
% 0.19/0.44 tff(14,plain,
% 0.19/0.44 (memberP(U!45, Z!47)),
% 0.19/0.44 inference(or_elim,[status(thm)],[13])).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 (~memberP(V!46, Z!47)),
% 0.19/0.44 inference(or_elim,[status(thm)],[13])).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 ((~((~memberP(U!45, Z!47)) | memberP(V!46, Z!47))) | (~memberP(U!45, Z!47)) | memberP(V!46, Z!47)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(17,plain,
% 0.19/0.44 (~((~memberP(U!45, Z!47)) | memberP(V!46, Z!47))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[16, 15, 14])).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 (((~((~memberP(U!45, Z!47)) | memberP(V!46, Z!47))) | (~(memberP(U!45, Z!47) | (~memberP(V!46, Z!47))))) | ((~memberP(U!45, Z!47)) | memberP(V!46, Z!47))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 ((~((~memberP(U!45, Z!47)) | memberP(V!46, Z!47))) | (~(memberP(U!45, Z!47) | (~memberP(V!46, Z!47))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.44 tff(20,plain,
% 0.19/0.44 (ssItem(Z!47)),
% 0.19/0.44 inference(or_elim,[status(thm)],[13])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 (^[Y: $i] : refl(((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y))))))) <=> ((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y))))))) <=> ![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y))) <=> ((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y)))))), ((ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y)))) <=> (ssItem(Y) & ((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y)))))))), rewrite((ssItem(Y) & ((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y)))))) <=> (~((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y))))))))), ((ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y)))) <=> (~((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y)))))))))), ((~(ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y))))) <=> (~(~((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y))))))))))), rewrite((~(~((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y))))))))) <=> ((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y)))))))), ((~(ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y))))) <=> ((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (![Y: $i] : (~(ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y))))) <=> ![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 (![Y: $i] : (~(ssItem(Y) & (((~memberP(V!46, Y)) & memberP(U!45, Y)) | ((~memberP(U!45, Y)) & memberP(V!46, Y)))))),
% 0.19/0.45 inference(and_elim,[status(thm)],[12])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 (![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 (((~![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y)))))))) | ((~ssItem(Z!47)) | (~((~((~memberP(U!45, Z!47)) | memberP(V!46, Z!47))) | (~(memberP(U!45, Z!47) | (~memberP(V!46, Z!47)))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y)))))))) | (~ssItem(Z!47)) | (~((~((~memberP(U!45, Z!47)) | memberP(V!46, Z!47))) | (~(memberP(U!45, Z!47) | (~memberP(V!46, Z!47)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 ((~![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y)))))))) | ((~ssItem(Z!47)) | (~((~((~memberP(U!45, Z!47)) | memberP(V!46, Z!47))) | (~(memberP(U!45, Z!47) | (~memberP(V!46, Z!47)))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 ((~![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(U!45, Y)) | memberP(V!46, Y))) | (~(memberP(U!45, Y) | (~memberP(V!46, Y)))))))) | (~ssItem(Z!47)) | (~((~((~memberP(U!45, Z!47)) | memberP(V!46, Z!47))) | (~(memberP(U!45, Z!47) | (~memberP(V!46, Z!47))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[30, 27, 20, 19])).
% 0.19/0.45 % SZS output end Proof
% 0.19/0.45 % E exiting
%------------------------------------------------------------------------------