%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC381+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 05:31:04 AM UTC 2025
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC381+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.13 % 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 09:09:35 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 tff(memberP_type, type, (
% 0.21/0.45 memberP: ( $i * $i ) > $o)).
% 0.21/0.45 tff(tptp_fun_V_46_type, type, (
% 0.21/0.45 tptp_fun_V_46: $i)).
% 0.21/0.45 tff(tptp_fun_U_45_type, type, (
% 0.21/0.45 tptp_fun_U_45: $i)).
% 0.21/0.45 tff(cons_type, type, (
% 0.21/0.45 cons: ( $i * $i ) > $i)).
% 0.21/0.45 tff(nil_type, type, (
% 0.21/0.45 nil: $i)).
% 0.21/0.45 tff(ssItem_type, type, (
% 0.21/0.45 ssItem: $i > $o)).
% 0.21/0.45 tff(neq_type, type, (
% 0.21/0.45 neq: ( $i * $i ) > $o)).
% 0.21/0.45 tff(tptp_fun_Z_47_type, type, (
% 0.21/0.45 tptp_fun_Z_47: $i)).
% 0.21/0.45 tff(ssList_type, type, (
% 0.21/0.45 ssList: $i > $o)).
% 0.21/0.45 tff(1,plain,
% 0.21/0.45 (^[Y: $i] : refl(((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y))) <=> ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(2,plain,
% 0.21/0.45 (![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y))) <=> ![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.45 tff(3,plain,
% 0.21/0.45 (^[Y: $i] : trans(monotonicity(rewrite((ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y)) <=> (~((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y))))), ((~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) <=> (~(~((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y))))))), rewrite((~(~((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y))))) <=> ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))), ((~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) <=> ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(4,plain,
% 0.21/0.46 (![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) <=> ![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.46 tff(5,plain,
% 0.21/0.46 ((ssList(U!45) & (ssList(V!46) & (~((~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47)))) & ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil))) <=> (ssList(U!45) & ssList(V!46) & (~((~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47)))) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(6,plain,
% 0.21/0.46 ((ssList(V!46) & (~((~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47)))) & ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil)) <=> (ssList(V!46) & (~((~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47)))) & ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(7,plain,
% 0.21/0.46 ((ssList(U!45) & (ssList(V!46) & (~((~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47)))) & ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil))) <=> (ssList(U!45) & (ssList(V!46) & (~((~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47)))) & ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[6])).
% 0.21/0.46 tff(8,plain,
% 0.21/0.46 ((ssList(U!45) & (ssList(V!46) & (~((~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47)))) & ssList(U!45) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil))) <=> (ssList(U!45) & ssList(V!46) & (~((~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47)))) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil))),
% 0.21/0.46 inference(transitivity,[status(thm)],[7, 5])).
% 0.21/0.46 tff(9,plain,
% 0.21/0.46 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Z: $i] : ((~(cons(Z, nil) = U)) | (~memberP(V, Z)) | (~ssItem(Z))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & (cons(Y, nil) = U) & memberP(V, Y)) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Z: $i] : ((~(cons(Z, nil) = U)) | (~memberP(V, Z)) | (~ssItem(Z))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & (cons(Y, nil) = U) & memberP(V, Y)) | (~neq(V, nil)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(10,plain,
% 0.21/0.46 ((~![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) & (cons(Y, nil) = U)) & memberP(V, Y))) | ![Z: $i] : (ssItem(Z) => ((~(cons(Z, nil) = W)) | (~memberP(X, Z))))) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Z: $i] : ((~(cons(Z, nil) = U)) | (~memberP(V, Z)) | (~ssItem(Z))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & (cons(Y, nil) = U) & memberP(V, Y)) | (~neq(V, nil)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(11,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ?[Y: $i] : ((ssItem(Y) & (cons(Y, nil) = U)) & memberP(V, Y))) | ![Z: $i] : (ssItem(Z) => ((~(cons(Z, nil) = W)) | (~memberP(X, Z))))) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.21/0.46 tff(12,plain,
% 0.21/0.46 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Z: $i] : ((~(cons(Z, nil) = U)) | (~memberP(V, Z)) | (~ssItem(Z))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & (cons(Y, nil) = U) & memberP(V, Y)) | (~neq(V, nil))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.46 tff(13,plain,
% 0.21/0.46 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Z: $i] : ((~(cons(Z, nil) = U)) | (~memberP(V, Z)) | (~ssItem(Z))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & (cons(Y, nil) = U) & memberP(V, Y)) | (~neq(V, nil))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.21/0.46 tff(14,plain,
% 0.21/0.46 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Z: $i] : ((~(cons(Z, nil) = U)) | (~memberP(V, Z)) | (~ssItem(Z))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & (cons(Y, nil) = U) & memberP(V, Y)) | (~neq(V, nil))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.46 tff(15,plain,
% 0.21/0.46 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Z: $i] : ((~(cons(Z, nil) = U)) | (~memberP(V, Z)) | (~ssItem(Z))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & (cons(Y, nil) = U) & memberP(V, Y)) | (~neq(V, nil))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.21/0.46 tff(16,plain,
% 0.21/0.46 (ssList(U!45) & ssList(V!46) & (~((~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47)))) & ![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y))) & neq(V!46, nil)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.21/0.46 tff(17,plain,
% 0.21/0.46 (![Y: $i] : (~(ssItem(Y) & (cons(Y, nil) = U!45) & memberP(V!46, Y)))),
% 0.21/0.46 inference(and_elim,[status(thm)],[16])).
% 0.21/0.46 tff(18,plain,
% 0.21/0.46 (![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[17, 4])).
% 0.21/0.46 tff(19,plain,
% 0.21/0.46 (![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.21/0.46 tff(20,plain,
% 0.21/0.46 (~((~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47)))),
% 0.21/0.46 inference(and_elim,[status(thm)],[16])).
% 0.21/0.46 tff(21,plain,
% 0.21/0.46 (ssItem(Z!47)),
% 0.21/0.46 inference(or_elim,[status(thm)],[20])).
% 0.21/0.46 tff(22,plain,
% 0.21/0.46 (memberP(V!46, Z!47)),
% 0.21/0.46 inference(or_elim,[status(thm)],[20])).
% 0.21/0.46 tff(23,plain,
% 0.21/0.46 (cons(Z!47, nil) = U!45),
% 0.21/0.46 inference(or_elim,[status(thm)],[20])).
% 0.21/0.46 tff(24,plain,
% 0.21/0.46 (((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | ((~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47)))) <=> ((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | (~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(25,plain,
% 0.21/0.46 (((~ssItem(Z!47)) | (~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47))) <=> ((~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(26,plain,
% 0.21/0.46 (((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | ((~ssItem(Z!47)) | (~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)))) <=> ((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | ((~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[25])).
% 0.21/0.46 tff(27,plain,
% 0.21/0.46 (((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | ((~ssItem(Z!47)) | (~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)))) <=> ((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | (~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[26, 24])).
% 0.21/0.46 tff(28,plain,
% 0.21/0.46 ((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | ((~ssItem(Z!47)) | (~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(29,plain,
% 0.21/0.46 ((~![Y: $i] : ((~ssItem(Y)) | (~(cons(Y, nil) = U!45)) | (~memberP(V!46, Y)))) | (~(cons(Z!47, nil) = U!45)) | (~memberP(V!46, Z!47)) | (~ssItem(Z!47))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.46 tff(30,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[29, 23, 22, 21, 19])).
% 0.21/0.46 % SZS output end Proof
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------