%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC419+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 8.75s 8.97s
% Output : Proof 8.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC419+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:18:46 EDT 2025
% 0.12/0.33 % CPUTime :
% 8.75/8.97 % SZS status Theorem
% 8.75/8.97 % SZS output start Proof
% 8.75/8.97 tff(tptp_fun_V_46_type, type, (
% 8.75/8.97 tptp_fun_V_46: $i)).
% 8.75/8.97 tff(app_type, type, (
% 8.75/8.97 app: ( $i * $i ) > $i)).
% 8.75/8.97 tff(tptp_fun_X3_48_type, type, (
% 8.75/8.97 tptp_fun_X3_48: $i)).
% 8.75/8.97 tff(cons_type, type, (
% 8.75/8.97 cons: ( $i * $i ) > $i)).
% 8.75/8.97 tff(nil_type, type, (
% 8.75/8.97 nil: $i)).
% 8.75/8.97 tff(tptp_fun_X2_47_type, type, (
% 8.75/8.97 tptp_fun_X2_47: $i)).
% 8.75/8.97 tff(ssList_type, type, (
% 8.75/8.97 ssList: $i > $o)).
% 8.75/8.97 tff(tptp_fun_U_45_type, type, (
% 8.75/8.97 tptp_fun_U_45: $i)).
% 8.75/8.97 tff(ssItem_type, type, (
% 8.75/8.97 ssItem: $i > $o)).
% 8.75/8.97 tff(neq_type, type, (
% 8.75/8.97 neq: ( $i * $i ) > $o)).
% 8.75/8.97 tff(1,plain,
% 8.75/8.97 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (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) & neq(V!46, nil) & ![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))))))) <=> (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))))) & neq(V!46, nil) & ![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))))))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(2,plain,
% 8.75/8.97 (((~((~(nil = U!45)) & (nil = V!46))) & 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))))) | (~neq(V!46, nil))) & ssList(U!45) & neq(V!46, nil) & ![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)))))) <=> ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (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) & neq(V!46, nil) & ![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))))))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(3,plain,
% 8.75/8.97 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & 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))))) | (~neq(V!46, nil))) & ssList(U!45) & neq(V!46, nil) & ![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))))))) <=> (ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (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) & neq(V!46, nil) & ![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)))))))),
% 8.75/8.97 inference(monotonicity,[status(thm)],[2])).
% 8.75/8.97 tff(4,plain,
% 8.75/8.97 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & 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))))) | (~neq(V!46, nil))) & ssList(U!45) & neq(V!46, nil) & ![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))))))) <=> (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))))) & neq(V!46, nil) & ![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))))))),
% 8.75/8.97 inference(transitivity,[status(thm)],[3, 1])).
% 8.75/8.97 tff(5,plain,
% 8.75/8.97 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = U)) | (~(app(cons(X2, nil), X3) = V)) | (~ssList(X3)))) & neq(V, nil)) | (~ssList(U)) | (~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))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = U)) | (~(app(cons(X2, nil), X3) = V)) | (~ssList(X3)))) & neq(V, nil)) | (~ssList(U)) | (~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)))))))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(6,plain,
% 8.75/8.97 ((~![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))))) | ((~(nil = W)) & (nil = X))) | (![X2: $i] : (ssItem(X2) => ![X3: $i] : (((~ssList(X3)) | (~(app(cons(X2, nil), X3) = X))) | (~(app(X3, cons(X2, nil)) = W)))) & neq(X, nil))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = U)) | (~(app(cons(X2, nil), X3) = V)) | (~ssList(X3)))) & neq(V, nil)) | (~ssList(U)) | (~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)))))))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(7,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))))) | ((~(nil = W)) & (nil = X))) | (![X2: $i] : (ssItem(X2) => ![X3: $i] : (((~ssList(X3)) | (~(app(cons(X2, nil), X3) = X))) | (~(app(X3, cons(X2, nil)) = W)))) & neq(X, nil))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 8.75/8.97 tff(8,plain,
% 8.75/8.97 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = U)) | (~(app(cons(X2, nil), X3) = V)) | (~ssList(X3)))) & neq(V, nil)) | (~ssList(U)) | (~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))))))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[7, 6])).
% 8.75/8.97 tff(9,plain,
% 8.75/8.97 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = U)) | (~(app(cons(X2, nil), X3) = V)) | (~ssList(X3)))) & neq(V, nil)) | (~ssList(U)) | (~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))))))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[8, 5])).
% 8.75/8.97 tff(10,plain,
% 8.75/8.97 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = U)) | (~(app(cons(X2, nil), X3) = V)) | (~ssList(X3)))) & neq(V, nil)) | (~ssList(U)) | (~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))))))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[9, 5])).
% 8.75/8.97 tff(11,plain,
% 8.75/8.97 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = U)) | (~(app(cons(X2, nil), X3) = V)) | (~ssList(X3)))) & neq(V, nil)) | (~ssList(U)) | (~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))))))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[10, 5])).
% 8.75/8.97 tff(12,plain,
% 8.75/8.97 (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))))) & neq(V!46, nil) & ![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)))))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[11, 4])).
% 8.75/8.97 tff(13,plain,
% 8.75/8.97 (neq(V!46, nil)),
% 8.75/8.97 inference(and_elim,[status(thm)],[12])).
% 8.75/8.97 tff(14,plain,
% 8.75/8.97 (((~neq(V!46, nil)) | (ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))))) <=> ((~neq(V!46, nil)) | (~((~ssItem(X2!47)) | (~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(15,plain,
% 8.75/8.97 ((~neq(V!46, nil)) | (ssItem(X2!47) & (~((~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))))),
% 8.75/8.97 inference(and_elim,[status(thm)],[12])).
% 8.75/8.97 tff(16,plain,
% 8.75/8.97 ((~neq(V!46, nil)) | (~((~ssItem(X2!47)) | (~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48))))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[15, 14])).
% 8.75/8.97 tff(17,plain,
% 8.75/8.97 (~((~ssItem(X2!47)) | (~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48)))),
% 8.75/8.97 inference(unit_resolution,[status(thm)],[16, 13])).
% 8.75/8.97 tff(18,plain,
% 8.75/8.97 (((~ssItem(X2!47)) | (~(app(X3!48, cons(X2!47, nil)) = U!45)) | (~(app(cons(X2!47, nil), X3!48) = V!46)) | (~ssList(X3!48))) | (app(cons(X2!47, nil), X3!48) = V!46)),
% 8.75/8.97 inference(tautology,[status(thm)],[])).
% 8.75/8.97 tff(19,plain,
% 8.75/8.97 (app(cons(X2!47, nil), X3!48) = V!46),
% 8.75/8.97 inference(unit_resolution,[status(thm)],[18, 17])).
% 8.75/8.97 tff(20,plain,
% 8.75/8.97 (^[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)))))),
% 8.75/8.97 inference(bind,[status(th)],[])).
% 8.75/8.97 tff(21,plain,
% 8.75/8.97 (![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))))),
% 8.75/8.97 inference(quant_intro,[status(thm)],[20])).
% 8.75/8.97 tff(22,plain,
% 8.75/8.97 (^[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)))))),
% 8.75/8.97 inference(bind,[status(th)],[])).
% 8.75/8.97 tff(23,plain,
% 8.75/8.97 (![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))))),
% 8.75/8.97 inference(quant_intro,[status(thm)],[22])).
% 8.75/8.97 tff(24,plain,
% 8.75/8.97 (![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))))),
% 8.75/8.97 inference(transitivity,[status(thm)],[23, 21])).
% 8.75/8.97 tff(25,plain,
% 8.75/8.97 (![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))))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(26,plain,
% 8.75/8.97 (^[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))))))),
% 8.75/8.97 inference(bind,[status(th)],[])).
% 8.75/8.97 tff(27,plain,
% 8.75/8.97 (![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))))),
% 8.75/8.97 inference(quant_intro,[status(thm)],[26])).
% 8.75/8.97 tff(28,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')).
% 8.75/8.97 tff(29,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[28, 27])).
% 8.75/8.97 tff(30,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[29, 25])).
% 8.75/8.97 tff(31,plain,(
% 8.75/8.97 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 8.75/8.97 inference(skolemize,[status(sab)],[30])).
% 8.75/8.97 tff(32,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[31, 24])).
% 8.75/8.97 tff(33,plain,
% 8.75/8.97 (ssList(nil) <=> ssList(nil)),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(34,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 8.75/8.97 tff(35,plain,
% 8.75/8.97 (ssList(nil)),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[34, 33])).
% 8.75/8.97 tff(36,plain,
% 8.75/8.97 (((~![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))))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(37,plain,
% 8.75/8.97 (((~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))))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(38,plain,
% 8.75/8.97 (((~![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)))))),
% 8.75/8.97 inference(monotonicity,[status(thm)],[37])).
% 8.75/8.97 tff(39,plain,
% 8.75/8.97 (((~![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))))),
% 8.75/8.97 inference(transitivity,[status(thm)],[38, 36])).
% 8.75/8.97 tff(40,plain,
% 8.75/8.97 ((~![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))))),
% 8.75/8.97 inference(quant_inst,[status(thm)],[])).
% 8.75/8.97 tff(41,plain,
% 8.75/8.97 ((~![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)))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[40, 39])).
% 8.75/8.97 tff(42,plain,
% 8.75/8.97 (![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))),
% 8.75/8.97 inference(unit_resolution,[status(thm)],[41, 35, 32])).
% 8.75/8.97 tff(43,plain,
% 8.75/8.97 (((~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)),
% 8.75/8.97 inference(tautology,[status(thm)],[])).
% 8.75/8.97 tff(44,plain,
% 8.75/8.97 (ssItem(X2!47)),
% 8.75/8.97 inference(unit_resolution,[status(thm)],[43, 17])).
% 8.75/8.97 tff(45,plain,
% 8.75/8.97 (((~![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)))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(46,plain,
% 8.75/8.97 ((~![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)))),
% 8.75/8.97 inference(quant_inst,[status(thm)],[])).
% 8.75/8.97 tff(47,plain,
% 8.75/8.97 ((~![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))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[46, 45])).
% 8.75/8.97 tff(48,plain,
% 8.75/8.97 (cons(X2!47, nil) = app(cons(X2!47, nil), nil)),
% 8.75/8.97 inference(unit_resolution,[status(thm)],[47, 44, 42])).
% 8.75/8.97 tff(49,plain,
% 8.75/8.97 (app(cons(X2!47, nil), nil) = cons(X2!47, nil)),
% 8.75/8.97 inference(symmetry,[status(thm)],[48])).
% 8.75/8.97 tff(50,plain,
% 8.75/8.97 (ssList(app(cons(X2!47, nil), nil)) <=> ssList(cons(X2!47, nil))),
% 8.75/8.97 inference(monotonicity,[status(thm)],[49])).
% 8.75/8.97 tff(51,plain,
% 8.75/8.97 (ssList(cons(X2!47, nil)) <=> ssList(app(cons(X2!47, nil), nil))),
% 8.75/8.97 inference(symmetry,[status(thm)],[50])).
% 8.75/8.97 tff(52,plain,
% 8.75/8.97 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 8.75/8.97 inference(bind,[status(th)],[])).
% 8.75/8.97 tff(53,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.75/8.97 inference(quant_intro,[status(thm)],[52])).
% 8.75/8.97 tff(54,plain,
% 8.75/8.97 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 8.75/8.97 inference(bind,[status(th)],[])).
% 8.75/8.97 tff(55,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.75/8.97 inference(quant_intro,[status(thm)],[54])).
% 8.75/8.97 tff(56,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.75/8.97 inference(transitivity,[status(thm)],[55, 53])).
% 8.75/8.97 tff(57,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(58,plain,
% 8.75/8.97 (^[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))))))),
% 8.75/8.97 inference(bind,[status(th)],[])).
% 8.75/8.97 tff(59,plain,
% 8.75/8.97 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.75/8.97 inference(quant_intro,[status(thm)],[58])).
% 8.75/8.97 tff(60,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax16')).
% 8.75/8.97 tff(61,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[60, 59])).
% 8.75/8.97 tff(62,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[61, 57])).
% 8.75/8.97 tff(63,plain,(
% 8.75/8.97 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.75/8.97 inference(skolemize,[status(sab)],[62])).
% 8.75/8.97 tff(64,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[63, 56])).
% 8.75/8.97 tff(65,plain,
% 8.75/8.97 (((~![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))))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(66,plain,
% 8.75/8.97 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 8.75/8.97 inference(quant_inst,[status(thm)],[])).
% 8.75/8.97 tff(67,plain,
% 8.75/8.97 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[66, 65])).
% 8.75/8.97 tff(68,plain,
% 8.75/8.97 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 8.75/8.97 inference(unit_resolution,[status(thm)],[67, 64, 35])).
% 8.75/8.97 tff(69,plain,
% 8.75/8.97 (((~![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)))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(70,plain,
% 8.75/8.97 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(X2!47)) | ssList(cons(X2!47, nil)))),
% 8.75/8.97 inference(quant_inst,[status(thm)],[])).
% 8.75/8.97 tff(71,plain,
% 8.75/8.97 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(X2!47)) | ssList(cons(X2!47, nil))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[70, 69])).
% 8.75/8.97 tff(72,plain,
% 8.75/8.97 (ssList(cons(X2!47, nil))),
% 8.75/8.97 inference(unit_resolution,[status(thm)],[71, 44, 68])).
% 8.75/8.97 tff(73,plain,
% 8.75/8.97 (ssList(app(cons(X2!47, nil), nil))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[72, 51])).
% 8.75/8.97 tff(74,plain,
% 8.75/8.97 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 8.75/8.97 inference(bind,[status(th)],[])).
% 8.75/8.97 tff(75,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 8.75/8.97 inference(quant_intro,[status(thm)],[74])).
% 8.75/8.97 tff(76,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(77,plain,
% 8.75/8.97 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 8.75/8.97 inference(bind,[status(th)],[])).
% 8.75/8.97 tff(78,plain,
% 8.75/8.97 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 8.75/8.97 inference(quant_intro,[status(thm)],[77])).
% 8.75/8.97 tff(79,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 8.75/8.97 tff(80,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[79, 78])).
% 8.75/8.97 tff(81,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[80, 76])).
% 8.75/8.97 tff(82,plain,(
% 8.75/8.97 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 8.75/8.97 inference(skolemize,[status(sab)],[81])).
% 8.75/8.97 tff(83,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[82, 75])).
% 8.75/8.97 tff(84,plain,
% 8.75/8.97 (((~![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)))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(85,plain,
% 8.75/8.97 ((~![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)))),
% 8.75/8.97 inference(quant_inst,[status(thm)],[])).
% 8.75/8.97 tff(86,plain,
% 8.75/8.97 ((~![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))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[85, 84])).
% 8.75/8.97 tff(87,plain,
% 8.75/8.97 ((~ssList(app(cons(X2!47, nil), nil))) | (app(nil, app(cons(X2!47, nil), nil)) = app(cons(X2!47, nil), nil))),
% 8.75/8.97 inference(unit_resolution,[status(thm)],[86, 83])).
% 8.75/8.97 tff(88,plain,
% 8.75/8.97 (app(nil, app(cons(X2!47, nil), nil)) = app(cons(X2!47, nil), nil)),
% 8.75/8.97 inference(unit_resolution,[status(thm)],[87, 73])).
% 8.75/8.97 tff(89,plain,
% 8.75/8.97 (app(nil, cons(X2!47, nil)) = app(nil, app(cons(X2!47, nil), nil))),
% 8.75/8.97 inference(monotonicity,[status(thm)],[48])).
% 8.75/8.97 tff(90,plain,
% 8.75/8.97 (app(nil, cons(X2!47, nil)) = cons(X2!47, nil)),
% 8.75/8.97 inference(transitivity,[status(thm)],[89, 88, 49])).
% 8.75/8.97 tff(91,plain,
% 8.75/8.97 (app(app(nil, cons(X2!47, nil)), X3!48) = app(cons(X2!47, nil), X3!48)),
% 8.75/8.97 inference(monotonicity,[status(thm)],[90])).
% 8.75/8.97 tff(92,plain,
% 8.75/8.97 (app(app(nil, cons(X2!47, nil)), X3!48) = V!46),
% 8.75/8.97 inference(transitivity,[status(thm)],[91, 19])).
% 8.75/8.97 tff(93,plain,
% 8.75/8.97 (ssList(U!45)),
% 8.75/8.97 inference(and_elim,[status(thm)],[12])).
% 8.75/8.97 tff(94,plain,
% 8.75/8.97 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 8.75/8.97 inference(bind,[status(th)],[])).
% 8.75/8.97 tff(95,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 8.75/8.97 inference(quant_intro,[status(thm)],[94])).
% 8.75/8.97 tff(96,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(97,plain,
% 8.75/8.97 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 8.75/8.97 inference(bind,[status(th)],[])).
% 8.75/8.97 tff(98,plain,
% 8.75/8.97 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 8.75/8.97 inference(quant_intro,[status(thm)],[97])).
% 8.75/8.97 tff(99,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax84')).
% 8.75/8.97 tff(100,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[99, 98])).
% 8.75/8.97 tff(101,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[100, 96])).
% 8.75/8.97 tff(102,plain,(
% 8.75/8.97 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 8.75/8.97 inference(skolemize,[status(sab)],[101])).
% 8.75/8.97 tff(103,plain,
% 8.75/8.97 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[102, 95])).
% 8.75/8.97 tff(104,plain,
% 8.75/8.97 (((~![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))),
% 8.75/8.97 inference(rewrite,[status(thm)],[])).
% 8.75/8.97 tff(105,plain,
% 8.75/8.97 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(U!45)) | (app(U!45, nil) = U!45))),
% 8.75/8.97 inference(quant_inst,[status(thm)],[])).
% 8.75/8.97 tff(106,plain,
% 8.75/8.97 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(U!45)) | (app(U!45, nil) = U!45)),
% 8.75/8.97 inference(modus_ponens,[status(thm)],[105, 104])).
% 8.75/8.97 tff(107,plain,
% 8.75/8.97 (app(U!45, nil) = U!45),
% 8.75/8.97 inference(unit_resolution,[status(thm)],[106, 103, 93])).
% 8.75/8.97 tff(108,plain,
% 8.75/8.97 (((~ssItem(X2!47)) | (~(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)),
% 8.75/8.97 inference(tautology,[status(thm)],[])).
% 8.75/8.97 tff(109,plain,
% 8.75/8.97 (app(X3!48, cons(X2!47, nil)) = U!45),
% 8.75/8.97 inference(unit_resolution,[status(thm)],[108, 17])).
% 8.75/8.97 tff(110,plain,
% 8.75/8.97 (app(app(X3!48, cons(X2!47, nil)), nil) = app(U!45, nil)),
% 8.75/8.97 inference(monotonicity,[status(thm)],[109])).
% 8.75/8.97 tff(111,plain,
% 8.75/8.97 (app(app(X3!48, cons(X2!47, nil)), nil) = U!45),
% 8.75/8.97 inference(transitivity,[status(thm)],[110, 107])).
% 8.75/8.97 tff(112,plain,
% 8.75/8.97 (^[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))))))),
% 8.75/8.98 inference(bind,[status(th)],[])).
% 8.75/8.98 tff(113,plain,
% 8.75/8.98 (![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)))))),
% 8.75/8.98 inference(quant_intro,[status(thm)],[112])).
% 8.75/8.98 tff(114,plain,
% 8.75/8.98 (^[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))))))),
% 8.75/8.98 inference(bind,[status(th)],[])).
% 8.75/8.98 tff(115,plain,
% 8.75/8.98 (![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)))))),
% 8.75/8.98 inference(quant_intro,[status(thm)],[114])).
% 8.75/8.98 tff(116,plain,
% 8.75/8.98 (![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)))))),
% 8.75/8.98 inference(transitivity,[status(thm)],[115, 113])).
% 8.75/8.98 tff(117,plain,
% 8.75/8.98 (^[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))))))),
% 8.75/8.98 inference(bind,[status(th)],[])).
% 8.75/8.98 tff(118,plain,
% 8.75/8.98 (![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)))))),
% 8.75/8.98 inference(quant_intro,[status(thm)],[117])).
% 8.75/8.98 tff(119,plain,
% 8.75/8.98 (![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)))))),
% 8.75/8.98 inference(and_elim,[status(thm)],[12])).
% 8.75/8.98 tff(120,plain,
% 8.75/8.98 (![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)))))),
% 8.75/8.98 inference(modus_ponens,[status(thm)],[119, 118])).
% 8.75/8.98 tff(121,plain,
% 8.75/8.98 (![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)))))),
% 8.75/8.98 inference(modus_ponens,[status(thm)],[120, 116])).
% 8.75/8.98 tff(122,plain,
% 8.75/8.98 (((~![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)))))),
% 8.75/8.98 inference(rewrite,[status(thm)],[])).
% 8.75/8.98 tff(123,plain,
% 8.75/8.98 ((~![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)))))),
% 8.75/8.98 inference(quant_inst,[status(thm)],[])).
% 8.75/8.98 tff(124,plain,
% 8.75/8.98 ((~![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))))),
% 8.75/8.98 inference(modus_ponens,[status(thm)],[123, 122])).
% 8.75/8.98 tff(125,plain,
% 8.75/8.98 (![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))))),
% 8.75/8.98 inference(unit_resolution,[status(thm)],[124, 44, 121])).
% 8.75/8.98 tff(126,plain,
% 8.75/8.98 (((~![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))))),
% 8.75/8.98 inference(rewrite,[status(thm)],[])).
% 8.75/8.98 tff(127,plain,
% 8.75/8.98 ((~![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))))),
% 8.75/8.98 inference(quant_inst,[status(thm)],[])).
% 8.75/8.98 tff(128,plain,
% 8.75/8.98 ((~![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)))),
% 8.75/8.98 inference(modus_ponens,[status(thm)],[127, 126])).
% 8.75/8.98 tff(129,plain,
% 8.75/8.98 (![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), nil) = U!45)))),
% 8.75/8.98 inference(unit_resolution,[status(thm)],[128, 35, 125])).
% 8.75/8.98 tff(130,plain,
% 8.75/8.98 (((~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(X3!48)),
% 8.75/8.98 inference(tautology,[status(thm)],[])).
% 8.75/8.98 tff(131,plain,
% 8.75/8.98 (ssList(X3!48)),
% 8.75/8.98 inference(unit_resolution,[status(thm)],[130, 17])).
% 8.75/8.98 tff(132,plain,
% 8.75/8.98 (((~![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)))),
% 8.75/8.98 inference(rewrite,[status(thm)],[])).
% 8.75/8.98 tff(133,plain,
% 8.75/8.98 ((~![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)))),
% 8.75/8.98 inference(quant_inst,[status(thm)],[])).
% 8.75/8.98 tff(134,plain,
% 8.83/9.01 ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, cons(X2!47, nil)), X1) = V!46)) | (~(app(app(X1, cons(X2!47, nil)), nil) = U!45)))) | (~ssList(X3!48)) | (~(app(app(nil, cons(X2!47, nil)), X3!48) = V!46)) | (~(app(app(X3!48, cons(X2!47, nil)), nil) = U!45))),
% 8.83/9.01 inference(modus_ponens,[status(thm)],[133, 132])).
% 8.83/9.01 tff(135,plain,
% 8.83/9.01 ((~(app(app(nil, cons(X2!47, nil)), X3!48) = V!46)) | (~(app(app(X3!48, cons(X2!47, nil)), nil) = U!45))),
% 8.83/9.01 inference(unit_resolution,[status(thm)],[134, 131, 129])).
% 8.83/9.01 tff(136,plain,
% 8.83/9.01 (~(app(app(nil, cons(X2!47, nil)), X3!48) = V!46)),
% 8.83/9.01 inference(unit_resolution,[status(thm)],[135, 111])).
% 8.83/9.01 tff(137,plain,
% 8.83/9.01 ($false),
% 8.83/9.01 inference(unit_resolution,[status(thm)],[136, 92])).
% 8.83/9.01 % SZS output end Proof
% 8.83/9.02 % E exiting
%------------------------------------------------------------------------------