%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC252+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:30:41 AM UTC 2025
% Result : Theorem 138.45s 138.71s
% Output : Proof 138.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC252+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 08:44:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 138.45/138.71 % SZS status Theorem
% 138.45/138.71 % SZS output start Proof
% 138.45/138.71 tff(ssItem_type, type, (
% 138.45/138.71 ssItem: $i > $o)).
% 138.45/138.71 tff(tptp_fun_X2_48_type, type, (
% 138.45/138.71 tptp_fun_X2_48: ( $i * $i * $i ) > $i)).
% 138.45/138.71 tff(tptp_fun_X3_47_type, type, (
% 138.45/138.71 tptp_fun_X3_47: $i)).
% 138.45/138.71 tff(nil_type, type, (
% 138.45/138.71 nil: $i)).
% 138.45/138.71 tff(lt_type, type, (
% 138.45/138.71 lt: ( $i * $i ) > $o)).
% 138.45/138.71 tff(memberP_type, type, (
% 138.45/138.71 memberP: ( $i * $i ) > $o)).
% 138.45/138.71 tff(leq_type, type, (
% 138.45/138.71 leq: ( $i * $i ) > $o)).
% 138.45/138.71 tff(tptp_fun_U_45_type, type, (
% 138.45/138.71 tptp_fun_U_45: $i)).
% 138.45/138.71 tff(app_type, type, (
% 138.45/138.71 app: ( $i * $i ) > $i)).
% 138.45/138.71 tff(cons_type, type, (
% 138.45/138.71 cons: ( $i * $i ) > $i)).
% 138.45/138.71 tff(ssList_type, type, (
% 138.45/138.71 ssList: $i > $o)).
% 138.45/138.71 tff(tptp_fun_V_46_type, type, (
% 138.45/138.71 tptp_fun_V_46: $i)).
% 138.45/138.71 tff(1,plain,
% 138.45/138.71 ((ssList(U!45) & ((~(nil = U!45)) & ssList(V!46) & ((~((~(cons(X3!47, nil) = U!45)) | (~memberP(V!46, X3!47)) | (~ssItem(X3!47)))) | (~((~(nil = U!45)) | (~(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) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y)))))))))) <=> (ssList(U!45) & (~(nil = U!45)) & ssList(V!46) & ((~((~(cons(X3!47, nil) = U!45)) | (~memberP(V!46, X3!47)) | (~ssItem(X3!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y)))))))))),
% 138.45/138.71 inference(rewrite,[status(thm)],[])).
% 138.45/138.71 tff(2,plain,
% 138.45/138.71 (((~(nil = U!45)) & ssList(V!46) & ((~((~(cons(X3!47, nil) = U!45)) | (~memberP(V!46, X3!47)) | (~ssItem(X3!47)))) | (~((~(nil = V!46)) | (~(nil = U!45))))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y))))))))) <=> ((~(nil = U!45)) & ssList(V!46) & ((~((~(cons(X3!47, nil) = U!45)) | (~memberP(V!46, X3!47)) | (~ssItem(X3!47)))) | (~((~(nil = U!45)) | (~(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) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y)))))))))),
% 138.45/138.71 inference(rewrite,[status(thm)],[])).
% 138.45/138.71 tff(3,plain,
% 138.45/138.71 ((ssList(U!45) & ((~(nil = U!45)) & ssList(V!46) & ((~((~(cons(X3!47, nil) = U!45)) | (~memberP(V!46, X3!47)) | (~ssItem(X3!47)))) | (~((~(nil = V!46)) | (~(nil = U!45))))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y)))))))))) <=> (ssList(U!45) & ((~(nil = U!45)) & ssList(V!46) & ((~((~(cons(X3!47, nil) = U!45)) | (~memberP(V!46, X3!47)) | (~ssItem(X3!47)))) | (~((~(nil = U!45)) | (~(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) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y))))))))))),
% 138.45/138.71 inference(monotonicity,[status(thm)],[2])).
% 138.45/138.71 tff(4,plain,
% 138.45/138.71 ((ssList(U!45) & ((~(nil = U!45)) & ssList(V!46) & ((~((~(cons(X3!47, nil) = U!45)) | (~memberP(V!46, X3!47)) | (~ssItem(X3!47)))) | (~((~(nil = V!46)) | (~(nil = U!45))))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y)))))))))) <=> (ssList(U!45) & (~(nil = U!45)) & ssList(V!46) & ((~((~(cons(X3!47, nil) = U!45)) | (~memberP(V!46, X3!47)) | (~ssItem(X3!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y)))))))))),
% 138.50/138.71 inference(transitivity,[status(thm)],[3, 1])).
% 138.50/138.71 tff(5,plain,
% 138.50/138.71 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (~ssList(V)) | (![X3: $i] : ((~(cons(X3, nil) = U)) | (~memberP(V, X3)) | (~ssItem(X3))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U) & ![X2: $i] : (leq(Y, X2) | (~memberP(Z, X2)) | (~memberP(X1, X2)) | (~lt(Y, X2)) | (~ssItem(X2))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (~ssList(V)) | (![X3: $i] : ((~(cons(X3, nil) = U)) | (~memberP(V, X3)) | (~ssItem(X3))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U) & ![X2: $i] : (leq(Y, X2) | (~memberP(Z, X2)) | (~memberP(X1, X2)) | (~lt(Y, X2)) | (~ssItem(X2)))))))))),
% 138.50/138.71 inference(rewrite,[status(thm)],[])).
% 138.50/138.71 tff(6,plain,
% 138.50/138.71 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (nil = U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U)) & ![X2: $i] : (ssItem(X2) => ((((~memberP(Z, X2)) | (~memberP(X1, X2))) | (~lt(Y, X2))) | leq(Y, X2))))))) | (![X3: $i] : (ssItem(X3) => ((~(cons(X3, nil) = W)) | (~memberP(X, X3)))) & ((~(nil = X)) | (~(nil = W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (~ssList(V)) | (![X3: $i] : ((~(cons(X3, nil) = U)) | (~memberP(V, X3)) | (~ssItem(X3))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U) & ![X2: $i] : (leq(Y, X2) | (~memberP(Z, X2)) | (~memberP(X1, X2)) | (~lt(Y, X2)) | (~ssItem(X2)))))))))),
% 138.50/138.71 inference(rewrite,[status(thm)],[])).
% 138.50/138.71 tff(7,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (nil = U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U)) & ![X2: $i] : (ssItem(X2) => ((((~memberP(Z, X2)) | (~memberP(X1, X2))) | (~lt(Y, X2))) | leq(Y, X2))))))) | (![X3: $i] : (ssItem(X3) => ((~(cons(X3, nil) = W)) | (~memberP(X, X3)))) & ((~(nil = X)) | (~(nil = W)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 138.50/138.71 tff(8,plain,
% 138.50/138.71 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (~ssList(V)) | (![X3: $i] : ((~(cons(X3, nil) = U)) | (~memberP(V, X3)) | (~ssItem(X3))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U) & ![X2: $i] : (leq(Y, X2) | (~memberP(Z, X2)) | (~memberP(X1, X2)) | (~lt(Y, X2)) | (~ssItem(X2))))))))),
% 138.50/138.71 inference(modus_ponens,[status(thm)],[7, 6])).
% 138.50/138.71 tff(9,plain,
% 138.50/138.71 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (~ssList(V)) | (![X3: $i] : ((~(cons(X3, nil) = U)) | (~memberP(V, X3)) | (~ssItem(X3))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U) & ![X2: $i] : (leq(Y, X2) | (~memberP(Z, X2)) | (~memberP(X1, X2)) | (~lt(Y, X2)) | (~ssItem(X2))))))))),
% 138.50/138.71 inference(modus_ponens,[status(thm)],[8, 5])).
% 138.50/138.71 tff(10,plain,
% 138.50/138.71 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (~ssList(V)) | (![X3: $i] : ((~(cons(X3, nil) = U)) | (~memberP(V, X3)) | (~ssItem(X3))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U) & ![X2: $i] : (leq(Y, X2) | (~memberP(Z, X2)) | (~memberP(X1, X2)) | (~lt(Y, X2)) | (~ssItem(X2))))))))),
% 138.50/138.71 inference(modus_ponens,[status(thm)],[9, 5])).
% 138.50/138.71 tff(11,plain,
% 138.50/138.71 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (~ssList(V)) | (![X3: $i] : ((~(cons(X3, nil) = U)) | (~memberP(V, X3)) | (~ssItem(X3))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U) & ![X2: $i] : (leq(Y, X2) | (~memberP(Z, X2)) | (~memberP(X1, X2)) | (~lt(Y, X2)) | (~ssItem(X2))))))))),
% 138.50/138.71 inference(modus_ponens,[status(thm)],[10, 5])).
% 138.50/138.71 tff(12,plain,
% 138.50/138.71 (ssList(U!45) & (~(nil = U!45)) & ssList(V!46) & ((~((~(cons(X3!47, nil) = U!45)) | (~memberP(V!46, X3!47)) | (~ssItem(X3!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y))))))))),
% 138.50/138.71 inference(modus_ponens,[status(thm)],[11, 4])).
% 138.50/138.71 tff(13,plain,
% 138.50/138.71 (ssList(U!45)),
% 138.50/138.71 inference(and_elim,[status(thm)],[12])).
% 138.50/138.71 tff(14,plain,
% 138.50/138.71 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 138.50/138.71 inference(bind,[status(th)],[])).
% 138.50/138.71 tff(15,plain,
% 138.50/138.71 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 138.50/138.71 inference(quant_intro,[status(thm)],[14])).
% 138.50/138.71 tff(16,plain,
% 138.50/138.71 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 138.50/138.71 inference(rewrite,[status(thm)],[])).
% 138.50/138.71 tff(17,plain,
% 138.50/138.71 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 138.50/138.71 inference(bind,[status(th)],[])).
% 138.50/138.71 tff(18,plain,
% 138.50/138.71 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 138.50/138.71 inference(quant_intro,[status(thm)],[17])).
% 138.50/138.71 tff(19,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax84')).
% 138.50/138.71 tff(20,plain,
% 138.50/138.71 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 138.50/138.71 inference(modus_ponens,[status(thm)],[19, 18])).
% 138.50/138.71 tff(21,plain,
% 138.50/138.71 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 138.50/138.71 inference(modus_ponens,[status(thm)],[20, 16])).
% 138.50/138.71 tff(22,plain,(
% 138.50/138.71 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 138.50/138.71 inference(skolemize,[status(sab)],[21])).
% 138.50/138.71 tff(23,plain,
% 138.50/138.71 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 138.50/138.71 inference(modus_ponens,[status(thm)],[22, 15])).
% 138.50/138.71 tff(24,plain,
% 138.50/138.71 (((~![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))),
% 138.50/138.71 inference(rewrite,[status(thm)],[])).
% 138.50/138.71 tff(25,plain,
% 138.50/138.71 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(U!45)) | (app(U!45, nil) = U!45))),
% 138.50/138.71 inference(quant_inst,[status(thm)],[])).
% 138.50/138.71 tff(26,plain,
% 138.50/138.71 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(U!45)) | (app(U!45, nil) = U!45)),
% 138.50/138.71 inference(modus_ponens,[status(thm)],[25, 24])).
% 138.50/138.71 tff(27,plain,
% 138.50/138.71 (app(U!45, nil) = U!45),
% 138.50/138.71 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 138.50/138.71 tff(28,plain,
% 138.50/138.71 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 138.50/138.71 inference(bind,[status(th)],[])).
% 138.50/138.71 tff(29,plain,
% 138.50/138.71 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 138.50/138.72 inference(quant_intro,[status(thm)],[28])).
% 138.50/138.72 tff(30,plain,
% 138.50/138.72 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 138.50/138.72 inference(rewrite,[status(thm)],[])).
% 138.50/138.72 tff(31,plain,
% 138.50/138.72 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 138.50/138.72 inference(bind,[status(th)],[])).
% 138.50/138.72 tff(32,plain,
% 138.50/138.72 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 138.50/138.72 inference(quant_intro,[status(thm)],[31])).
% 138.50/138.72 tff(33,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax28')).
% 138.50/138.72 tff(34,plain,
% 138.50/138.72 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 138.50/138.72 inference(modus_ponens,[status(thm)],[33, 32])).
% 138.50/138.72 tff(35,plain,
% 138.50/138.72 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 138.50/138.72 inference(modus_ponens,[status(thm)],[34, 30])).
% 138.50/138.72 tff(36,plain,(
% 138.50/138.72 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 138.50/138.72 inference(skolemize,[status(sab)],[35])).
% 138.50/138.72 tff(37,plain,
% 138.50/138.72 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 138.50/138.72 inference(modus_ponens,[status(thm)],[36, 29])).
% 138.50/138.72 tff(38,plain,
% 138.50/138.72 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 138.50/138.72 inference(rewrite,[status(thm)],[])).
% 138.50/138.72 tff(39,plain,
% 138.50/138.72 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 138.50/138.72 inference(quant_inst,[status(thm)],[])).
% 138.50/138.72 tff(40,plain,
% 138.50/138.72 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45)),
% 138.50/138.72 inference(modus_ponens,[status(thm)],[39, 38])).
% 138.50/138.72 tff(41,plain,
% 138.50/138.72 (app(nil, U!45) = U!45),
% 138.50/138.72 inference(unit_resolution,[status(thm)],[40, 37, 13])).
% 138.50/138.72 tff(42,plain,
% 138.50/138.72 (~(nil = U!45)),
% 138.50/138.72 inference(and_elim,[status(thm)],[12])).
% 138.50/138.72 tff(43,plain,
% 138.50/138.72 (((~(nil = U!45)) | (~(nil = V!46))) | (nil = U!45)),
% 138.50/138.72 inference(tautology,[status(thm)],[])).
% 138.50/138.72 tff(44,plain,
% 138.50/138.72 ((~(nil = U!45)) | (~(nil = V!46))),
% 138.50/138.72 inference(unit_resolution,[status(thm)],[43, 42])).
% 138.50/138.72 tff(45,plain,
% 138.50/138.72 ((~((~(cons(X3!47, nil) = U!45)) | (~memberP(V!46, X3!47)) | (~ssItem(X3!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))),
% 138.50/138.72 inference(and_elim,[status(thm)],[12])).
% 138.50/138.72 tff(46,plain,
% 138.50/138.72 (~((~(cons(X3!47, nil) = U!45)) | (~memberP(V!46, X3!47)) | (~ssItem(X3!47)))),
% 138.50/138.72 inference(unit_resolution,[status(thm)],[45, 44])).
% 138.50/138.72 tff(47,plain,
% 138.50/138.72 (((~(cons(X3!47, nil) = U!45)) | (~memberP(V!46, X3!47)) | (~ssItem(X3!47))) | (cons(X3!47, nil) = U!45)),
% 138.50/138.72 inference(tautology,[status(thm)],[])).
% 138.50/138.72 tff(48,plain,
% 138.50/138.72 (cons(X3!47, nil) = U!45),
% 138.50/138.72 inference(unit_resolution,[status(thm)],[47, 46])).
% 138.50/138.72 tff(49,plain,
% 138.50/138.72 (app(nil, cons(X3!47, nil)) = app(nil, U!45)),
% 138.50/138.72 inference(monotonicity,[status(thm)],[48])).
% 138.50/138.72 tff(50,plain,
% 138.50/138.72 (app(nil, cons(X3!47, nil)) = U!45),
% 138.50/138.72 inference(transitivity,[status(thm)],[49, 41])).
% 138.50/138.72 tff(51,plain,
% 138.50/138.72 (app(app(nil, cons(X3!47, nil)), nil) = app(U!45, nil)),
% 138.50/138.72 inference(monotonicity,[status(thm)],[50])).
% 138.50/138.72 tff(52,plain,
% 138.50/138.72 (app(app(nil, cons(X3!47, nil)), nil) = U!45),
% 138.50/138.72 inference(transitivity,[status(thm)],[51, 27])).
% 138.50/138.72 tff(53,plain,
% 138.50/138.72 (^[Y: $i] : refl(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y)))))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y)))))))))),
% 138.50/138.72 inference(bind,[status(th)],[])).
% 138.50/138.72 tff(54,plain,
% 138.50/138.72 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y)))))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y))))))))),
% 138.50/138.72 inference(quant_intro,[status(thm)],[53])).
% 138.50/138.72 tff(55,plain,
% 138.50/138.72 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y)))))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y)))))))))),
% 138.50/138.72 inference(bind,[status(th)],[])).
% 138.50/138.72 tff(56,plain,
% 138.50/138.72 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y)))))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y))))))))),
% 138.50/138.72 inference(quant_intro,[status(thm)],[55])).
% 138.50/138.72 tff(57,plain,
% 138.50/138.72 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y)))))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y))))))))),
% 138.50/138.72 inference(transitivity,[status(thm)],[56, 54])).
% 138.50/138.72 tff(58,plain,
% 138.50/138.72 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y))))))))),
% 138.50/138.72 inference(and_elim,[status(thm)],[12])).
% 138.50/138.72 tff(59,plain,
% 138.50/138.72 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y))))))))),
% 138.50/138.72 inference(modus_ponens,[status(thm)],[58, 57])).
% 138.50/138.72 tff(60,plain,
% 138.50/138.72 (((~(cons(X3!47, nil) = U!45)) | (~memberP(V!46, X3!47)) | (~ssItem(X3!47))) | ssItem(X3!47)),
% 138.50/138.72 inference(tautology,[status(thm)],[])).
% 138.50/138.72 tff(61,plain,
% 138.50/138.72 (ssItem(X3!47)),
% 138.50/138.72 inference(unit_resolution,[status(thm)],[60, 46])).
% 138.50/138.72 tff(62,plain,
% 138.50/138.72 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y))))))))) | ((~ssItem(X3!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, Z, X3!47))))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y))))))))) | (~ssItem(X3!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, Z, X3!47))))))))),
% 138.50/138.72 inference(rewrite,[status(thm)],[])).
% 138.50/138.72 tff(63,plain,
% 138.50/138.72 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y))))))))) | ((~ssItem(X3!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, Z, X3!47))))))))),
% 138.50/138.72 inference(quant_inst,[status(thm)],[])).
% 138.50/138.72 tff(64,plain,
% 138.50/138.72 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_48(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_48(X1, Z, Y))) | (~ssItem(tptp_fun_X2_48(X1, Z, Y))))))))) | (~ssItem(X3!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, Z, X3!47)))))))),
% 138.50/138.72 inference(modus_ponens,[status(thm)],[63, 62])).
% 138.50/138.72 tff(65,plain,
% 138.50/138.72 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, Z, X3!47)))))))),
% 138.50/138.72 inference(unit_resolution,[status(thm)],[64, 61, 59])).
% 138.50/138.72 tff(66,plain,
% 138.50/138.72 (ssList(nil) <=> ssList(nil)),
% 138.50/138.72 inference(rewrite,[status(thm)],[])).
% 138.50/138.72 tff(67,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 138.50/138.72 tff(68,plain,
% 138.50/138.72 (ssList(nil)),
% 138.50/138.72 inference(modus_ponens,[status(thm)],[67, 66])).
% 138.50/138.72 tff(69,plain,
% 138.50/138.72 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, Z, X3!47)))))))) | ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(X1, nil, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, nil, X3!47)))))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, Z, X3!47)))))))) | (~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(X1, nil, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, nil, X3!47)))))))),
% 138.50/138.72 inference(rewrite,[status(thm)],[])).
% 138.50/138.72 tff(70,plain,
% 138.50/138.72 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, Z, X3!47)))))))) | ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(X1, nil, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, nil, X3!47)))))))),
% 138.50/138.72 inference(quant_inst,[status(thm)],[])).
% 138.50/138.72 tff(71,plain,
% 138.50/138.72 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_48(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, Z, X3!47)))))))) | (~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(X1, nil, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, nil, X3!47))))))),
% 138.50/138.72 inference(modus_ponens,[status(thm)],[70, 69])).
% 138.50/138.72 tff(72,plain,
% 138.50/138.72 (![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(X1, nil, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, nil, X3!47))))))),
% 138.50/138.72 inference(unit_resolution,[status(thm)],[71, 68, 65])).
% 138.50/138.72 tff(73,plain,
% 138.50/138.72 (((~![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(X1, nil, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, nil, X3!47))))))) | ((~ssList(nil)) | (~(app(app(nil, cons(X3!47, nil)), nil) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(nil, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(nil, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47))))))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(X1, nil, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, nil, X3!47))))))) | (~ssList(nil)) | (~(app(app(nil, cons(X3!47, nil)), nil) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(nil, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(nil, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47))))))),
% 138.50/138.72 inference(rewrite,[status(thm)],[])).
% 138.50/138.72 tff(74,plain,
% 138.50/138.72 (((~ssList(nil)) | (~(app(app(nil, cons(X3!47, nil)), nil) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(nil, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(nil, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47)))))) <=> ((~ssList(nil)) | (~(app(app(nil, cons(X3!47, nil)), nil) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(nil, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(nil, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47))))))),
% 138.50/138.72 inference(rewrite,[status(thm)],[])).
% 138.50/138.72 tff(75,plain,
% 138.50/138.72 (((~![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(X1, nil, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, nil, X3!47))))))) | ((~ssList(nil)) | (~(app(app(nil, cons(X3!47, nil)), nil) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(nil, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(nil, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47))))))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(X1, nil, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, nil, X3!47))))))) | ((~ssList(nil)) | (~(app(app(nil, cons(X3!47, nil)), nil) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(nil, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(nil, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47)))))))),
% 138.50/138.72 inference(monotonicity,[status(thm)],[74])).
% 138.50/138.72 tff(76,plain,
% 138.50/138.72 (((~![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(X1, nil, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, nil, X3!47))))))) | ((~ssList(nil)) | (~(app(app(nil, cons(X3!47, nil)), nil) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(nil, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(nil, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47))))))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(X1, nil, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, nil, X3!47))))))) | (~ssList(nil)) | (~(app(app(nil, cons(X3!47, nil)), nil) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(nil, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(nil, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47))))))),
% 138.50/138.72 inference(transitivity,[status(thm)],[75, 73])).
% 138.50/138.72 tff(77,plain,
% 138.50/138.72 ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(X1, nil, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, nil, X3!47))))))) | ((~ssList(nil)) | (~(app(app(nil, cons(X3!47, nil)), nil) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(nil, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(nil, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47))))))),
% 138.50/138.72 inference(quant_inst,[status(thm)],[])).
% 138.50/138.72 tff(78,plain,
% 138.50/138.72 ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(X1, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(X1, nil, X3!47))) | (~memberP(X1, tptp_fun_X2_48(X1, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(X1, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(X1, nil, X3!47))))))) | (~ssList(nil)) | (~(app(app(nil, cons(X3!47, nil)), nil) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(nil, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(nil, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47)))))),
% 138.89/139.10 inference(modus_ponens,[status(thm)],[77, 76])).
% 138.89/139.10 tff(79,plain,
% 138.89/139.10 ((~(app(app(nil, cons(X3!47, nil)), nil) = U!45)) | (~(leq(X3!47, tptp_fun_X2_48(nil, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(nil, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47)))))),
% 138.89/139.10 inference(unit_resolution,[status(thm)],[78, 68, 72])).
% 138.89/139.10 tff(80,plain,
% 138.89/139.10 (~(leq(X3!47, tptp_fun_X2_48(nil, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(nil, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47))))),
% 138.89/139.10 inference(unit_resolution,[status(thm)],[79, 52])).
% 138.89/139.10 tff(81,plain,
% 138.89/139.10 ((leq(X3!47, tptp_fun_X2_48(nil, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(nil, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47)))) | ssItem(tptp_fun_X2_48(nil, nil, X3!47))),
% 138.89/139.10 inference(tautology,[status(thm)],[])).
% 138.89/139.10 tff(82,plain,
% 138.89/139.10 (ssItem(tptp_fun_X2_48(nil, nil, X3!47))),
% 138.89/139.10 inference(unit_resolution,[status(thm)],[81, 80])).
% 138.89/139.10 tff(83,plain,
% 138.89/139.10 ((leq(X3!47, tptp_fun_X2_48(nil, nil, X3!47)) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))) | (~lt(X3!47, tptp_fun_X2_48(nil, nil, X3!47))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47)))) | memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))),
% 138.89/139.10 inference(tautology,[status(thm)],[])).
% 138.89/139.10 tff(84,plain,
% 138.89/139.10 (memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))),
% 138.89/139.10 inference(unit_resolution,[status(thm)],[83, 80])).
% 138.89/139.10 tff(85,plain,
% 138.89/139.10 (^[U: $i] : refl(((~ssItem(U)) | (~memberP(nil, U))) <=> ((~ssItem(U)) | (~memberP(nil, U))))),
% 138.89/139.10 inference(bind,[status(th)],[])).
% 138.89/139.10 tff(86,plain,
% 138.89/139.10 (![U: $i] : ((~ssItem(U)) | (~memberP(nil, U))) <=> ![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))),
% 138.89/139.10 inference(quant_intro,[status(thm)],[85])).
% 138.89/139.10 tff(87,plain,
% 138.89/139.10 (![U: $i] : ((~ssItem(U)) | (~memberP(nil, U))) <=> ![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))),
% 138.89/139.10 inference(rewrite,[status(thm)],[])).
% 138.89/139.10 tff(88,plain,
% 138.89/139.10 (^[U: $i] : rewrite((ssItem(U) => (~memberP(nil, U))) <=> ((~ssItem(U)) | (~memberP(nil, U))))),
% 138.89/139.10 inference(bind,[status(th)],[])).
% 138.89/139.10 tff(89,plain,
% 138.89/139.10 (![U: $i] : (ssItem(U) => (~memberP(nil, U))) <=> ![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))),
% 138.89/139.10 inference(quant_intro,[status(thm)],[88])).
% 138.89/139.10 tff(90,axiom,(![U: $i] : (ssItem(U) => (~memberP(nil, U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax38')).
% 138.89/139.10 tff(91,plain,
% 138.89/139.10 (![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))),
% 138.89/139.10 inference(modus_ponens,[status(thm)],[90, 89])).
% 138.89/139.10 tff(92,plain,
% 138.89/139.10 (![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))),
% 138.89/139.10 inference(modus_ponens,[status(thm)],[91, 87])).
% 138.89/139.10 tff(93,plain,(
% 138.89/139.10 ![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))),
% 138.89/139.10 inference(skolemize,[status(sab)],[92])).
% 138.89/139.10 tff(94,plain,
% 138.89/139.10 (![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))),
% 138.89/139.10 inference(modus_ponens,[status(thm)],[93, 86])).
% 138.89/139.10 tff(95,plain,
% 138.89/139.10 (((~![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))) | ((~ssItem(tptp_fun_X2_48(nil, nil, X3!47))) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))))) <=> ((~![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47))) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))))),
% 138.89/139.10 inference(rewrite,[status(thm)],[])).
% 138.89/139.10 tff(96,plain,
% 138.89/139.10 ((~![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))) | ((~ssItem(tptp_fun_X2_48(nil, nil, X3!47))) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47))))),
% 138.89/139.10 inference(quant_inst,[status(thm)],[])).
% 138.89/139.10 tff(97,plain,
% 138.89/139.10 ((~![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))) | (~ssItem(tptp_fun_X2_48(nil, nil, X3!47))) | (~memberP(nil, tptp_fun_X2_48(nil, nil, X3!47)))),
% 138.89/139.10 inference(modus_ponens,[status(thm)],[96, 95])).
% 138.89/139.10 tff(98,plain,
% 138.89/139.10 ($false),
% 138.89/139.10 inference(unit_resolution,[status(thm)],[97, 94, 84, 82])).
% 138.89/139.10 % SZS output end Proof
% 138.89/139.10 % E exiting
%------------------------------------------------------------------------------