%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC241+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:30:38 AM UTC 2025
% Result : Theorem 31.84s 32.01s
% Output : Proof 31.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWC241+1 : TPTP v9.0.0. Released v2.4.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n013.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 08:43:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 31.84/32.01 % SZS status Theorem
% 31.84/32.01 % SZS output start Proof
% 31.84/32.01 tff(lt_type, type, (
% 31.84/32.01 lt: ( $i * $i ) > $o)).
% 31.84/32.01 tff(tptp_fun_X2_50_type, type, (
% 31.84/32.01 tptp_fun_X2_50: ( $i * $i * $i ) > $i)).
% 31.84/32.01 tff(tptp_fun_X3_47_type, type, (
% 31.84/32.01 tptp_fun_X3_47: $i)).
% 31.84/32.01 tff(tptp_fun_X4_48_type, type, (
% 31.84/32.01 tptp_fun_X4_48: $i)).
% 31.84/32.01 tff(tptp_fun_X5_49_type, type, (
% 31.84/32.01 tptp_fun_X5_49: $i)).
% 31.84/32.01 tff(leq_type, type, (
% 31.84/32.01 leq: ( $i * $i ) > $o)).
% 31.84/32.01 tff(ssItem_type, type, (
% 31.84/32.01 ssItem: $i > $o)).
% 31.84/32.01 tff(memberP_type, type, (
% 31.84/32.01 memberP: ( $i * $i ) > $o)).
% 31.84/32.01 tff(tptp_fun_U_45_type, type, (
% 31.84/32.01 tptp_fun_U_45: $i)).
% 31.84/32.01 tff(app_type, type, (
% 31.84/32.01 app: ( $i * $i ) > $i)).
% 31.84/32.01 tff(cons_type, type, (
% 31.84/32.01 cons: ( $i * $i ) > $i)).
% 31.84/32.01 tff(nil_type, type, (
% 31.84/32.01 nil: $i)).
% 31.84/32.01 tff(ssList_type, type, (
% 31.84/32.01 ssList: $i > $o)).
% 31.84/32.01 tff(tptp_fun_V_46_type, type, (
% 31.84/32.01 tptp_fun_V_46: $i)).
% 31.84/32.01 tff(1,plain,
% 31.84/32.01 (^[Y: $i] : refl(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y)))))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y)))))))))),
% 31.84/32.01 inference(bind,[status(th)],[])).
% 31.84/32.01 tff(2,plain,
% 31.84/32.01 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y)))))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y))))))))),
% 31.84/32.01 inference(quant_intro,[status(thm)],[1])).
% 31.84/32.01 tff(3,plain,
% 31.84/32.01 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y)))))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y)))))))))),
% 31.84/32.01 inference(bind,[status(th)],[])).
% 31.84/32.01 tff(4,plain,
% 31.84/32.01 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y)))))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y))))))))),
% 31.84/32.01 inference(quant_intro,[status(thm)],[3])).
% 31.84/32.01 tff(5,plain,
% 31.84/32.01 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y)))))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y))))))))),
% 31.84/32.01 inference(transitivity,[status(thm)],[4, 2])).
% 31.84/32.01 tff(6,plain,
% 31.84/32.01 ((ssList(U!45) & ((~(nil = U!45)) & ssList(V!46) & ssList(U!45) & ((nil = U!45) | (ssItem(X3!47) & ssList(X4!48) & (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y)))))))))) <=> (ssList(U!45) & (~(nil = U!45)) & ssList(V!46) & ((nil = U!45) | (ssItem(X3!47) & ssList(X4!48) & (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y)))))))))),
% 31.84/32.01 inference(rewrite,[status(thm)],[])).
% 31.84/32.01 tff(7,plain,
% 31.84/32.01 (((~(nil = U!45)) & ssList(V!46) & ssList(U!45) & ((nil = U!45) | (ssItem(X3!47) & (ssList(X4!48) & ((app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))))))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y))))))))) <=> ((~(nil = U!45)) & ssList(V!46) & ssList(U!45) & ((nil = U!45) | (ssItem(X3!47) & ssList(X4!48) & (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y)))))))))),
% 31.84/32.01 inference(rewrite,[status(thm)],[])).
% 31.84/32.01 tff(8,plain,
% 31.84/32.01 ((ssList(U!45) & ((~(nil = U!45)) & ssList(V!46) & ssList(U!45) & ((nil = U!45) | (ssItem(X3!47) & (ssList(X4!48) & ((app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))))))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y)))))))))) <=> (ssList(U!45) & ((~(nil = U!45)) & ssList(V!46) & ssList(U!45) & ((nil = U!45) | (ssItem(X3!47) & ssList(X4!48) & (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y))))))))))),
% 31.84/32.01 inference(monotonicity,[status(thm)],[7])).
% 31.84/32.01 tff(9,plain,
% 31.84/32.01 ((ssList(U!45) & ((~(nil = U!45)) & ssList(V!46) & ssList(U!45) & ((nil = U!45) | (ssItem(X3!47) & (ssList(X4!48) & ((app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))))))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y)))))))))) <=> (ssList(U!45) & (~(nil = U!45)) & ssList(V!46) & ((nil = U!45) | (ssItem(X3!47) & ssList(X4!48) & (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y)))))))))),
% 31.84/32.01 inference(transitivity,[status(thm)],[8, 6])).
% 31.84/32.01 tff(10,plain,
% 31.84/32.01 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (~ssList(V)) | (~ssList(U)) | ((~(nil = U)) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ?[X6: $i] : (ssItem(X6) & (~leq(X6, X3)) & memberP(X4, X6) & memberP(X5, X6) & leq(X3, X6)))))) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U) & ![X2: $i] : (leq(Y, X2) | (~memberP(Z, X2)) | (~memberP(X1, X2)) | (~lt(Y, X2)) | (~ssItem(X2))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (~ssList(V)) | (~ssList(U)) | ((~(nil = U)) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ?[X6: $i] : (ssItem(X6) & (~leq(X6, X3)) & memberP(X4, X6) & memberP(X5, X6) & leq(X3, X6)))))) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U) & ![X2: $i] : (leq(Y, X2) | (~memberP(Z, X2)) | (~memberP(X1, X2)) | (~lt(Y, X2)) | (~ssItem(X2)))))))))),
% 31.84/32.01 inference(rewrite,[status(thm)],[])).
% 31.84/32.01 tff(11,plain,
% 31.84/32.01 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : ((((((~ssList(X)) | (~(V = X))) | (~(U = W))) | (nil = U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U)) & ![X2: $i] : (((((~ssItem(X2)) | (~memberP(Z, X2))) | (~memberP(X1, X2))) | (~lt(Y, X2))) | leq(Y, X2)))))) | ((~(nil = W)) & ![X3: $i] : (ssItem(X3) => ![X4: $i] : (ssList(X4) => ![X5: $i] : (((~ssList(X5)) | (~(app(app(X4, cons(X3, nil)), X5) = W))) | ?[X6: $i] : ((((ssItem(X6) & (~leq(X6, X3))) & memberP(X4, X6)) & memberP(X5, X6)) & leq(X3, X6))))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (~ssList(V)) | (~ssList(U)) | ((~(nil = U)) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ?[X6: $i] : (ssItem(X6) & (~leq(X6, X3)) & memberP(X4, X6) & memberP(X5, X6) & leq(X3, X6)))))) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U) & ![X2: $i] : (leq(Y, X2) | (~memberP(Z, X2)) | (~memberP(X1, X2)) | (~lt(Y, X2)) | (~ssItem(X2)))))))))),
% 31.84/32.01 inference(rewrite,[status(thm)],[])).
% 31.84/32.01 tff(12,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : ((((((~ssList(X)) | (~(V = X))) | (~(U = W))) | (nil = U)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U)) & ![X2: $i] : (((((~ssItem(X2)) | (~memberP(Z, X2))) | (~memberP(X1, X2))) | (~lt(Y, X2))) | leq(Y, X2)))))) | ((~(nil = W)) & ![X3: $i] : (ssItem(X3) => ![X4: $i] : (ssList(X4) => ![X5: $i] : (((~ssList(X5)) | (~(app(app(X4, cons(X3, nil)), X5) = W))) | ?[X6: $i] : ((((ssItem(X6) & (~leq(X6, X3))) & memberP(X4, X6)) & memberP(X5, X6)) & leq(X3, X6))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 31.84/32.01 tff(13,plain,
% 31.84/32.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (~ssList(V)) | (~ssList(U)) | ((~(nil = U)) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ?[X6: $i] : (ssItem(X6) & (~leq(X6, X3)) & memberP(X4, X6) & memberP(X5, X6) & leq(X3, X6)))))) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U) & ![X2: $i] : (leq(Y, X2) | (~memberP(Z, X2)) | (~memberP(X1, X2)) | (~lt(Y, X2)) | (~ssItem(X2))))))))),
% 31.84/32.01 inference(modus_ponens,[status(thm)],[12, 11])).
% 31.84/32.01 tff(14,plain,
% 31.84/32.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (~ssList(V)) | (~ssList(U)) | ((~(nil = U)) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ?[X6: $i] : (ssItem(X6) & (~leq(X6, X3)) & memberP(X4, X6) & memberP(X5, X6) & leq(X3, X6)))))) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U) & ![X2: $i] : (leq(Y, X2) | (~memberP(Z, X2)) | (~memberP(X1, X2)) | (~lt(Y, X2)) | (~ssItem(X2))))))))),
% 31.84/32.01 inference(modus_ponens,[status(thm)],[13, 10])).
% 31.84/32.01 tff(15,plain,
% 31.84/32.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (~ssList(V)) | (~ssList(U)) | ((~(nil = U)) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ?[X6: $i] : (ssItem(X6) & (~leq(X6, X3)) & memberP(X4, X6) & memberP(X5, X6) & leq(X3, X6)))))) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U) & ![X2: $i] : (leq(Y, X2) | (~memberP(Z, X2)) | (~memberP(X1, X2)) | (~lt(Y, X2)) | (~ssItem(X2))))))))),
% 31.84/32.01 inference(modus_ponens,[status(thm)],[14, 10])).
% 31.84/32.01 tff(16,plain,
% 31.84/32.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (~ssList(V)) | (~ssList(U)) | ((~(nil = U)) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ?[X6: $i] : (ssItem(X6) & (~leq(X6, X3)) & memberP(X4, X6) & memberP(X5, X6) & leq(X3, X6)))))) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = U) & ![X2: $i] : (leq(Y, X2) | (~memberP(Z, X2)) | (~memberP(X1, X2)) | (~lt(Y, X2)) | (~ssItem(X2))))))))),
% 31.84/32.01 inference(modus_ponens,[status(thm)],[15, 10])).
% 31.84/32.01 tff(17,plain,
% 31.84/32.01 (ssList(U!45) & (~(nil = U!45)) & ssList(V!46) & ((nil = U!45) | (ssItem(X3!47) & ssList(X4!48) & (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y))))))))),
% 31.84/32.01 inference(modus_ponens,[status(thm)],[16, 9])).
% 31.84/32.01 tff(18,plain,
% 31.84/32.01 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y))))))))),
% 31.84/32.01 inference(and_elim,[status(thm)],[17])).
% 31.84/32.01 tff(19,plain,
% 31.84/32.01 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y))))))))),
% 31.84/32.01 inference(modus_ponens,[status(thm)],[18, 5])).
% 31.84/32.01 tff(20,plain,
% 31.84/32.01 (~(nil = U!45)),
% 31.84/32.01 inference(and_elim,[status(thm)],[17])).
% 31.84/32.01 tff(21,plain,
% 31.84/32.01 (((nil = U!45) | (~((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6))))))) <=> ((nil = U!45) | (~((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6)))))))),
% 31.84/32.01 inference(rewrite,[status(thm)],[])).
% 31.84/32.01 tff(22,plain,
% 31.84/32.01 (((nil = U!45) | (~((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6))))))) <=> ((nil = U!45) | (~((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6)))))))),
% 31.84/32.01 inference(rewrite,[status(thm)],[])).
% 31.84/32.01 tff(23,plain,
% 31.84/32.01 ((ssItem(X3!47) & ssList(X4!48) & (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6)))) <=> (~((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6))))))),
% 31.84/32.01 inference(rewrite,[status(thm)],[])).
% 31.84/32.01 tff(24,plain,
% 31.84/32.01 (^[X6: $i] : trans(monotonicity(rewrite((ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6)) <=> (~((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6))))), ((~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))) <=> (~(~((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6))))))), rewrite((~(~((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6))))) <=> ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6)))), ((~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))) <=> ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6)))))),
% 31.84/32.01 inference(bind,[status(th)],[])).
% 31.84/32.01 tff(25,plain,
% 31.84/32.01 (![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))) <=> ![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6)))),
% 31.84/32.01 inference(quant_intro,[status(thm)],[24])).
% 31.84/32.01 tff(26,plain,
% 31.84/32.01 ((ssItem(X3!47) & ssList(X4!48) & (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6)))) <=> (ssItem(X3!47) & ssList(X4!48) & (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6))))),
% 31.84/32.01 inference(monotonicity,[status(thm)],[25])).
% 31.84/32.01 tff(27,plain,
% 31.84/32.01 ((ssItem(X3!47) & ssList(X4!48) & (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6)))) <=> (~((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6))))))),
% 31.84/32.01 inference(transitivity,[status(thm)],[26, 23])).
% 31.84/32.01 tff(28,plain,
% 31.84/32.01 (((nil = U!45) | (ssItem(X3!47) & ssList(X4!48) & (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))))) <=> ((nil = U!45) | (~((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6)))))))),
% 31.84/32.01 inference(monotonicity,[status(thm)],[27])).
% 31.84/32.01 tff(29,plain,
% 31.84/32.01 (((nil = U!45) | (ssItem(X3!47) & ssList(X4!48) & (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))))) <=> ((nil = U!45) | (~((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6)))))))),
% 31.84/32.01 inference(transitivity,[status(thm)],[28, 22])).
% 31.84/32.01 tff(30,plain,
% 31.84/32.01 ((nil = U!45) | (ssItem(X3!47) & ssList(X4!48) & (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45) & ssList(X5!49) & ![X6: $i] : (~(ssItem(X6) & (~leq(X6, X3!47)) & memberP(X4!48, X6) & memberP(X5!49, X6) & leq(X3!47, X6))))),
% 31.84/32.01 inference(and_elim,[status(thm)],[17])).
% 31.84/32.01 tff(31,plain,
% 31.84/32.01 ((nil = U!45) | (~((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6))))))),
% 31.84/32.01 inference(modus_ponens,[status(thm)],[30, 29])).
% 31.84/32.01 tff(32,plain,
% 31.84/32.01 ((nil = U!45) | (~((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6))))))),
% 31.84/32.01 inference(modus_ponens,[status(thm)],[31, 21])).
% 31.84/32.01 tff(33,plain,
% 31.84/32.01 (~((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6)))))),
% 31.84/32.01 inference(unit_resolution,[status(thm)],[32, 20])).
% 31.84/32.01 tff(34,plain,
% 31.84/32.01 (((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6))))) | ssItem(X3!47)),
% 31.84/32.01 inference(tautology,[status(thm)],[])).
% 31.84/32.01 tff(35,plain,
% 31.84/32.01 (ssItem(X3!47)),
% 31.84/32.01 inference(unit_resolution,[status(thm)],[34, 33])).
% 31.84/32.01 tff(36,plain,
% 31.84/32.01 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y))))))))) | ((~ssItem(X3!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, Z, X3!47))))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y))))))))) | (~ssItem(X3!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, Z, X3!47))))))))),
% 31.84/32.01 inference(rewrite,[status(thm)],[])).
% 31.84/32.01 tff(37,plain,
% 31.84/32.01 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y))))))))) | ((~ssItem(X3!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, Z, X3!47))))))))),
% 31.84/32.01 inference(quant_inst,[status(thm)],[])).
% 31.84/32.01 tff(38,plain,
% 31.84/32.01 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U!45)) | (~(leq(Y, tptp_fun_X2_50(X1, Z, Y)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, Y))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, Y))) | (~lt(Y, tptp_fun_X2_50(X1, Z, Y))) | (~ssItem(tptp_fun_X2_50(X1, Z, Y))))))))) | (~ssItem(X3!47)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, Z, X3!47)))))))),
% 31.84/32.01 inference(modus_ponens,[status(thm)],[37, 36])).
% 31.84/32.01 tff(39,plain,
% 31.84/32.01 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, Z, X3!47)))))))),
% 31.84/32.01 inference(unit_resolution,[status(thm)],[38, 35, 19])).
% 31.84/32.01 tff(40,plain,
% 31.84/32.01 (((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6))))) | ssList(X4!48)),
% 31.84/32.01 inference(tautology,[status(thm)],[])).
% 31.84/32.01 tff(41,plain,
% 31.84/32.01 (ssList(X4!48)),
% 31.84/32.01 inference(unit_resolution,[status(thm)],[40, 33])).
% 31.84/32.01 tff(42,plain,
% 31.84/32.01 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, Z, X3!47)))))))) | ((~ssList(X4!48)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!48, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, X4!48, X3!47)))))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, Z, X3!47)))))))) | (~ssList(X4!48)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!48, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, X4!48, X3!47)))))))),
% 31.84/32.01 inference(rewrite,[status(thm)],[])).
% 31.84/32.01 tff(43,plain,
% 31.84/32.01 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, Z, X3!47)))))))) | ((~ssList(X4!48)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!48, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, X4!48, X3!47)))))))),
% 31.84/32.02 inference(quant_inst,[status(thm)],[])).
% 31.84/32.02 tff(44,plain,
% 31.84/32.02 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, Z, X3!47)) | (~memberP(Z, tptp_fun_X2_50(X1, Z, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, Z, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, Z, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, Z, X3!47)))))))) | (~ssList(X4!48)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!48, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, X4!48, X3!47))))))),
% 31.84/32.02 inference(modus_ponens,[status(thm)],[43, 42])).
% 31.84/32.02 tff(45,plain,
% 31.84/32.02 (![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!48, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, X4!48, X3!47))))))),
% 31.84/32.02 inference(unit_resolution,[status(thm)],[44, 41, 39])).
% 31.84/32.02 tff(46,plain,
% 31.84/32.02 (((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6))))) | (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)),
% 31.84/32.02 inference(tautology,[status(thm)],[])).
% 31.84/32.02 tff(47,plain,
% 31.84/32.02 (app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45),
% 31.84/32.02 inference(unit_resolution,[status(thm)],[46, 33])).
% 31.84/32.02 tff(48,plain,
% 31.84/32.02 (((~ssItem(X3!47)) | (~ssList(X4!48)) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~![X6: $i] : ((~ssItem(X6)) | leq(X6, X3!47) | (~memberP(X4!48, X6)) | (~memberP(X5!49, X6)) | (~leq(X3!47, X6))))) | ssList(X5!49)),
% 31.84/32.02 inference(tautology,[status(thm)],[])).
% 31.84/32.02 tff(49,plain,
% 31.84/32.02 (ssList(X5!49)),
% 31.84/32.02 inference(unit_resolution,[status(thm)],[48, 33])).
% 31.84/32.02 tff(50,plain,
% 31.84/32.02 (((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!48, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, X4!48, X3!47))))))) | ((~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~((~memberP(X4!48, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)) | (~memberP(X5!49, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47))))))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!48, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, X4!48, X3!47))))))) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~((~memberP(X4!48, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)) | (~memberP(X5!49, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47))))))),
% 31.84/32.02 inference(rewrite,[status(thm)],[])).
% 31.84/32.02 tff(51,plain,
% 31.84/32.02 (((~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~memberP(X5!49, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47)))))) <=> ((~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~((~memberP(X4!48, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)) | (~memberP(X5!49, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47))))))),
% 31.84/32.02 inference(rewrite,[status(thm)],[])).
% 31.84/32.02 tff(52,plain,
% 31.84/32.02 (((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!48, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, X4!48, X3!47))))))) | ((~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~memberP(X5!49, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47))))))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!48, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, X4!48, X3!47))))))) | ((~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~((~memberP(X4!48, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)) | (~memberP(X5!49, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47)))))))),
% 31.84/32.02 inference(monotonicity,[status(thm)],[51])).
% 31.84/32.02 tff(53,plain,
% 31.84/32.02 (((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!48, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, X4!48, X3!47))))))) | ((~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~memberP(X5!49, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47))))))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!48, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, X4!48, X3!47))))))) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~((~memberP(X4!48, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)) | (~memberP(X5!49, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47))))))),
% 31.84/32.02 inference(transitivity,[status(thm)],[52, 50])).
% 31.84/32.02 tff(54,plain,
% 31.84/32.02 ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!48, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, X4!48, X3!47))))))) | ((~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~memberP(X5!49, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47))))))),
% 31.84/32.02 inference(quant_inst,[status(thm)],[])).
% 31.84/32.02 tff(55,plain,
% 31.84/32.02 ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!48, cons(X3!47, nil)), X1) = U!45)) | (~(leq(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47)) | (~memberP(X4!48, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~memberP(X1, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X1, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X1, X4!48, X3!47))))))) | (~ssList(X5!49)) | (~(app(app(X4!48, cons(X3!47, nil)), X5!49) = U!45)) | (~((~memberP(X4!48, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)) | (~memberP(X5!49, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47)))))),
% 31.84/32.02 inference(modus_ponens,[status(thm)],[54, 53])).
% 31.84/32.02 tff(56,plain,
% 31.84/32.02 (~((~memberP(X4!48, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)) | (~memberP(X5!49, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47))))),
% 31.84/32.02 inference(unit_resolution,[status(thm)],[55, 49, 47, 45])).
% 31.84/32.02 tff(57,plain,
% 31.84/32.02 (((~memberP(X4!48, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)) | (~memberP(X5!49, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47)))) | (~leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)))),
% 31.84/32.02 inference(tautology,[status(thm)],[])).
% 31.84/32.02 tff(58,plain,
% 31.84/32.02 (~leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))),
% 31.84/32.02 inference(unit_resolution,[status(thm)],[57, 56])).
% 31.84/32.02 tff(59,plain,
% 31.84/32.02 (((~leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (X3!47 = tptp_fun_X2_50(X5!49, X4!48, X3!47))) | leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))),
% 31.84/32.02 inference(tautology,[status(thm)],[])).
% 31.84/32.02 tff(60,plain,
% 31.84/32.02 ((~leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (X3!47 = tptp_fun_X2_50(X5!49, X4!48, X3!47))),
% 31.84/32.02 inference(unit_resolution,[status(thm)],[59, 58])).
% 31.84/32.02 tff(61,plain,
% 31.84/32.02 (((~memberP(X4!48, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)) | (~memberP(X5!49, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47)))) | lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))),
% 31.84/32.02 inference(tautology,[status(thm)],[])).
% 31.84/32.02 tff(62,plain,
% 31.84/32.02 (lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))),
% 31.84/32.02 inference(unit_resolution,[status(thm)],[61, 56])).
% 31.84/32.02 tff(63,plain,
% 31.84/32.02 ((((~leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (X3!47 = tptp_fun_X2_50(X5!49, X4!48, X3!47))) <=> lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~((~leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (X3!47 = tptp_fun_X2_50(X5!49, X4!48, X3!47)))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)))),
% 31.84/32.02 inference(tautology,[status(thm)],[])).
% 31.84/32.02 tff(64,plain,
% 31.84/32.02 (((~leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (X3!47 = tptp_fun_X2_50(X5!49, X4!48, X3!47))) <=> lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))),
% 31.84/32.02 inference(unit_resolution,[status(thm)],[63, 62, 60])).
% 31.84/32.02 tff(65,plain,
% 31.84/32.02 (((~memberP(X4!48, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)) | (~memberP(X5!49, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47)))) | ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47))),
% 31.84/32.02 inference(tautology,[status(thm)],[])).
% 31.84/32.02 tff(66,plain,
% 31.84/32.02 (ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47))),
% 31.84/32.02 inference(unit_resolution,[status(thm)],[65, 56])).
% 31.84/32.02 tff(67,plain,
% 31.84/32.02 (^[U: $i] : refl(((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V))))))),
% 31.84/32.02 inference(bind,[status(th)],[])).
% 31.84/32.02 tff(68,plain,
% 31.84/32.02 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V)))))),
% 31.84/32.02 inference(quant_intro,[status(thm)],[67])).
% 31.84/32.02 tff(69,plain,
% 31.84/32.02 (^[U: $i] : rewrite(((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V))))))),
% 31.84/32.02 inference(bind,[status(th)],[])).
% 31.84/32.02 tff(70,plain,
% 31.84/32.02 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V)))))),
% 31.84/32.02 inference(quant_intro,[status(thm)],[69])).
% 31.84/32.02 tff(71,plain,
% 31.84/32.02 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V)))))),
% 31.84/32.02 inference(transitivity,[status(thm)],[70, 68])).
% 31.84/32.02 tff(72,plain,
% 31.84/32.02 (^[U: $i] : rewrite(((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (lt(U, V) <=> ((~(U = V)) & leq(U, V))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V))))))),
% 31.84/32.02 inference(bind,[status(th)],[])).
% 31.84/32.02 tff(73,plain,
% 31.84/32.02 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (lt(U, V) <=> ((~(U = V)) & leq(U, V))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V)))))),
% 31.84/32.02 inference(quant_intro,[status(thm)],[72])).
% 31.84/32.02 tff(74,plain,
% 31.84/32.02 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (lt(U, V) <=> ((~(U = V)) & leq(U, V))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (lt(U, V) <=> ((~(U = V)) & leq(U, V)))))),
% 31.84/32.02 inference(rewrite,[status(thm)],[])).
% 31.84/32.02 tff(75,plain,
% 31.84/32.02 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (lt(U, V) <=> ((~(U = V)) & leq(U, V)))) <=> ((~ssItem(V)) | (lt(U, V) <=> ((~(U = V)) & leq(U, V)))))), (![V: $i] : (ssItem(V) => (lt(U, V) <=> ((~(U = V)) & leq(U, V)))) <=> ![V: $i] : ((~ssItem(V)) | (lt(U, V) <=> ((~(U = V)) & leq(U, V)))))), ((ssItem(U) => ![V: $i] : (ssItem(V) => (lt(U, V) <=> ((~(U = V)) & leq(U, V))))) <=> (ssItem(U) => ![V: $i] : ((~ssItem(V)) | (lt(U, V) <=> ((~(U = V)) & leq(U, V))))))), rewrite((ssItem(U) => ![V: $i] : ((~ssItem(V)) | (lt(U, V) <=> ((~(U = V)) & leq(U, V))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (lt(U, V) <=> ((~(U = V)) & leq(U, V)))))), ((ssItem(U) => ![V: $i] : (ssItem(V) => (lt(U, V) <=> ((~(U = V)) & leq(U, V))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (lt(U, V) <=> ((~(U = V)) & leq(U, V)))))))),
% 31.84/32.02 inference(bind,[status(th)],[])).
% 31.84/32.02 tff(76,plain,
% 31.84/32.02 (![U: $i] : (ssItem(U) => ![V: $i] : (ssItem(V) => (lt(U, V) <=> ((~(U = V)) & leq(U, V))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (lt(U, V) <=> ((~(U = V)) & leq(U, V)))))),
% 31.84/32.02 inference(quant_intro,[status(thm)],[75])).
% 31.84/32.02 tff(77,axiom,(![U: $i] : (ssItem(U) => ![V: $i] : (ssItem(V) => (lt(U, V) <=> ((~(U = V)) & leq(U, V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax93')).
% 31.84/32.02 tff(78,plain,
% 31.84/32.02 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (lt(U, V) <=> ((~(U = V)) & leq(U, V)))))),
% 31.84/32.02 inference(modus_ponens,[status(thm)],[77, 76])).
% 31.84/32.02 tff(79,plain,
% 31.84/32.02 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (lt(U, V) <=> ((~(U = V)) & leq(U, V)))))),
% 31.84/32.02 inference(modus_ponens,[status(thm)],[78, 74])).
% 31.84/32.02 tff(80,plain,(
% 31.84/32.02 ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (lt(U, V) <=> ((~(U = V)) & leq(U, V)))))),
% 31.84/32.02 inference(skolemize,[status(sab)],[79])).
% 31.84/32.02 tff(81,plain,
% 31.84/32.02 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V)))))),
% 31.84/32.02 inference(modus_ponens,[status(thm)],[80, 73])).
% 31.84/32.02 tff(82,plain,
% 31.84/32.02 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V)))))),
% 31.96/32.11 inference(modus_ponens,[status(thm)],[81, 71])).
% 31.96/32.11 tff(83,plain,
% 31.96/32.11 (((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V)))))) | ((~ssItem(X3!47)) | ![V: $i] : ((~ssItem(V)) | (~(((~leq(X3!47, V)) | (X3!47 = V)) <=> lt(X3!47, V)))))) <=> ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V)))))) | (~ssItem(X3!47)) | ![V: $i] : ((~ssItem(V)) | (~(((~leq(X3!47, V)) | (X3!47 = V)) <=> lt(X3!47, V)))))),
% 31.96/32.11 inference(rewrite,[status(thm)],[])).
% 31.96/32.11 tff(84,plain,
% 31.96/32.11 (((~ssItem(X3!47)) | ![V: $i] : ((~ssItem(V)) | (~(((X3!47 = V) | (~leq(X3!47, V))) <=> lt(X3!47, V))))) <=> ((~ssItem(X3!47)) | ![V: $i] : ((~ssItem(V)) | (~(((~leq(X3!47, V)) | (X3!47 = V)) <=> lt(X3!47, V)))))),
% 31.96/32.11 inference(rewrite,[status(thm)],[])).
% 31.96/32.11 tff(85,plain,
% 31.96/32.11 (((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V)))))) | ((~ssItem(X3!47)) | ![V: $i] : ((~ssItem(V)) | (~(((X3!47 = V) | (~leq(X3!47, V))) <=> lt(X3!47, V)))))) <=> ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V)))))) | ((~ssItem(X3!47)) | ![V: $i] : ((~ssItem(V)) | (~(((~leq(X3!47, V)) | (X3!47 = V)) <=> lt(X3!47, V))))))),
% 31.96/32.11 inference(monotonicity,[status(thm)],[84])).
% 31.96/32.11 tff(86,plain,
% 31.96/32.11 (((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V)))))) | ((~ssItem(X3!47)) | ![V: $i] : ((~ssItem(V)) | (~(((X3!47 = V) | (~leq(X3!47, V))) <=> lt(X3!47, V)))))) <=> ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V)))))) | (~ssItem(X3!47)) | ![V: $i] : ((~ssItem(V)) | (~(((~leq(X3!47, V)) | (X3!47 = V)) <=> lt(X3!47, V)))))),
% 31.96/32.11 inference(transitivity,[status(thm)],[85, 83])).
% 31.96/32.11 tff(87,plain,
% 31.96/32.11 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V)))))) | ((~ssItem(X3!47)) | ![V: $i] : ((~ssItem(V)) | (~(((X3!47 = V) | (~leq(X3!47, V))) <=> lt(X3!47, V)))))),
% 31.96/32.11 inference(quant_inst,[status(thm)],[])).
% 31.96/32.11 tff(88,plain,
% 31.96/32.11 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | (~(((U = V) | (~leq(U, V))) <=> lt(U, V)))))) | (~ssItem(X3!47)) | ![V: $i] : ((~ssItem(V)) | (~(((~leq(X3!47, V)) | (X3!47 = V)) <=> lt(X3!47, V))))),
% 31.96/32.11 inference(modus_ponens,[status(thm)],[87, 86])).
% 31.96/32.11 tff(89,plain,
% 31.96/32.11 (![V: $i] : ((~ssItem(V)) | (~(((~leq(X3!47, V)) | (X3!47 = V)) <=> lt(X3!47, V))))),
% 31.96/32.11 inference(unit_resolution,[status(thm)],[88, 82, 35])).
% 31.96/32.11 tff(90,plain,
% 31.96/32.11 (((~![V: $i] : ((~ssItem(V)) | (~(((~leq(X3!47, V)) | (X3!47 = V)) <=> lt(X3!47, V))))) | ((~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~(((~leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (X3!47 = tptp_fun_X2_50(X5!49, X4!48, X3!47))) <=> lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)))))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(((~leq(X3!47, V)) | (X3!47 = V)) <=> lt(X3!47, V))))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~(((~leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (X3!47 = tptp_fun_X2_50(X5!49, X4!48, X3!47))) <=> lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)))))),
% 31.96/32.11 inference(rewrite,[status(thm)],[])).
% 31.96/32.11 tff(91,plain,
% 31.96/32.11 ((~![V: $i] : ((~ssItem(V)) | (~(((~leq(X3!47, V)) | (X3!47 = V)) <=> lt(X3!47, V))))) | ((~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~(((~leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (X3!47 = tptp_fun_X2_50(X5!49, X4!48, X3!47))) <=> lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47)))))),
% 31.96/32.11 inference(quant_inst,[status(thm)],[])).
% 31.96/32.11 tff(92,plain,
% 31.96/32.11 ((~![V: $i] : ((~ssItem(V)) | (~(((~leq(X3!47, V)) | (X3!47 = V)) <=> lt(X3!47, V))))) | (~ssItem(tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (~(((~leq(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))) | (X3!47 = tptp_fun_X2_50(X5!49, X4!48, X3!47))) <=> lt(X3!47, tptp_fun_X2_50(X5!49, X4!48, X3!47))))),
% 31.96/32.11 inference(modus_ponens,[status(thm)],[91, 90])).
% 31.96/32.11 tff(93,plain,
% 31.96/32.11 ($false),
% 31.96/32.11 inference(unit_resolution,[status(thm)],[92, 89, 66, 64])).
% 31.96/32.11 % SZS output end Proof
% 31.96/32.11 % E exiting
%------------------------------------------------------------------------------