%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC398+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:31:07 AM UTC 2025
% Result : Theorem 0.86s 1.06s
% Output : Proof 0.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC398+1 : TPTP v9.0.0. Released v2.4.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.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 09:14:39 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.86/1.06 % SZS status Theorem
% 0.86/1.06 % SZS output start Proof
% 0.86/1.06 tff(memberP_type, type, (
% 0.86/1.06 memberP: ( $i * $i ) > $o)).
% 0.86/1.06 tff(tptp_fun_X3_48_type, type, (
% 0.86/1.06 tptp_fun_X3_48: $i)).
% 0.86/1.06 tff(app_type, type, (
% 0.86/1.06 app: ( $i * $i ) > $i)).
% 0.86/1.06 tff(tptp_fun_Y_47_type, type, (
% 0.86/1.06 tptp_fun_Y_47: $i)).
% 0.86/1.06 tff(tptp_fun_U_45_type, type, (
% 0.86/1.06 tptp_fun_U_45: $i)).
% 0.86/1.06 tff(tptp_fun_V_46_type, type, (
% 0.86/1.06 tptp_fun_V_46: $i)).
% 0.86/1.06 tff(ssItem_type, type, (
% 0.86/1.06 ssItem: $i > $o)).
% 0.86/1.06 tff(cons_type, type, (
% 0.86/1.06 cons: ( $i * $i ) > $i)).
% 0.86/1.06 tff(nil_type, type, (
% 0.86/1.06 nil: $i)).
% 0.86/1.06 tff(ssList_type, type, (
% 0.86/1.06 ssList: $i > $o)).
% 0.86/1.06 tff(equalelemsP_type, type, (
% 0.86/1.06 equalelemsP: $i > $o)).
% 0.86/1.06 tff(1,plain,
% 0.86/1.06 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & ssList(U!45) & (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48)))))) <=> (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48)))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2,plain,
% 0.86/1.06 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48))))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & ssList(U!45) & (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48)))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3,plain,
% 0.86/1.06 ((~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48)))) <=> (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(4,plain,
% 0.86/1.06 (((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) <=> ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(5,plain,
% 0.86/1.06 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48))))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48)))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[4, 3])).
% 0.86/1.06 tff(6,plain,
% 0.86/1.06 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48))))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & ssList(U!45) & (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48)))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[5, 2])).
% 0.86/1.06 tff(7,plain,
% 0.86/1.06 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48)))))) <=> (ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & ssList(U!45) & (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[6])).
% 0.86/1.06 tff(8,plain,
% 0.86/1.06 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48)))))) <=> (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48)))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[7, 1])).
% 0.86/1.06 tff(9,plain,
% 0.86/1.06 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | ![X3: $i] : (memberP(V, X3) | (~ssItem(X3)) | (~memberP(U, X3)))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | ![X3: $i] : (memberP(V, X3) | (~ssItem(X3)) | (~memberP(U, X3))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(10,plain,
% 0.86/1.06 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~equalelemsP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))) | ![X3: $i] : (ssItem(X3) => ((~memberP(U, X3)) | memberP(V, X3)))) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | ![X3: $i] : (memberP(V, X3) | (~ssItem(X3)) | (~memberP(U, X3))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(11,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~equalelemsP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))) | ![X3: $i] : (ssItem(X3) => ((~memberP(U, X3)) | memberP(V, X3)))) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.86/1.06 tff(12,plain,
% 0.86/1.06 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | ![X3: $i] : (memberP(V, X3) | (~ssItem(X3)) | (~memberP(U, X3)))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.86/1.06 tff(13,plain,
% 0.86/1.06 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | ![X3: $i] : (memberP(V, X3) | (~ssItem(X3)) | (~memberP(U, X3)))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.86/1.06 tff(14,plain,
% 0.86/1.06 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | ![X3: $i] : (memberP(V, X3) | (~ssItem(X3)) | (~memberP(U, X3)))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.86/1.06 tff(15,plain,
% 0.86/1.06 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | ![X3: $i] : (memberP(V, X3) | (~ssItem(X3)) | (~memberP(U, X3)))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.86/1.06 tff(16,plain,
% 0.86/1.06 (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.86/1.06 tff(17,plain,
% 0.86/1.06 (app(U!45, Y!47) = V!46),
% 0.86/1.06 inference(and_elim,[status(thm)],[16])).
% 0.86/1.06 tff(18,plain,
% 0.86/1.06 (memberP(app(U!45, Y!47), X3!48) <=> memberP(V!46, X3!48)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[17])).
% 0.86/1.06 tff(19,plain,
% 0.86/1.06 (memberP(V!46, X3!48) <=> memberP(app(U!45, Y!47), X3!48)),
% 0.86/1.06 inference(symmetry,[status(thm)],[18])).
% 0.86/1.06 tff(20,plain,
% 0.86/1.06 ((~memberP(V!46, X3!48)) <=> (~memberP(app(U!45, Y!47), X3!48))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[19])).
% 0.86/1.06 tff(21,plain,
% 0.86/1.06 (~(memberP(V!46, X3!48) | (~ssItem(X3!48)) | (~memberP(U!45, X3!48)))),
% 0.86/1.06 inference(and_elim,[status(thm)],[16])).
% 0.86/1.06 tff(22,plain,
% 0.86/1.06 (~memberP(V!46, X3!48)),
% 0.86/1.06 inference(or_elim,[status(thm)],[21])).
% 0.86/1.06 tff(23,plain,
% 0.86/1.06 (~memberP(app(U!45, Y!47), X3!48)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.86/1.06 tff(24,plain,
% 0.86/1.06 (ssItem(X3!48)),
% 0.86/1.06 inference(or_elim,[status(thm)],[21])).
% 0.86/1.06 tff(25,plain,
% 0.86/1.06 (^[U: $i] : refl(((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(26,plain,
% 0.86/1.06 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[25])).
% 0.86/1.06 tff(27,plain,
% 0.86/1.06 (^[U: $i] : rewrite(((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(28,plain,
% 0.86/1.06 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[27])).
% 0.86/1.06 tff(29,plain,
% 0.86/1.06 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[28, 26])).
% 0.86/1.06 tff(30,plain,
% 0.86/1.06 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(31,plain,
% 0.86/1.06 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite((memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))) <=> (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))), ((ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> (ssList(W) => (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), rewrite((ssList(W) => (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))) <=> ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))), ((ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), (![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), ((ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> (ssItem(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))), rewrite((ssItem(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), ((ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(32,plain,
% 0.86/1.06 (![U: $i] : (ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[31])).
% 0.86/1.06 tff(33,axiom,(![U: $i] : (ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax36')).
% 0.86/1.06 tff(34,plain,
% 0.86/1.06 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.86/1.06 tff(35,plain,
% 0.86/1.06 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.86/1.06 tff(36,plain,(
% 0.86/1.06 ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.86/1.06 inference(skolemize,[status(sab)],[35])).
% 0.86/1.06 tff(37,plain,
% 0.86/1.06 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.86/1.06 tff(38,plain,
% 0.86/1.06 (((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | ((~ssItem(X3!48)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!48) <=> (memberP(W, X3!48) | memberP(V, X3!48))))))) <=> ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | (~ssItem(X3!48)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!48) <=> (memberP(W, X3!48) | memberP(V, X3!48))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(39,plain,
% 0.86/1.06 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | ((~ssItem(X3!48)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!48) <=> (memberP(W, X3!48) | memberP(V, X3!48))))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(40,plain,
% 0.86/1.06 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | (~ssItem(X3!48)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!48) <=> (memberP(W, X3!48) | memberP(V, X3!48)))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.86/1.06 tff(41,plain,
% 0.86/1.06 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!48) <=> (memberP(W, X3!48) | memberP(V, X3!48)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[40, 37, 24])).
% 0.86/1.06 tff(42,plain,
% 0.86/1.06 (ssList(U!45)),
% 0.86/1.06 inference(and_elim,[status(thm)],[16])).
% 0.86/1.06 tff(43,plain,
% 0.86/1.06 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!48) <=> (memberP(W, X3!48) | memberP(V, X3!48)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(U!45, X3!48) | memberP(W, X3!48)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!48) <=> (memberP(W, X3!48) | memberP(V, X3!48)))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(U!45, X3!48) | memberP(W, X3!48)))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(44,plain,
% 0.86/1.06 (((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(W, X3!48) | memberP(U!45, X3!48))))) <=> ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(U!45, X3!48) | memberP(W, X3!48)))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(45,plain,
% 0.86/1.06 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!48) <=> (memberP(W, X3!48) | memberP(V, X3!48)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(W, X3!48) | memberP(U!45, X3!48)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!48) <=> (memberP(W, X3!48) | memberP(V, X3!48)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(U!45, X3!48) | memberP(W, X3!48))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[44])).
% 0.86/1.06 tff(46,plain,
% 0.86/1.06 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!48) <=> (memberP(W, X3!48) | memberP(V, X3!48)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(W, X3!48) | memberP(U!45, X3!48)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!48) <=> (memberP(W, X3!48) | memberP(V, X3!48)))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(U!45, X3!48) | memberP(W, X3!48)))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[45, 43])).
% 0.86/1.06 tff(47,plain,
% 0.86/1.06 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!48) <=> (memberP(W, X3!48) | memberP(V, X3!48)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(W, X3!48) | memberP(U!45, X3!48)))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(48,plain,
% 0.86/1.06 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X3!48) <=> (memberP(W, X3!48) | memberP(V, X3!48)))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(U!45, X3!48) | memberP(W, X3!48))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.86/1.06 tff(49,plain,
% 0.86/1.06 (![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(U!45, X3!48) | memberP(W, X3!48))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[48, 42, 41])).
% 0.86/1.06 tff(50,plain,
% 0.86/1.06 (ssList(Y!47)),
% 0.86/1.06 inference(and_elim,[status(thm)],[16])).
% 0.86/1.06 tff(51,plain,
% 0.86/1.06 (((~![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(U!45, X3!48) | memberP(W, X3!48))))) | ((~ssList(Y!47)) | (memberP(app(U!45, Y!47), X3!48) <=> (memberP(U!45, X3!48) | memberP(Y!47, X3!48))))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(U!45, X3!48) | memberP(W, X3!48))))) | (~ssList(Y!47)) | (memberP(app(U!45, Y!47), X3!48) <=> (memberP(U!45, X3!48) | memberP(Y!47, X3!48))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(52,plain,
% 0.86/1.06 ((~![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(U!45, X3!48) | memberP(W, X3!48))))) | ((~ssList(Y!47)) | (memberP(app(U!45, Y!47), X3!48) <=> (memberP(U!45, X3!48) | memberP(Y!47, X3!48))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(53,plain,
% 0.86/1.06 ((~![W: $i] : ((~ssList(W)) | (memberP(app(U!45, W), X3!48) <=> (memberP(U!45, X3!48) | memberP(W, X3!48))))) | (~ssList(Y!47)) | (memberP(app(U!45, Y!47), X3!48) <=> (memberP(U!45, X3!48) | memberP(Y!47, X3!48)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.86/1.06 tff(54,plain,
% 0.86/1.06 (memberP(app(U!45, Y!47), X3!48) <=> (memberP(U!45, X3!48) | memberP(Y!47, X3!48))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[53, 50, 49])).
% 0.86/1.06 tff(55,plain,
% 0.86/1.06 (memberP(U!45, X3!48)),
% 0.86/1.06 inference(or_elim,[status(thm)],[21])).
% 0.86/1.06 tff(56,plain,
% 0.86/1.06 ((memberP(U!45, X3!48) | memberP(Y!47, X3!48)) | (~memberP(U!45, X3!48))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(57,plain,
% 0.86/1.06 (memberP(U!45, X3!48) | memberP(Y!47, X3!48)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.86/1.06 tff(58,plain,
% 0.86/1.06 ((~(memberP(app(U!45, Y!47), X3!48) <=> (memberP(U!45, X3!48) | memberP(Y!47, X3!48)))) | memberP(app(U!45, Y!47), X3!48) | (~(memberP(U!45, X3!48) | memberP(Y!47, X3!48)))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(59,plain,
% 0.86/1.06 ((~(memberP(app(U!45, Y!47), X3!48) <=> (memberP(U!45, X3!48) | memberP(Y!47, X3!48)))) | memberP(app(U!45, Y!47), X3!48)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.86/1.06 tff(60,plain,
% 0.86/1.06 (memberP(app(U!45, Y!47), X3!48)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[59, 54])).
% 0.86/1.07 tff(61,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[60, 23])).
% 0.86/1.07 % SZS output end Proof
% 0.86/1.08 % E exiting
%------------------------------------------------------------------------------