%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC417+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:31:11 AM UTC 2025
% Result : Theorem 8.56s 8.76s
% Output : Proof 8.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC417+1 : TPTP v9.0.0. Released v2.4.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:16:23 EDT 2025
% 0.11/0.33 % CPUTime :
% 8.56/8.76 % SZS status Theorem
% 8.56/8.76 % SZS output start Proof
% 8.56/8.76 tff(tptp_fun_V_46_type, type, (
% 8.56/8.76 tptp_fun_V_46: $i)).
% 8.56/8.76 tff(app_type, type, (
% 8.56/8.76 app: ( $i * $i ) > $i)).
% 8.56/8.76 tff(tptp_fun_X3_48_type, type, (
% 8.56/8.76 tptp_fun_X3_48: $i)).
% 8.56/8.76 tff(cons_type, type, (
% 8.56/8.76 cons: ( $i * $i ) > $i)).
% 8.56/8.76 tff(nil_type, type, (
% 8.56/8.76 nil: $i)).
% 8.56/8.76 tff(tptp_fun_X2_47_type, type, (
% 8.56/8.76 tptp_fun_X2_47: $i)).
% 8.56/8.76 tff(ssList_type, type, (
% 8.56/8.76 ssList: $i > $o)).
% 8.56/8.76 tff(tptp_fun_U_45_type, type, (
% 8.56/8.76 tptp_fun_U_45: $i)).
% 8.56/8.76 tff(neq_type, type, (
% 8.56/8.76 neq: ( $i * $i ) > $o)).
% 8.56/8.76 tff(ssItem_type, type, (
% 8.56/8.76 ssItem: $i > $o)).
% 8.56/8.76 tff(1,plain,
% 8.56/8.76 ((ssList(U!45) & (ssList(V!46) & ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) & neq(V!46, nil))) <=> (ssList(U!45) & ssList(V!46) & ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) & neq(V!46, nil))),
% 8.56/8.76 inference(rewrite,[status(thm)],[])).
% 8.56/8.76 tff(2,plain,
% 8.56/8.76 ((ssList(V!46) & (ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48))))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) & neq(V!46, nil)) <=> (ssList(V!46) & ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) & neq(V!46, nil))),
% 8.56/8.76 inference(rewrite,[status(thm)],[])).
% 8.56/8.76 tff(3,plain,
% 8.56/8.76 ((~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))) <=> (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48))))),
% 8.56/8.76 inference(rewrite,[status(thm)],[])).
% 8.56/8.76 tff(4,plain,
% 8.56/8.76 ((ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48))))) <=> (ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))))),
% 8.56/8.76 inference(monotonicity,[status(thm)],[3])).
% 8.56/8.76 tff(5,plain,
% 8.56/8.76 ((ssList(V!46) & (ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48))))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) & neq(V!46, nil)) <=> (ssList(V!46) & (ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48))))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) & neq(V!46, nil))),
% 8.56/8.76 inference(monotonicity,[status(thm)],[4])).
% 8.56/8.76 tff(6,plain,
% 8.56/8.76 ((ssList(V!46) & (ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48))))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) & neq(V!46, nil)) <=> (ssList(V!46) & ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) & neq(V!46, nil))),
% 8.56/8.76 inference(transitivity,[status(thm)],[5, 2])).
% 8.56/8.76 tff(7,plain,
% 8.56/8.76 ((ssList(U!45) & (ssList(V!46) & (ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48))))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) & neq(V!46, nil))) <=> (ssList(U!45) & (ssList(V!46) & ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) & neq(V!46, nil)))),
% 8.56/8.76 inference(monotonicity,[status(thm)],[6])).
% 8.56/8.76 tff(8,plain,
% 8.56/8.76 ((ssList(U!45) & (ssList(V!46) & (ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48))))) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) & neq(V!46, nil))) <=> (ssList(U!45) & ssList(V!46) & ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) & neq(V!46, nil))),
% 8.56/8.76 inference(transitivity,[status(thm)],[7, 1])).
% 8.56/8.76 tff(9,plain,
% 8.56/8.76 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = U)) | (~(app(cons(X2, nil), X3) = V)) | (~ssList(X3)))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = U)) | (~(app(cons(X2, nil), X3) = V)) | (~ssList(X3)))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (~neq(V, nil)))))),
% 8.56/8.76 inference(rewrite,[status(thm)],[])).
% 8.56/8.76 tff(10,plain,
% 8.56/8.76 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V)) & (app(app(X1, cons(Y, nil)), Z) = U))))) | ![X2: $i] : (ssItem(X2) => ![X3: $i] : (ssList(X3) => ((~(app(cons(X2, nil), X3) = X)) | (~(app(X3, cons(X2, nil)) = W)))))) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = U)) | (~(app(cons(X2, nil), X3) = V)) | (~ssList(X3)))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (~neq(V, nil)))))),
% 8.56/8.76 inference(rewrite,[status(thm)],[])).
% 8.56/8.76 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) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V)) & (app(app(X1, cons(Y, nil)), Z) = U))))) | ![X2: $i] : (ssItem(X2) => ![X3: $i] : (ssList(X3) => ((~(app(cons(X2, nil), X3) = X)) | (~(app(X3, cons(X2, nil)) = W)))))) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 8.56/8.76 tff(12,plain,
% 8.56/8.76 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = U)) | (~(app(cons(X2, nil), X3) = V)) | (~ssList(X3)))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (~neq(V, nil))))),
% 8.56/8.76 inference(modus_ponens,[status(thm)],[11, 10])).
% 8.56/8.76 tff(13,plain,
% 8.56/8.76 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = U)) | (~(app(cons(X2, nil), X3) = V)) | (~ssList(X3)))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (~neq(V, nil))))),
% 8.56/8.76 inference(modus_ponens,[status(thm)],[12, 9])).
% 8.56/8.76 tff(14,plain,
% 8.56/8.76 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = U)) | (~(app(cons(X2, nil), X3) = V)) | (~ssList(X3)))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (~neq(V, nil))))),
% 8.56/8.76 inference(modus_ponens,[status(thm)],[13, 9])).
% 8.56/8.76 tff(15,plain,
% 8.56/8.76 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = U)) | (~(app(cons(X2, nil), X3) = V)) | (~ssList(X3)))) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (~neq(V, nil))))),
% 8.56/8.76 inference(modus_ponens,[status(thm)],[14, 9])).
% 8.56/8.76 tff(16,plain,
% 8.56/8.76 (ssList(U!45) & ssList(V!46) & ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) & neq(V!46, nil)),
% 8.56/8.76 inference(modus_ponens,[status(thm)],[15, 8])).
% 8.56/8.76 tff(17,plain,
% 8.56/8.76 (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))),
% 8.56/8.76 inference(and_elim,[status(thm)],[16])).
% 8.56/8.76 tff(18,plain,
% 8.56/8.76 (app(cons(X2!47, nil), X3!48) = V!46),
% 8.56/8.76 inference(or_elim,[status(thm)],[17])).
% 8.56/8.76 tff(19,plain,
% 8.56/8.76 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 8.56/8.76 inference(bind,[status(th)],[])).
% 8.56/8.76 tff(20,plain,
% 8.56/8.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 8.56/8.76 inference(quant_intro,[status(thm)],[19])).
% 8.56/8.76 tff(21,plain,
% 8.56/8.76 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 8.56/8.76 inference(bind,[status(th)],[])).
% 8.56/8.76 tff(22,plain,
% 8.56/8.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 8.56/8.76 inference(quant_intro,[status(thm)],[21])).
% 8.56/8.76 tff(23,plain,
% 8.56/8.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 8.56/8.76 inference(transitivity,[status(thm)],[22, 20])).
% 8.56/8.76 tff(24,plain,
% 8.56/8.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 8.56/8.76 inference(rewrite,[status(thm)],[])).
% 8.56/8.76 tff(25,plain,
% 8.56/8.76 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), (![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))))),
% 8.56/8.76 inference(bind,[status(th)],[])).
% 8.56/8.76 tff(26,plain,
% 8.56/8.76 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 8.56/8.76 inference(quant_intro,[status(thm)],[25])).
% 8.56/8.76 tff(27,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax81')).
% 8.56/8.76 tff(28,plain,
% 8.56/8.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 8.56/8.76 inference(modus_ponens,[status(thm)],[27, 26])).
% 8.56/8.76 tff(29,plain,
% 8.56/8.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 8.56/8.76 inference(modus_ponens,[status(thm)],[28, 24])).
% 8.56/8.76 tff(30,plain,(
% 8.56/8.76 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 8.56/8.76 inference(skolemize,[status(sab)],[29])).
% 8.56/8.76 tff(31,plain,
% 8.56/8.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 8.56/8.76 inference(modus_ponens,[status(thm)],[30, 23])).
% 8.56/8.76 tff(32,plain,
% 8.56/8.76 (ssList(nil) <=> ssList(nil)),
% 8.56/8.76 inference(rewrite,[status(thm)],[])).
% 8.56/8.76 tff(33,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 8.56/8.76 tff(34,plain,
% 8.56/8.76 (ssList(nil)),
% 8.56/8.76 inference(modus_ponens,[status(thm)],[33, 32])).
% 8.56/8.76 tff(35,plain,
% 8.56/8.76 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 8.56/8.76 inference(rewrite,[status(thm)],[])).
% 8.56/8.76 tff(36,plain,
% 8.56/8.76 (((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 8.56/8.76 inference(rewrite,[status(thm)],[])).
% 8.56/8.76 tff(37,plain,
% 8.56/8.76 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))))),
% 8.56/8.76 inference(monotonicity,[status(thm)],[36])).
% 8.56/8.76 tff(38,plain,
% 8.56/8.76 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 8.56/8.76 inference(transitivity,[status(thm)],[37, 35])).
% 8.56/8.76 tff(39,plain,
% 8.56/8.76 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 8.56/8.76 inference(quant_inst,[status(thm)],[])).
% 8.56/8.76 tff(40,plain,
% 8.56/8.76 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))),
% 8.56/8.76 inference(modus_ponens,[status(thm)],[39, 38])).
% 8.56/8.76 tff(41,plain,
% 8.56/8.76 (![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))),
% 8.56/8.76 inference(unit_resolution,[status(thm)],[40, 34, 31])).
% 8.56/8.76 tff(42,plain,
% 8.56/8.76 (ssItem(X2!47)),
% 8.56/8.76 inference(and_elim,[status(thm)],[16])).
% 8.56/8.76 tff(43,plain,
% 8.56/8.76 (((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | ((~ssItem(X2!47)) | (cons(X2!47, nil) = app(cons(X2!47, nil), nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | (~ssItem(X2!47)) | (cons(X2!47, nil) = app(cons(X2!47, nil), nil)))),
% 8.56/8.76 inference(rewrite,[status(thm)],[])).
% 8.56/8.76 tff(44,plain,
% 8.56/8.76 ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | ((~ssItem(X2!47)) | (cons(X2!47, nil) = app(cons(X2!47, nil), nil)))),
% 8.56/8.76 inference(quant_inst,[status(thm)],[])).
% 8.56/8.76 tff(45,plain,
% 8.56/8.76 ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | (~ssItem(X2!47)) | (cons(X2!47, nil) = app(cons(X2!47, nil), nil))),
% 8.56/8.76 inference(modus_ponens,[status(thm)],[44, 43])).
% 8.56/8.76 tff(46,plain,
% 8.56/8.76 (cons(X2!47, nil) = app(cons(X2!47, nil), nil)),
% 8.56/8.76 inference(unit_resolution,[status(thm)],[45, 42, 41])).
% 8.56/8.76 tff(47,plain,
% 8.56/8.76 (app(cons(X2!47, nil), nil) = cons(X2!47, nil)),
% 8.56/8.76 inference(symmetry,[status(thm)],[46])).
% 8.56/8.76 tff(48,plain,
% 8.56/8.76 (ssList(app(cons(X2!47, nil), nil)) <=> ssList(cons(X2!47, nil))),
% 8.56/8.76 inference(monotonicity,[status(thm)],[47])).
% 8.56/8.76 tff(49,plain,
% 8.56/8.76 (ssList(cons(X2!47, nil)) <=> ssList(app(cons(X2!47, nil), nil))),
% 8.56/8.76 inference(symmetry,[status(thm)],[48])).
% 8.56/8.76 tff(50,plain,
% 8.56/8.76 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 8.56/8.76 inference(bind,[status(th)],[])).
% 8.56/8.76 tff(51,plain,
% 8.56/8.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.56/8.76 inference(quant_intro,[status(thm)],[50])).
% 8.56/8.76 tff(52,plain,
% 8.56/8.76 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 8.56/8.76 inference(bind,[status(th)],[])).
% 8.56/8.76 tff(53,plain,
% 8.56/8.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.56/8.76 inference(quant_intro,[status(thm)],[52])).
% 8.56/8.76 tff(54,plain,
% 8.56/8.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.56/8.76 inference(transitivity,[status(thm)],[53, 51])).
% 8.56/8.76 tff(55,plain,
% 8.56/8.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.56/8.76 inference(rewrite,[status(thm)],[])).
% 8.56/8.76 tff(56,plain,
% 8.56/8.76 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => ssList(cons(V, U))) <=> ((~ssItem(V)) | ssList(cons(V, U))))), (![V: $i] : (ssItem(V) => ssList(cons(V, U))) <=> ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))))),
% 8.56/8.76 inference(bind,[status(th)],[])).
% 8.56/8.76 tff(57,plain,
% 8.56/8.76 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.56/8.76 inference(quant_intro,[status(thm)],[56])).
% 8.56/8.76 tff(58,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax16')).
% 8.56/8.76 tff(59,plain,
% 8.56/8.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.56/8.76 inference(modus_ponens,[status(thm)],[58, 57])).
% 8.56/8.76 tff(60,plain,
% 8.56/8.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.56/8.76 inference(modus_ponens,[status(thm)],[59, 55])).
% 8.56/8.77 tff(61,plain,(
% 8.56/8.77 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.56/8.77 inference(skolemize,[status(sab)],[60])).
% 8.56/8.77 tff(62,plain,
% 8.56/8.77 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[61, 54])).
% 8.56/8.77 tff(63,plain,
% 8.56/8.77 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 8.56/8.77 inference(rewrite,[status(thm)],[])).
% 8.56/8.77 tff(64,plain,
% 8.56/8.77 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 8.56/8.77 inference(quant_inst,[status(thm)],[])).
% 8.56/8.77 tff(65,plain,
% 8.56/8.77 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[64, 63])).
% 8.56/8.77 tff(66,plain,
% 8.56/8.77 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 8.56/8.77 inference(unit_resolution,[status(thm)],[65, 62, 34])).
% 8.56/8.77 tff(67,plain,
% 8.56/8.77 (((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(X2!47)) | ssList(cons(X2!47, nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(X2!47)) | ssList(cons(X2!47, nil)))),
% 8.56/8.77 inference(rewrite,[status(thm)],[])).
% 8.56/8.77 tff(68,plain,
% 8.56/8.77 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(X2!47)) | ssList(cons(X2!47, nil)))),
% 8.56/8.77 inference(quant_inst,[status(thm)],[])).
% 8.56/8.77 tff(69,plain,
% 8.56/8.77 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(X2!47)) | ssList(cons(X2!47, nil))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[68, 67])).
% 8.56/8.77 tff(70,plain,
% 8.56/8.77 (ssList(cons(X2!47, nil))),
% 8.56/8.77 inference(unit_resolution,[status(thm)],[69, 42, 66])).
% 8.56/8.77 tff(71,plain,
% 8.56/8.77 (ssList(app(cons(X2!47, nil), nil))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[70, 49])).
% 8.56/8.77 tff(72,plain,
% 8.56/8.77 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 8.56/8.77 inference(bind,[status(th)],[])).
% 8.56/8.77 tff(73,plain,
% 8.56/8.77 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 8.56/8.77 inference(quant_intro,[status(thm)],[72])).
% 8.56/8.77 tff(74,plain,
% 8.56/8.77 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 8.56/8.77 inference(rewrite,[status(thm)],[])).
% 8.56/8.77 tff(75,plain,
% 8.56/8.77 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 8.56/8.77 inference(bind,[status(th)],[])).
% 8.56/8.77 tff(76,plain,
% 8.56/8.77 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 8.56/8.77 inference(quant_intro,[status(thm)],[75])).
% 8.56/8.77 tff(77,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 8.56/8.77 tff(78,plain,
% 8.56/8.77 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[77, 76])).
% 8.56/8.77 tff(79,plain,
% 8.56/8.77 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[78, 74])).
% 8.56/8.77 tff(80,plain,(
% 8.56/8.77 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 8.56/8.77 inference(skolemize,[status(sab)],[79])).
% 8.56/8.77 tff(81,plain,
% 8.56/8.77 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[80, 73])).
% 8.56/8.77 tff(82,plain,
% 8.56/8.77 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(app(cons(X2!47, nil), nil))) | (app(nil, app(cons(X2!47, nil), nil)) = app(cons(X2!47, nil), nil)))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(app(cons(X2!47, nil), nil))) | (app(nil, app(cons(X2!47, nil), nil)) = app(cons(X2!47, nil), nil)))),
% 8.56/8.77 inference(rewrite,[status(thm)],[])).
% 8.56/8.77 tff(83,plain,
% 8.56/8.77 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(app(cons(X2!47, nil), nil))) | (app(nil, app(cons(X2!47, nil), nil)) = app(cons(X2!47, nil), nil)))),
% 8.56/8.77 inference(quant_inst,[status(thm)],[])).
% 8.56/8.77 tff(84,plain,
% 8.56/8.77 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(app(cons(X2!47, nil), nil))) | (app(nil, app(cons(X2!47, nil), nil)) = app(cons(X2!47, nil), nil))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[83, 82])).
% 8.56/8.77 tff(85,plain,
% 8.56/8.77 ((~ssList(app(cons(X2!47, nil), nil))) | (app(nil, app(cons(X2!47, nil), nil)) = app(cons(X2!47, nil), nil))),
% 8.56/8.77 inference(unit_resolution,[status(thm)],[84, 81])).
% 8.56/8.77 tff(86,plain,
% 8.56/8.77 (app(nil, app(cons(X2!47, nil), nil)) = app(cons(X2!47, nil), nil)),
% 8.56/8.77 inference(unit_resolution,[status(thm)],[85, 71])).
% 8.56/8.77 tff(87,plain,
% 8.56/8.77 (app(nil, cons(X2!47, nil)) = app(nil, app(cons(X2!47, nil), nil))),
% 8.56/8.77 inference(monotonicity,[status(thm)],[46])).
% 8.56/8.77 tff(88,plain,
% 8.56/8.77 (app(nil, cons(X2!47, nil)) = cons(X2!47, nil)),
% 8.56/8.77 inference(transitivity,[status(thm)],[87, 86, 47])).
% 8.56/8.77 tff(89,plain,
% 8.56/8.77 (app(app(nil, cons(X2!47, nil)), X3!48) = app(cons(X2!47, nil), X3!48)),
% 8.56/8.77 inference(monotonicity,[status(thm)],[88])).
% 8.56/8.77 tff(90,plain,
% 8.56/8.77 (app(app(nil, cons(X2!47, nil)), X3!48) = V!46),
% 8.56/8.77 inference(transitivity,[status(thm)],[89, 18])).
% 8.56/8.77 tff(91,plain,
% 8.56/8.77 (ssList(U!45)),
% 8.56/8.77 inference(and_elim,[status(thm)],[16])).
% 8.56/8.77 tff(92,plain,
% 8.56/8.77 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 8.56/8.77 inference(bind,[status(th)],[])).
% 8.56/8.77 tff(93,plain,
% 8.56/8.77 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 8.56/8.77 inference(quant_intro,[status(thm)],[92])).
% 8.56/8.77 tff(94,plain,
% 8.56/8.77 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 8.56/8.77 inference(rewrite,[status(thm)],[])).
% 8.56/8.77 tff(95,plain,
% 8.56/8.77 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 8.56/8.77 inference(bind,[status(th)],[])).
% 8.56/8.77 tff(96,plain,
% 8.56/8.77 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 8.56/8.77 inference(quant_intro,[status(thm)],[95])).
% 8.56/8.77 tff(97,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax84')).
% 8.56/8.77 tff(98,plain,
% 8.56/8.77 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[97, 96])).
% 8.56/8.77 tff(99,plain,
% 8.56/8.77 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[98, 94])).
% 8.56/8.77 tff(100,plain,(
% 8.56/8.77 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 8.56/8.77 inference(skolemize,[status(sab)],[99])).
% 8.56/8.77 tff(101,plain,
% 8.56/8.77 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[100, 93])).
% 8.56/8.77 tff(102,plain,
% 8.56/8.77 (((~![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))),
% 8.56/8.77 inference(rewrite,[status(thm)],[])).
% 8.56/8.77 tff(103,plain,
% 8.56/8.77 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(U!45)) | (app(U!45, nil) = U!45))),
% 8.56/8.77 inference(quant_inst,[status(thm)],[])).
% 8.56/8.77 tff(104,plain,
% 8.56/8.77 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(U!45)) | (app(U!45, nil) = U!45)),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[103, 102])).
% 8.56/8.77 tff(105,plain,
% 8.56/8.77 (app(U!45, nil) = U!45),
% 8.56/8.77 inference(unit_resolution,[status(thm)],[104, 101, 91])).
% 8.56/8.77 tff(106,plain,
% 8.56/8.77 (app(X3!48, cons(X2!47, nil)) = U!45),
% 8.56/8.77 inference(or_elim,[status(thm)],[17])).
% 8.56/8.77 tff(107,plain,
% 8.56/8.77 (app(app(X3!48, cons(X2!47, nil)), nil) = app(U!45, nil)),
% 8.56/8.77 inference(monotonicity,[status(thm)],[106])).
% 8.56/8.77 tff(108,plain,
% 8.56/8.77 (app(app(X3!48, cons(X2!47, nil)), nil) = U!45),
% 8.56/8.77 inference(transitivity,[status(thm)],[107, 105])).
% 8.56/8.77 tff(109,plain,
% 8.56/8.77 (^[Y: $i] : refl(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45))))))),
% 8.56/8.77 inference(bind,[status(th)],[])).
% 8.56/8.77 tff(110,plain,
% 8.56/8.77 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45)))))),
% 8.56/8.77 inference(quant_intro,[status(thm)],[109])).
% 8.56/8.77 tff(111,plain,
% 8.56/8.77 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45))))))),
% 8.56/8.77 inference(bind,[status(th)],[])).
% 8.56/8.77 tff(112,plain,
% 8.56/8.77 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45)))))),
% 8.56/8.77 inference(quant_intro,[status(thm)],[111])).
% 8.56/8.77 tff(113,plain,
% 8.56/8.77 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45)))))),
% 8.56/8.77 inference(transitivity,[status(thm)],[112, 110])).
% 8.56/8.77 tff(114,plain,
% 8.56/8.77 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45))))))),
% 8.56/8.77 inference(bind,[status(th)],[])).
% 8.56/8.77 tff(115,plain,
% 8.56/8.77 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45)))))),
% 8.56/8.77 inference(quant_intro,[status(thm)],[114])).
% 8.56/8.77 tff(116,plain,
% 8.56/8.77 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!46) & (app(app(X1, cons(Y, nil)), Z) = U!45)))))),
% 8.56/8.77 inference(and_elim,[status(thm)],[16])).
% 8.56/8.77 tff(117,plain,
% 8.56/8.77 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45)))))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[116, 115])).
% 8.56/8.77 tff(118,plain,
% 8.56/8.77 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45)))))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[117, 113])).
% 8.56/8.77 tff(119,plain,
% 8.56/8.77 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45)))))) | ((~ssItem(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), Z) = U!45)))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45)))))) | (~ssItem(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), Z) = U!45)))))),
% 8.56/8.77 inference(rewrite,[status(thm)],[])).
% 8.56/8.77 tff(120,plain,
% 8.56/8.77 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45)))))) | ((~ssItem(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), Z) = U!45)))))),
% 8.56/8.77 inference(quant_inst,[status(thm)],[])).
% 8.56/8.77 tff(121,plain,
% 8.56/8.77 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!46)) | (~(app(app(X1, cons(Y, nil)), Z) = U!45)))))) | (~ssItem(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), Z) = U!45))))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[120, 119])).
% 8.56/8.77 tff(122,plain,
% 8.56/8.77 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), Z) = U!45))))),
% 8.56/8.77 inference(unit_resolution,[status(thm)],[121, 42, 118])).
% 8.56/8.77 tff(123,plain,
% 8.56/8.77 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), Z) = U!45))))) | ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), nil) = U!45))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), Z) = U!45))))) | (~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), nil) = U!45))))),
% 8.56/8.77 inference(rewrite,[status(thm)],[])).
% 8.56/8.77 tff(124,plain,
% 8.56/8.77 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), Z) = U!45))))) | ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), nil) = U!45))))),
% 8.56/8.77 inference(quant_inst,[status(thm)],[])).
% 8.56/8.77 tff(125,plain,
% 8.56/8.77 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), Z) = U!45))))) | (~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), nil) = U!45)))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[124, 123])).
% 8.56/8.77 tff(126,plain,
% 8.56/8.77 (![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), nil) = U!45)))),
% 8.56/8.77 inference(unit_resolution,[status(thm)],[125, 34, 122])).
% 8.56/8.77 tff(127,plain,
% 8.56/8.77 (ssList(X3!48)),
% 8.56/8.77 inference(or_elim,[status(thm)],[17])).
% 8.56/8.77 tff(128,plain,
% 8.56/8.77 (((~![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), nil) = U!45)))) | ((~ssList(X3!48)) | (~(app(app(nil, cons(X2!47, nil)), X3!48) = V!46)) | (~(app(app(X3!48, cons(X2!47, nil)), nil) = U!45)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), nil) = U!45)))) | (~ssList(X3!48)) | (~(app(app(nil, cons(X2!47, nil)), X3!48) = V!46)) | (~(app(app(X3!48, cons(X2!47, nil)), nil) = U!45)))),
% 8.56/8.77 inference(rewrite,[status(thm)],[])).
% 8.56/8.77 tff(129,plain,
% 8.56/8.77 ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), nil) = U!45)))) | ((~ssList(X3!48)) | (~(app(app(nil, cons(X2!47, nil)), X3!48) = V!46)) | (~(app(app(X3!48, cons(X2!47, nil)), nil) = U!45)))),
% 8.56/8.77 inference(quant_inst,[status(thm)],[])).
% 8.56/8.77 tff(130,plain,
% 8.56/8.77 ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), nil) = U!45)))) | (~ssList(X3!48)) | (~(app(app(nil, cons(X2!47, nil)), X3!48) = V!46)) | (~(app(app(X3!48, cons(X2!47, nil)), nil) = U!45))),
% 8.56/8.77 inference(modus_ponens,[status(thm)],[129, 128])).
% 8.56/8.77 tff(131,plain,
% 8.56/8.77 ((~(app(app(nil, cons(X2!47, nil)), X3!48) = V!46)) | (~(app(app(X3!48, cons(X2!47, nil)), nil) = U!45))),
% 8.56/8.77 inference(unit_resolution,[status(thm)],[130, 127, 126])).
% 8.56/8.77 tff(132,plain,
% 8.56/8.77 (~(app(app(nil, cons(X2!47, nil)), X3!48) = V!46)),
% 8.56/8.77 inference(unit_resolution,[status(thm)],[131, 108])).
% 8.56/8.80 tff(133,plain,
% 8.56/8.80 ($false),
% 8.56/8.80 inference(unit_resolution,[status(thm)],[132, 90])).
% 8.56/8.80 % SZS output end Proof
% 8.66/8.80 % E exiting
%------------------------------------------------------------------------------