%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC009+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 0.84s 1.00s
% Output : Proof 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC009+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 07:59:48 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.84/1.00 % SZS status Theorem
% 0.84/1.00 % SZS output start Proof
% 0.84/1.00 tff(tptp_fun_V_46_type, type, (
% 0.84/1.00 tptp_fun_V_46: $i)).
% 0.84/1.00 tff(app_type, type, (
% 0.84/1.00 app: ( $i * $i ) > $i)).
% 0.84/1.00 tff(nil_type, type, (
% 0.84/1.00 nil: $i)).
% 0.84/1.00 tff(tptp_fun_X2_47_type, type, (
% 0.84/1.00 tptp_fun_X2_47: $i)).
% 0.84/1.00 tff(tptp_fun_U_45_type, type, (
% 0.84/1.00 tptp_fun_U_45: $i)).
% 0.84/1.00 tff(ssList_type, type, (
% 0.84/1.00 ssList: $i > $o)).
% 0.84/1.00 tff(lt_type, type, (
% 0.84/1.00 lt: ( $i * $i ) > $o)).
% 0.84/1.00 tff(cons_type, type, (
% 0.84/1.00 cons: ( $i * $i ) > $i)).
% 0.84/1.00 tff(ssItem_type, type, (
% 0.84/1.00 ssItem: $i > $o)).
% 0.84/1.00 tff(strictorderedP_type, type, (
% 0.84/1.00 strictorderedP: $i > $o)).
% 0.84/1.00 tff(1,plain,
% 0.84/1.00 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3)))))) & 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(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3)))))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(2,plain,
% 0.84/1.00 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3))))))) & 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)))))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3)))))) & 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))))))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(3,plain,
% 0.84/1.00 ((strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3))))))) <=> (strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3)))))))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(4,plain,
% 0.84/1.00 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3))))))) & 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)))))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3))))))) & 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))))))),
% 0.84/1.01 inference(monotonicity,[status(thm)],[3])).
% 0.84/1.01 tff(5,plain,
% 0.84/1.01 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3))))))) & 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)))))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3)))))) & 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))))))),
% 0.84/1.01 inference(transitivity,[status(thm)],[4, 2])).
% 0.84/1.01 tff(6,plain,
% 0.84/1.01 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3))))))) & 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(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3)))))) & 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)))))))),
% 0.84/1.01 inference(monotonicity,[status(thm)],[5])).
% 0.84/1.01 tff(7,plain,
% 0.84/1.01 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3))))))) & 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(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3)))))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))))),
% 0.84/1.01 inference(transitivity,[status(thm)],[6, 1])).
% 0.84/1.01 tff(8,plain,
% 0.84/1.01 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![X2: $i] : ((~strictorderedP(U)) | (~(app(U, X2) = V)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = U) & lt(X5, X3)))))) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![X2: $i] : ((~strictorderedP(U)) | (~(app(U, X2) = V)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = U) & lt(X5, X3)))))) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))))))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(9,plain,
% 0.84/1.01 ((~![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) => (((~(app(W, X2) = X)) | (~strictorderedP(W))) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : ((ssList(X4) & (app(cons(X3, nil), X4) = X2)) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : ((ssList(X6) & (app(X6, cons(X5, nil)) = W)) & lt(X5, X3)))))))) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![X2: $i] : ((~strictorderedP(U)) | (~(app(U, X2) = V)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = U) & lt(X5, X3)))))) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))))))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 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) => (((~(app(W, X2) = X)) | (~strictorderedP(W))) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : ((ssList(X4) & (app(cons(X3, nil), X4) = X2)) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : ((ssList(X6) & (app(X6, cons(X5, nil)) = W)) & lt(X5, X3)))))))) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.84/1.01 tff(11,plain,
% 0.84/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![X2: $i] : ((~strictorderedP(U)) | (~(app(U, X2) = V)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = U) & lt(X5, X3)))))) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.84/1.01 tff(12,plain,
% 0.84/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![X2: $i] : ((~strictorderedP(U)) | (~(app(U, X2) = V)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = U) & lt(X5, X3)))))) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.84/1.01 tff(13,plain,
% 0.84/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![X2: $i] : ((~strictorderedP(U)) | (~(app(U, X2) = V)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = U) & lt(X5, X3)))))) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.84/1.01 tff(14,plain,
% 0.84/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![X2: $i] : ((~strictorderedP(U)) | (~(app(U, X2) = V)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = U) & lt(X5, X3)))))) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.84/1.01 tff(15,plain,
% 0.84/1.01 (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, X2!47) = V!46) & ssList(X2!47) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!47)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = U!45) & lt(X5, X3)))))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45)))))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.84/1.01 tff(16,plain,
% 0.84/1.01 (ssList(V!46)),
% 0.84/1.01 inference(and_elim,[status(thm)],[15])).
% 0.84/1.01 tff(17,plain,
% 0.84/1.01 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(18,plain,
% 0.84/1.01 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[17])).
% 0.84/1.01 tff(19,plain,
% 0.84/1.01 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(20,plain,
% 0.84/1.01 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(21,plain,
% 0.84/1.01 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[20])).
% 0.84/1.01 tff(22,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax84')).
% 0.84/1.01 tff(23,plain,
% 0.84/1.01 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.84/1.01 tff(24,plain,
% 0.84/1.01 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.84/1.01 tff(25,plain,(
% 0.84/1.01 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.84/1.01 inference(skolemize,[status(sab)],[24])).
% 0.84/1.01 tff(26,plain,
% 0.84/1.01 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.84/1.01 tff(27,plain,
% 0.84/1.01 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(28,plain,
% 0.84/1.01 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(29,plain,
% 0.84/1.01 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46)),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.84/1.01 tff(30,plain,
% 0.84/1.01 (app(V!46, nil) = V!46),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[29, 26, 16])).
% 0.84/1.01 tff(31,plain,
% 0.84/1.01 (app(U!45, X2!47) = V!46),
% 0.84/1.01 inference(and_elim,[status(thm)],[15])).
% 0.84/1.01 tff(32,plain,
% 0.84/1.01 (app(app(U!45, X2!47), nil) = app(V!46, nil)),
% 0.84/1.01 inference(monotonicity,[status(thm)],[31])).
% 0.84/1.01 tff(33,plain,
% 0.84/1.01 (app(app(U!45, X2!47), nil) = V!46),
% 0.84/1.01 inference(transitivity,[status(thm)],[32, 30])).
% 0.84/1.01 tff(34,plain,
% 0.84/1.01 (^[Y: $i] : refl(((~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(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45))))))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(35,plain,
% 0.84/1.01 (![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(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[34])).
% 0.84/1.01 tff(36,plain,
% 0.84/1.01 (^[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(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45))))))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(37,plain,
% 0.84/1.01 (![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(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[36])).
% 0.84/1.01 tff(38,plain,
% 0.84/1.01 (![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(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))),
% 0.84/1.01 inference(transitivity,[status(thm)],[37, 35])).
% 0.84/1.01 tff(39,plain,
% 0.84/1.01 (^[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(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45))))))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(40,plain,
% 0.84/1.01 (![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(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[39])).
% 0.84/1.01 tff(41,plain,
% 0.84/1.01 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45)))))),
% 0.84/1.01 inference(and_elim,[status(thm)],[15])).
% 0.84/1.01 tff(42,plain,
% 0.84/1.01 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.84/1.01 tff(43,plain,
% 0.84/1.01 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.84/1.01 tff(44,plain,
% 0.84/1.01 (ssList(U!45)),
% 0.84/1.01 inference(and_elim,[status(thm)],[15])).
% 0.84/1.01 tff(45,plain,
% 0.84/1.01 (((~![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(U!45)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = 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(U!45)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45)))))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(46,plain,
% 0.84/1.01 ((~![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(U!45)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45)))))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(47,plain,
% 0.84/1.01 ((~![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(U!45)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.84/1.01 tff(48,plain,
% 0.84/1.01 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[47, 44, 43])).
% 0.84/1.01 tff(49,plain,
% 0.84/1.01 (ssList(X2!47)),
% 0.84/1.01 inference(and_elim,[status(thm)],[15])).
% 0.84/1.01 tff(50,plain,
% 0.84/1.01 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | ((~ssList(X2!47)) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, X2!47), X1) = V!46))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | (~ssList(X2!47)) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, X2!47), X1) = V!46))))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(51,plain,
% 0.84/1.01 (((~ssList(X2!47)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, X2!47), X1) = V!46)) | (~(app(U!45, X1) = U!45)))) <=> ((~ssList(X2!47)) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, X2!47), X1) = V!46))))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(52,plain,
% 0.84/1.01 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | ((~ssList(X2!47)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, X2!47), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | ((~ssList(X2!47)) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, X2!47), X1) = V!46)))))),
% 0.84/1.01 inference(monotonicity,[status(thm)],[51])).
% 0.84/1.01 tff(53,plain,
% 0.84/1.01 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | ((~ssList(X2!47)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, X2!47), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | (~ssList(X2!47)) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, X2!47), X1) = V!46))))),
% 0.84/1.01 inference(transitivity,[status(thm)],[52, 50])).
% 0.84/1.01 tff(54,plain,
% 0.84/1.01 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | ((~ssList(X2!47)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, X2!47), X1) = V!46)) | (~(app(U!45, X1) = U!45))))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(55,plain,
% 0.84/1.01 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | (~ssList(X2!47)) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, X2!47), X1) = V!46)))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.84/1.01 tff(56,plain,
% 0.84/1.01 (![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, X2!47), X1) = V!46)))),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[55, 49, 48])).
% 0.84/1.01 tff(57,plain,
% 0.84/1.01 (((~![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))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(58,plain,
% 0.84/1.01 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(U!45)) | (app(U!45, nil) = U!45))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(59,plain,
% 0.84/1.01 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(U!45)) | (app(U!45, nil) = U!45)),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.84/1.01 tff(60,plain,
% 0.84/1.01 (app(U!45, nil) = U!45),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[59, 26, 44])).
% 0.84/1.01 tff(61,plain,
% 0.84/1.01 (ssList(nil) <=> ssList(nil)),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(62,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.84/1.01 tff(63,plain,
% 0.84/1.01 (ssList(nil)),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.84/1.01 tff(64,plain,
% 0.84/1.01 (((~![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, X2!47), X1) = V!46)))) | ((~ssList(nil)) | (~(app(U!45, nil) = U!45)) | (~(app(app(U!45, X2!47), nil) = V!46)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, X2!47), X1) = V!46)))) | (~ssList(nil)) | (~(app(U!45, nil) = U!45)) | (~(app(app(U!45, X2!47), nil) = V!46)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(65,plain,
% 0.84/1.01 ((~![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, X2!47), X1) = V!46)))) | ((~ssList(nil)) | (~(app(U!45, nil) = U!45)) | (~(app(app(U!45, X2!47), nil) = V!46)))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(66,plain,
% 0.84/1.02 ((~![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, X2!47), X1) = V!46)))) | (~ssList(nil)) | (~(app(U!45, nil) = U!45)) | (~(app(app(U!45, X2!47), nil) = V!46))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.84/1.02 tff(67,plain,
% 0.84/1.02 (~(app(app(U!45, X2!47), nil) = V!46)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[66, 63, 60, 56])).
% 0.84/1.02 tff(68,plain,
% 0.84/1.02 ($false),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[67, 33])).
% 0.84/1.02 % SZS output end Proof
% 0.84/1.02 % E exiting
%------------------------------------------------------------------------------