%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC006+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:29:54 AM UTC 2025
% Result : Theorem 1.38s 1.58s
% Output : Proof 1.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWC006+1 : TPTP v9.0.0. Released v2.4.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 08:00:03 EDT 2025
% 0.14/0.35 % CPUTime :
% 1.38/1.58 % SZS status Theorem
% 1.38/1.58 % SZS output start Proof
% 1.38/1.58 tff(tptp_fun_V_46_type, type, (
% 1.38/1.58 tptp_fun_V_46: $i)).
% 1.38/1.58 tff(app_type, type, (
% 1.38/1.58 app: ( $i * $i ) > $i)).
% 1.38/1.58 tff(tptp_fun_X3_48_type, type, (
% 1.38/1.58 tptp_fun_X3_48: $i)).
% 1.38/1.58 tff(tptp_fun_X2_47_type, type, (
% 1.38/1.58 tptp_fun_X2_47: $i)).
% 1.38/1.58 tff(tptp_fun_U_45_type, type, (
% 1.38/1.58 tptp_fun_U_45: $i)).
% 1.38/1.58 tff(ssList_type, type, (
% 1.38/1.58 ssList: $i > $o)).
% 1.38/1.58 tff(tptp_fun_X4_49_type, type, (
% 1.38/1.58 tptp_fun_X4_49: $i)).
% 1.38/1.58 tff(1,plain,
% 1.38/1.58 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) & ssList(X2!47) & ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46)))))) <=> (ssList(U!45) & ssList(V!46) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) & ssList(X2!47) & ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46)))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(2,plain,
% 1.38/1.58 ((ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) & (ssList(X2!47) & ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46)))))) <=> (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) & ssList(X2!47) & ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46)))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(3,plain,
% 1.38/1.58 ((ssList(X2!47) & (ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46)))))) <=> (ssList(X2!47) & ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46)))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(4,plain,
% 1.38/1.58 ((ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) & (ssList(X2!47) & (ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46))))))) <=> (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) & (ssList(X2!47) & ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46))))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[3])).
% 1.38/1.58 tff(5,plain,
% 1.38/1.58 ((ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) & (ssList(X2!47) & (ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46))))))) <=> (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) & ssList(X2!47) & ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46)))))),
% 1.38/1.58 inference(transitivity,[status(thm)],[4, 2])).
% 1.38/1.58 tff(6,plain,
% 1.38/1.58 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) & (ssList(X2!47) & (ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46)))))))) <=> (ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) & ssList(X2!47) & ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46))))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[5])).
% 1.38/1.58 tff(7,plain,
% 1.38/1.58 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) & (ssList(X2!47) & (ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46)))))))) <=> (ssList(U!45) & ssList(V!46) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) & ssList(X2!47) & ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46)))))),
% 1.38/1.58 inference(transitivity,[status(thm)],[6, 1])).
% 1.38/1.58 tff(8,plain,
% 1.38/1.58 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(X2, X4) = U)) | (~(app(app(X2, X3), X4) = V)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(X2, X4) = U)) | (~(app(app(X2, X3), X4) = V))))))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(9,plain,
% 1.38/1.58 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (((((~ssList(X)) | (~(V = X))) | (~(U = W))) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = V)) & (app(Y, X1) = U))))) | ![X2: $i] : (ssList(X2) => ![X3: $i] : (ssList(X3) => ![X4: $i] : (((~ssList(X4)) | (~(app(app(X2, X3), X4) = X))) | (~(app(X2, X4) = W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(X2, X4) = U)) | (~(app(app(X2, X3), X4) = V))))))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(10,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (((((~ssList(X)) | (~(V = X))) | (~(U = W))) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = V)) & (app(Y, X1) = U))))) | ![X2: $i] : (ssList(X2) => ![X3: $i] : (ssList(X3) => ![X4: $i] : (((~ssList(X4)) | (~(app(app(X2, X3), X4) = X))) | (~(app(X2, X4) = W)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 1.38/1.58 tff(11,plain,
% 1.38/1.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(X2, X4) = U)) | (~(app(app(X2, X3), X4) = V)))))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[10, 9])).
% 1.38/1.58 tff(12,plain,
% 1.38/1.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(X2, X4) = U)) | (~(app(app(X2, X3), X4) = V)))))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[11, 8])).
% 1.38/1.58 tff(13,plain,
% 1.38/1.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(X2, X4) = U)) | (~(app(app(X2, X3), X4) = V)))))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.38/1.58 tff(14,plain,
% 1.38/1.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(X2, X4) = U)) | (~(app(app(X2, X3), X4) = V)))))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[13, 8])).
% 1.38/1.58 tff(15,plain,
% 1.38/1.58 (ssList(U!45) & ssList(V!46) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) & ssList(X2!47) & ssList(X3!48) & (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[14, 7])).
% 1.38/1.58 tff(16,plain,
% 1.38/1.58 (ssList(X2!47)),
% 1.38/1.58 inference(and_elim,[status(thm)],[15])).
% 1.38/1.58 tff(17,plain,
% 1.38/1.58 (^[Y: $i] : refl(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46))))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(18,plain,
% 1.38/1.58 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46)))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[17])).
% 1.38/1.58 tff(19,plain,
% 1.38/1.58 (^[Y: $i] : rewrite(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46))))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(20,plain,
% 1.38/1.58 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46)))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[19])).
% 1.38/1.58 tff(21,plain,
% 1.38/1.58 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46)))))),
% 1.38/1.58 inference(transitivity,[status(thm)],[20, 18])).
% 1.38/1.58 tff(22,plain,
% 1.38/1.58 (^[Y: $i] : rewrite(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46))))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(23,plain,
% 1.38/1.58 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46)))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[22])).
% 1.38/1.58 tff(24,plain,
% 1.38/1.58 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45)))))),
% 1.38/1.58 inference(and_elim,[status(thm)],[15])).
% 1.38/1.58 tff(25,plain,
% 1.38/1.58 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46)))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.38/1.58 tff(26,plain,
% 1.38/1.58 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46)))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[25, 21])).
% 1.38/1.58 tff(27,plain,
% 1.38/1.58 (((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46)))))) | ((~ssList(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, Z), X1) = V!46)))))) <=> ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46)))))) | (~ssList(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, Z), X1) = V!46)))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(28,plain,
% 1.38/1.58 ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46)))))) | ((~ssList(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, Z), X1) = V!46)))))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(29,plain,
% 1.38/1.58 ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(Y, X1) = U!45)) | (~(app(app(Y, Z), X1) = V!46)))))) | (~ssList(X2!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, Z), X1) = V!46))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.38/1.58 tff(30,plain,
% 1.38/1.58 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, Z), X1) = V!46))))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[29, 26, 16])).
% 1.38/1.58 tff(31,plain,
% 1.38/1.58 (ssList(X3!48)),
% 1.38/1.58 inference(and_elim,[status(thm)],[15])).
% 1.38/1.58 tff(32,plain,
% 1.38/1.58 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, Z), X1) = V!46))))) | ((~ssList(X3!48)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, X3!48), X1) = V!46))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, Z), X1) = V!46))))) | (~ssList(X3!48)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, X3!48), X1) = V!46))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(33,plain,
% 1.38/1.58 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, Z), X1) = V!46))))) | ((~ssList(X3!48)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, X3!48), X1) = V!46))))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(34,plain,
% 1.38/1.58 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, Z), X1) = V!46))))) | (~ssList(X3!48)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, X3!48), X1) = V!46)))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[33, 32])).
% 1.38/1.58 tff(35,plain,
% 1.38/1.58 (![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, X3!48), X1) = V!46)))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[34, 31, 30])).
% 1.38/1.58 tff(36,plain,
% 1.38/1.58 (~((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46)))),
% 1.38/1.58 inference(and_elim,[status(thm)],[15])).
% 1.38/1.58 tff(37,plain,
% 1.38/1.58 (app(app(X2!47, X3!48), X4!49) = V!46),
% 1.38/1.58 inference(or_elim,[status(thm)],[36])).
% 1.38/1.58 tff(38,plain,
% 1.38/1.58 (app(X2!47, X4!49) = U!45),
% 1.38/1.58 inference(or_elim,[status(thm)],[36])).
% 1.38/1.58 tff(39,plain,
% 1.38/1.58 (ssList(X4!49)),
% 1.38/1.58 inference(or_elim,[status(thm)],[36])).
% 1.38/1.58 tff(40,plain,
% 1.38/1.58 (((~![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, X3!48), X1) = V!46)))) | ((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, X3!48), X1) = V!46)))) | (~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(41,plain,
% 1.38/1.58 ((~![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, X3!48), X1) = V!46)))) | ((~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46)))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(42,plain,
% 1.38/1.58 ((~![X1: $i] : ((~ssList(X1)) | (~(app(X2!47, X1) = U!45)) | (~(app(app(X2!47, X3!48), X1) = V!46)))) | (~ssList(X4!49)) | (~(app(X2!47, X4!49) = U!45)) | (~(app(app(X2!47, X3!48), X4!49) = V!46))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.38/1.59 tff(43,plain,
% 1.38/1.59 ($false),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[42, 39, 38, 37, 35])).
% 1.38/1.59 % SZS output end Proof
% 1.38/1.60 % E exiting
%------------------------------------------------------------------------------