%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC317+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 05:30:53 AM UTC 2025
% Result : Theorem 0.21s 0.50s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWC317+1 : TPTP v9.0.0. Released v2.4.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 08:59:46 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50 % SZS output start Proof
% 0.21/0.50 tff(tptp_fun_V_46_type, type, (
% 0.21/0.50 tptp_fun_V_46: $i)).
% 0.21/0.50 tff(app_type, type, (
% 0.21/0.50 app: ( $i * $i ) > $i)).
% 0.21/0.50 tff(cons_type, type, (
% 0.21/0.50 cons: ( $i * $i ) > $i)).
% 0.21/0.50 tff(nil_type, type, (
% 0.21/0.50 nil: $i)).
% 0.21/0.50 tff(tptp_fun_X1_47_type, type, (
% 0.21/0.50 tptp_fun_X1_47: $i)).
% 0.21/0.50 tff(tptp_fun_U_45_type, type, (
% 0.21/0.50 tptp_fun_U_45: $i)).
% 0.21/0.50 tff(ssList_type, type, (
% 0.21/0.50 ssList: $i > $o)).
% 0.21/0.50 tff(ssItem_type, type, (
% 0.21/0.50 ssItem: $i > $o)).
% 0.21/0.50 tff(tptp_fun_X2_48_type, type, (
% 0.21/0.50 tptp_fun_X2_48: $i)).
% 0.21/0.50 tff(neq_type, type, (
% 0.21/0.50 neq: ( $i * $i ) > $o)).
% 0.21/0.50 tff(1,plain,
% 0.21/0.50 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))))) <=> (ssList(U!45) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(2,plain,
% 0.21/0.50 ((ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & (ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))))) <=> (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(3,plain,
% 0.21/0.50 ((~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))) <=> (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(4,plain,
% 0.21/0.50 ((ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46))))) <=> (ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[3])).
% 0.21/0.50 tff(5,plain,
% 0.21/0.50 ((ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & (ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))))) <=> (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & (ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[4])).
% 0.21/0.50 tff(6,plain,
% 0.21/0.50 ((ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & (ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))))) <=> (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[5, 2])).
% 0.21/0.50 tff(7,plain,
% 0.21/0.50 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & (ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46))))))) <=> (ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[6])).
% 0.21/0.50 tff(8,plain,
% 0.21/0.50 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & (ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46))))))) <=> (ssList(U!45) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[7, 1])).
% 0.21/0.50 tff(9,plain,
% 0.21/0.50 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (app(cons(Y, nil), Z) = U) & (app(Z, cons(Y, nil)) = V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = U)) | (~(app(X2, cons(X1, nil)) = V))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (app(cons(Y, nil), Z) = U) & (app(Z, cons(Y, nil)) = V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = U)) | (~(app(X2, cons(X1, nil)) = V)))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(10,plain,
% 0.21/0.50 ((~![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) & (app(cons(Y, nil), Z) = U)) & (app(Z, cons(Y, nil)) = V)))) | ![X1: $i] : (ssItem(X1) => ![X2: $i] : (ssList(X2) => ((~(app(cons(X1, nil), X2) = W)) | (~(app(X2, cons(X1, nil)) = X)))))) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (app(cons(Y, nil), Z) = U) & (app(Z, cons(Y, nil)) = V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = U)) | (~(app(X2, cons(X1, nil)) = V)))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 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) & (app(cons(Y, nil), Z) = U)) & (app(Z, cons(Y, nil)) = V)))) | ![X1: $i] : (ssItem(X1) => ![X2: $i] : (ssList(X2) => ((~(app(cons(X1, nil), X2) = W)) | (~(app(X2, cons(X1, nil)) = X)))))) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.21/0.50 tff(12,plain,
% 0.21/0.50 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (app(cons(Y, nil), Z) = U) & (app(Z, cons(Y, nil)) = V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = U)) | (~(app(X2, cons(X1, nil)) = V))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.50 tff(13,plain,
% 0.21/0.50 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (app(cons(Y, nil), Z) = U) & (app(Z, cons(Y, nil)) = V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = U)) | (~(app(X2, cons(X1, nil)) = V))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.21/0.50 tff(14,plain,
% 0.21/0.50 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (app(cons(Y, nil), Z) = U) & (app(Z, cons(Y, nil)) = V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = U)) | (~(app(X2, cons(X1, nil)) = V))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.51 tff(15,plain,
% 0.21/0.51 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (app(cons(Y, nil), Z) = U) & (app(Z, cons(Y, nil)) = V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = U)) | (~(app(X2, cons(X1, nil)) = V))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.21/0.51 tff(16,plain,
% 0.21/0.51 (ssList(U!45) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.21/0.51 tff(17,plain,
% 0.21/0.51 (ssItem(X1!47)),
% 0.21/0.51 inference(and_elim,[status(thm)],[16])).
% 0.21/0.51 tff(18,plain,
% 0.21/0.51 (^[Y: $i] : refl(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(19,plain,
% 0.21/0.51 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.51 tff(20,plain,
% 0.21/0.51 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(21,plain,
% 0.21/0.51 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.51 tff(22,plain,
% 0.21/0.51 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[21, 19])).
% 0.21/0.51 tff(23,plain,
% 0.21/0.51 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(24,plain,
% 0.21/0.51 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.51 tff(25,plain,
% 0.21/0.51 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = U!45) & (app(Z, cons(Y, nil)) = V!46))))),
% 0.21/0.51 inference(and_elim,[status(thm)],[16])).
% 0.21/0.51 tff(26,plain,
% 0.21/0.51 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.51 tff(27,plain,
% 0.21/0.51 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.21/0.51 tff(28,plain,
% 0.21/0.51 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))) | ((~ssItem(X1!47)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(X1!47, nil), Z) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))) | (~ssItem(X1!47)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(X1!47, nil), Z) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(29,plain,
% 0.21/0.51 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))) | ((~ssItem(X1!47)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(X1!47, nil), Z) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(30,plain,
% 0.21/0.51 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U!45)) | (~(app(Z, cons(Y, nil)) = V!46))))) | (~ssItem(X1!47)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(X1!47, nil), Z) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.51 tff(31,plain,
% 0.21/0.51 (![Z: $i] : ((~ssList(Z)) | (~(app(cons(X1!47, nil), Z) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[30, 27, 17])).
% 0.21/0.51 tff(32,plain,
% 0.21/0.51 (~((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))),
% 0.21/0.51 inference(and_elim,[status(thm)],[16])).
% 0.21/0.51 tff(33,plain,
% 0.21/0.51 (app(X2!48, cons(X1!47, nil)) = V!46),
% 0.21/0.51 inference(or_elim,[status(thm)],[32])).
% 0.21/0.51 tff(34,plain,
% 0.21/0.51 (app(cons(X1!47, nil), X2!48) = U!45),
% 0.21/0.51 inference(or_elim,[status(thm)],[32])).
% 0.21/0.51 tff(35,plain,
% 0.21/0.51 (ssList(X2!48)),
% 0.21/0.51 inference(or_elim,[status(thm)],[32])).
% 0.21/0.51 tff(36,plain,
% 0.21/0.51 (((~![Z: $i] : ((~ssList(Z)) | (~(app(cons(X1!47, nil), Z) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46)))) | ((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))) <=> ((~![Z: $i] : ((~ssList(Z)) | (~(app(cons(X1!47, nil), Z) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46)))) | (~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(37,plain,
% 0.21/0.51 ((~![Z: $i] : ((~ssList(Z)) | (~(app(cons(X1!47, nil), Z) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46)))) | ((~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(38,plain,
% 0.21/0.51 ((~![Z: $i] : ((~ssList(Z)) | (~(app(cons(X1!47, nil), Z) = U!45)) | (~(app(Z, cons(X1!47, nil)) = V!46)))) | (~ssList(X2!48)) | (~(app(cons(X1!47, nil), X2!48) = U!45)) | (~(app(X2!48, cons(X1!47, nil)) = V!46))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.51 tff(39,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[38, 35, 34, 33, 31])).
% 0.21/0.51 % SZS output end Proof
% 0.21/0.51 % E exiting
%------------------------------------------------------------------------------