%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL778-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:02:59 PM UTC 2026
% Result : Unsatisfiable 21.17s 8.14s
% Output : Proof 21.17s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t207,axiom,
sF1 = hBOOL(hAPP(c_InductTermi_OIT,v_s)),
introduced(definition) ).
cnf(t206,axiom,
sF0 = hAPP(c_InductTermi_OIT,v_s),
introduced(definition) ).
cnf(t237,plain,
hAPP(c_InductTermi_OIT,v_s) = sF0,
inference(orient,[status(thm)],[t206]) ).
cnf(t3735,plain,
sF1 = hBOOL(sF0),
inference(step,[status(thm)],[t207,t237]) ).
cnf(f517,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f517_nnf,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
inference(nnf_transformation,[status(thm)],[f517]) ).
cnf(c517,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
inference(cnf_transformation,[status(esa)],[f517_nnf]) ).
cnf(t9,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_s)) = true,
inference(equality_encoding,[status(esa)],[c517]) ).
cnf(t3734,plain,
hBOOL(sF0) = true,
inference(step,[status(thm)],[t9,t237]) ).
cnf(t240,plain,
hBOOL(sF0) = true,
inference(orient,[status(thm)],[t3734]) ).
cnf(t3736,plain,
sF1 = true,
inference(step,[status(thm)],[t3735,t240]) ).
cnf(t241,plain,
true = sF1,
inference(orient,[status(thm)],[t3736]) ).
cnf(f516,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f516_nnf,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(nnf_transformation,[status(thm)],[f516]) ).
cnf(c516,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(cnf_transformation,[status(esa)],[f516_nnf]) ).
cnf(t148,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))) = true,
inference(equality_encoding,[status(esa)],[c516]) ).
cnf(t213,axiom,
sF7 = hAPP(c_Lambda_Osubst,v_r),
introduced(definition) ).
cnf(t239,plain,
hAPP(c_Lambda_Osubst,v_r) = sF7,
inference(orient,[status(thm)],[t213]) ).
cnf(t4117,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(sF7,v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))) = true,
inference(step,[status(thm)],[t148,t239]) ).
cnf(t214,axiom,
sF8 = hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),
introduced(definition) ).
cnf(t3747,plain,
sF8 = hAPP(sF7,v_s),
inference(step,[status(thm)],[t214,t239]) ).
cnf(t266,plain,
hAPP(sF7,v_s) = sF8,
inference(orient,[status(thm)],[t3747]) ).
cnf(t4118,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(sF8,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))) = true,
inference(step,[status(thm)],[t4117,t266]) ).
cnf(t215,axiom,
sF9 = c_HOL_Ozero__class_Ozero(tc_nat),
introduced(definition) ).
cnf(t227,plain,
c_HOL_Ozero__class_Ozero(tc_nat) = sF9,
inference(orient,[status(thm)],[t215]) ).
cnf(t4119,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(sF8,sF9),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))) = true,
inference(step,[status(thm)],[t4118,t227]) ).
cnf(t216,axiom,
sF10 = hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),
introduced(definition) ).
cnf(t3765,plain,
sF10 = hAPP(hAPP(sF7,v_s),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(step,[status(thm)],[t216,t239]) ).
cnf(t3766,plain,
sF10 = hAPP(sF8,c_HOL_Ozero__class_Ozero(tc_nat)),
inference(step,[status(thm)],[t3765,t266]) ).
cnf(t3767,plain,
sF10 = hAPP(sF8,sF9),
inference(step,[status(thm)],[t3766,t227]) ).
cnf(t362,plain,
hAPP(sF8,sF9) = sF10,
inference(orient,[status(thm)],[t3767]) ).
cnf(t4120,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,sF10,v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))) = true,
inference(step,[status(thm)],[t4119,t362]) ).
cnf(t217,axiom,
sF11 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),
introduced(definition) ).
cnf(t3863,plain,
sF11 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(sF7,v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),
inference(step,[status(thm)],[t217,t239]) ).
cnf(t3864,plain,
sF11 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(sF8,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),
inference(step,[status(thm)],[t3863,t266]) ).
cnf(t3865,plain,
sF11 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(sF8,sF9),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),
inference(step,[status(thm)],[t3864,t227]) ).
cnf(t3866,plain,
sF11 = c_List_Ofoldl(c_Lambda_OdB_OApp,sF10,v_ss,tc_Lambda_OdB,tc_Lambda_OdB),
inference(step,[status(thm)],[t3865,t362]) ).
cnf(t1112,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,sF10,v_ss,tc_Lambda_OdB,tc_Lambda_OdB) = sF11,
inference(orient,[status(thm)],[t3866]) ).
cnf(t4121,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,sF11),c_Lambda_OdB_OVar(v_i)))) = true,
inference(step,[status(thm)],[t4120,t1112]) ).
cnf(t209,axiom,
sF3 = c_Lambda_OdB_OVar(v_i),
introduced(definition) ).
cnf(t226,plain,
c_Lambda_OdB_OVar(v_i) = sF3,
inference(orient,[status(thm)],[t209]) ).
cnf(t4122,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,sF11),sF3))) = true,
inference(step,[status(thm)],[t4121,t226]) ).
cnf(f519,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f519_nnf,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(nnf_transformation,[status(thm)],[f519]) ).
fof(f519_sk,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(skolemisation,[status(esa)],[f519_nnf]) ).
cnf(c519,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(cnf_transformation,[status(esa)],[f519_sk]) ).
cnf(t147,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))) = false,
inference(equality_encoding,[status(esa)],[c519]) ).
cnf(t4106,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(sF7,v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))) = false,
inference(step,[status(thm)],[t147,t239]) ).
cnf(t4107,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(sF8,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))) = false,
inference(step,[status(thm)],[t4106,t266]) ).
cnf(t4108,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(sF8,sF9),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))) = false,
inference(step,[status(thm)],[t4107,t227]) ).
cnf(t4109,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,sF10,v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))) = false,
inference(step,[status(thm)],[t4108,t362]) ).
cnf(t4110,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,sF11),c_Lambda_OdB_OVar(v_i)))) = false,
inference(step,[status(thm)],[t4109,t1112]) ).
cnf(t4111,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,sF11),sF3))) = false,
inference(step,[status(thm)],[t4110,t226]) ).
cnf(t3467,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,sF11),sF3))) = false,
inference(orient,[status(thm)],[t4111]) ).
cnf(t4123,plain,
false = true,
inference(step,[status(thm)],[t4122,t3467]) ).
cnf(t4124,plain,
false = sF1,
inference(step,[status(thm)],[t4123,t241]) ).
cnf(t3496,plain,
false = sF1,
inference(orient,[status(thm)],[t4124]) ).
cnf(f30,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f30_nnf,plain,
! [T_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [T_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(f62,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f62_nnf,plain,
! [T_a] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(nnf_transformation,[status(thm)],[f62]) ).
fof(f62_sk,plain,
! [T_a] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(skolemisation,[status(esa)],[f62_nnf]) ).
cnf(c62,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
cnf(f89,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
fof(f89_nnf,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f89]) ).
fof(f89_sk,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f89_nnf]) ).
cnf(c89,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ c_lessequals(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f89_sk]) ).
cnf(f91,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
fof(f91_nnf,plain,
! [T_a,V_x,V_y] :
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f91]) ).
fof(f91_sk,plain,
! [T_a,V_x,V_y] :
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f91_nnf]) ).
cnf(c91,plain,
( ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f91_sk]) ).
cnf(f93,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f93_nnf,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f93]) ).
fof(f93_sk,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f93_nnf]) ).
cnf(c93,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f93_sk]) ).
cnf(f95,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f95_nnf,plain,
! [T_a,V_y,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f95]) ).
fof(f95_sk,plain,
! [T_a,V_y,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemisation,[status(esa)],[f95_nnf]) ).
cnf(c95,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(f97,axiom,
( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f97_nnf,plain,
! [T_a] :
( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(nnf_transformation,[status(thm)],[f97]) ).
fof(f97_sk,plain,
! [T_a] :
( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(skolemisation,[status(esa)],[f97_nnf]) ).
cnf(c97,plain,
( c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(esa)],[f97_sk]) ).
cnf(f98,axiom,
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f98_nnf,plain,
! [T_a] :
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(nnf_transformation,[status(thm)],[f98]) ).
fof(f98_sk,plain,
! [T_a] :
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(skolemisation,[status(esa)],[f98_nnf]) ).
cnf(c98,plain,
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(esa)],[f98_sk]) ).
cnf(f211,axiom,
~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
fof(f211_nnf,plain,
! [V_r,T_a,V_xs] : ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a),
inference(nnf_transformation,[status(thm)],[f211]) ).
fof(f211_sk,plain,
! [V_r,T_a,V_xs] : ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a),
inference(skolemisation,[status(esa)],[f211_nnf]) ).
cnf(c211,plain,
~ c_ListOrder_Ostep1(X0,c_List_Olist_ONil(X1),X2,X1),
inference(cnf_transformation,[status(esa)],[f211_sk]) ).
cnf(f212,axiom,
~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
fof(f212_nnf,plain,
! [V_r,V_xs,T_a] : ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a),
inference(nnf_transformation,[status(thm)],[f212]) ).
fof(f212_sk,plain,
! [V_r,V_xs,T_a] : ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a),
inference(skolemisation,[status(esa)],[f212_nnf]) ).
cnf(c212,plain,
~ c_ListOrder_Ostep1(X0,X1,c_List_Olist_ONil(X2),X2),
inference(cnf_transformation,[status(esa)],[f212_sk]) ).
cnf(f222,axiom,
c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
fof(f222_nnf,plain,
! [V_x,V_xa,T_a] : c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a),
inference(nnf_transformation,[status(thm)],[f222]) ).
fof(f222_sk,plain,
! [V_x,V_xa,T_a] : c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a),
inference(skolemisation,[status(esa)],[f222_nnf]) ).
cnf(c222,plain,
c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(esa)],[f222_sk]) ).
cnf(f223,axiom,
c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
fof(f223_nnf,plain,
! [V_a_H,V_list_H,T_a] : c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a),
inference(nnf_transformation,[status(thm)],[f223]) ).
fof(f223_sk,plain,
! [V_a_H,V_list_H,T_a] : c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a),
inference(skolemisation,[status(esa)],[f223_nnf]) ).
cnf(c223,plain,
c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(esa)],[f223_sk]) ).
cnf(f261,axiom,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
fof(f261_nnf,plain,
! [T_a,V_m] :
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(nnf_transformation,[status(thm)],[f261]) ).
fof(f261_sk,plain,
! [T_a,V_m] :
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(skolemisation,[status(esa)],[f261_nnf]) ).
cnf(c261,plain,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(esa)],[f261_sk]) ).
cnf(f268,axiom,
c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
fof(f268_nnf,plain,
! [V_x,V_t,T_a] : c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
inference(nnf_transformation,[status(thm)],[f268]) ).
fof(f268_sk,plain,
! [V_x,V_t,T_a] : c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
inference(skolemisation,[status(esa)],[f268_nnf]) ).
cnf(c268,plain,
c_List_Olist_OCons(X0,X1,X2) != X1,
inference(cnf_transformation,[status(esa)],[f268_sk]) ).
cnf(f269,axiom,
V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
fof(f269_nnf,plain,
! [V_xs,V_x,T_a] : V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
inference(nnf_transformation,[status(thm)],[f269]) ).
fof(f269_sk,plain,
! [V_xs,V_x,T_a] : V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
inference(skolemisation,[status(esa)],[f269_nnf]) ).
cnf(c269,plain,
X0 != c_List_Olist_OCons(X1,X0,X2),
inference(cnf_transformation,[status(esa)],[f269_sk]) ).
cnf(f305,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
fof(f305_nnf,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(nnf_transformation,[status(thm)],[f305]) ).
fof(f305_sk,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f305_nnf]) ).
cnf(c305,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f305_sk]) ).
cnf(f313,axiom,
~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
fof(f313_nnf,plain,
! [V_m] : ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(nnf_transformation,[status(thm)],[f313]) ).
fof(f313_sk,plain,
! [V_m] : ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f313_nnf]) ).
cnf(c313,plain,
~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f313_sk]) ).
cnf(f314,axiom,
~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
fof(f314_nnf,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(nnf_transformation,[status(thm)],[f314]) ).
fof(f314_sk,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f314_nnf]) ).
cnf(c314,plain,
~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f314_sk]) ).
cnf(f328,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f328_nnf,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
inference(nnf_transformation,[status(thm)],[f328]) ).
fof(f328_sk,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
inference(skolemisation,[status(esa)],[f328_nnf]) ).
cnf(c328,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f328_sk]) ).
cnf(f329,axiom,
~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
fof(f329_nnf,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
inference(nnf_transformation,[status(thm)],[f329]) ).
fof(f329_sk,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
inference(skolemisation,[status(esa)],[f329_nnf]) ).
cnf(c329,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f329_sk]) ).
cnf(f330,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f330_nnf,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f330]) ).
fof(f330_sk,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f330_nnf]) ).
cnf(c330,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f330_sk]) ).
cnf(f331,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f331_nnf,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f331]) ).
fof(f331_sk,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f331_nnf]) ).
cnf(c331,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f331_sk]) ).
cnf(f332,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f332_nnf,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f332]) ).
fof(f332_sk,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemisation,[status(esa)],[f332_nnf]) ).
cnf(c332,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f332_sk]) ).
cnf(f353,axiom,
c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
fof(f353_nnf,plain,
! [T_a,V_a_H,V_list_H] : c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
inference(nnf_transformation,[status(thm)],[f353]) ).
fof(f353_sk,plain,
! [T_a,V_a_H,V_list_H] : c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
inference(skolemisation,[status(esa)],[f353_nnf]) ).
cnf(c353,plain,
c_List_Olist_ONil(X0) != c_List_Olist_OCons(X1,X2,X0),
inference(cnf_transformation,[status(esa)],[f353_sk]) ).
cnf(f373,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f373_nnf,plain,
! [V_i,V_j] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat),
inference(nnf_transformation,[status(thm)],[f373]) ).
fof(f373_sk,plain,
! [V_i,V_j] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat),
inference(skolemisation,[status(esa)],[f373_nnf]) ).
cnf(c373,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f373_sk]) ).
cnf(f374,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f374_nnf,plain,
! [V_j,V_i] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat),
inference(nnf_transformation,[status(thm)],[f374]) ).
fof(f374_sk,plain,
! [V_j,V_i] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat),
inference(skolemisation,[status(esa)],[f374_nnf]) ).
cnf(c374,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),X1,tc_nat),
inference(cnf_transformation,[status(esa)],[f374_sk]) ).
cnf(f407,axiom,
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f407_nnf,plain,
! [T_a,V_a,V_b] :
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f407]) ).
fof(f407_sk,plain,
! [T_a,V_a,V_b] :
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f407_nnf]) ).
cnf(c407,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f407_sk]) ).
cnf(f410,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f410_nnf,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f410]) ).
fof(f410_sk,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f410_nnf]) ).
cnf(c410,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f410_sk]) ).
cnf(f412,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f412_nnf,plain,
! [T_a,V_y,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f412]) ).
fof(f412_sk,plain,
! [T_a,V_y,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemisation,[status(esa)],[f412_nnf]) ).
cnf(c412,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f412_sk]) ).
cnf(f414,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f414_nnf,plain,
! [T_a,V_b,V_a] :
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f414]) ).
fof(f414_sk,plain,
! [T_a,V_b,V_a] :
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemisation,[status(esa)],[f414_nnf]) ).
cnf(c414,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f414_sk]) ).
cnf(f427,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
fof(f427_nnf,plain,
! [V_dB1,V_dB2,V_dB_H] : hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
inference(nnf_transformation,[status(thm)],[f427]) ).
fof(f427_sk,plain,
! [V_dB1,V_dB2,V_dB_H] : hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
inference(skolemisation,[status(esa)],[f427_nnf]) ).
cnf(c427,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1) != c_Lambda_OdB_OAbs(X2),
inference(cnf_transformation,[status(esa)],[f427_sk]) ).
cnf(f428,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
fof(f428_nnf,plain,
! [V_dB_H,V_dB1,V_dB2] : c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),
inference(nnf_transformation,[status(thm)],[f428]) ).
fof(f428_sk,plain,
! [V_dB_H,V_dB1,V_dB2] : c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),
inference(skolemisation,[status(esa)],[f428_nnf]) ).
cnf(c428,plain,
c_Lambda_OdB_OAbs(X0) != hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
inference(cnf_transformation,[status(esa)],[f428_sk]) ).
cnf(f464,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
fof(f464_nnf,plain,
! [V_dB_H,V_nat] : c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
inference(nnf_transformation,[status(thm)],[f464]) ).
fof(f464_sk,plain,
! [V_dB_H,V_nat] : c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
inference(skolemisation,[status(esa)],[f464_nnf]) ).
cnf(c464,plain,
c_Lambda_OdB_OAbs(X0) != c_Lambda_OdB_OVar(X1),
inference(cnf_transformation,[status(esa)],[f464_sk]) ).
cnf(f467,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
fof(f467_nnf,plain,
! [V_i,V_t] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
inference(nnf_transformation,[status(thm)],[f467]) ).
fof(f467_sk,plain,
! [V_i,V_t] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
inference(skolemisation,[status(esa)],[f467_nnf]) ).
cnf(c467,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X0)),X1)),
inference(cnf_transformation,[status(esa)],[f467_sk]) ).
cnf(f469,axiom,
c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
fof(f469_nnf,plain,
! [V_nat,V_dB_H] : c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
inference(nnf_transformation,[status(thm)],[f469]) ).
fof(f469_sk,plain,
! [V_nat,V_dB_H] : c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
inference(skolemisation,[status(esa)],[f469_nnf]) ).
cnf(c469,plain,
c_Lambda_OdB_OVar(X0) != c_Lambda_OdB_OAbs(X1),
inference(cnf_transformation,[status(esa)],[f469_sk]) ).
cnf(f479,axiom,
( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
fof(f479_nnf,plain,
! [T_a,V_a] :
( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(nnf_transformation,[status(thm)],[f479]) ).
fof(f479_sk,plain,
! [T_a,V_a] :
( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(skolemisation,[status(esa)],[f479_nnf]) ).
cnf(c479,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(esa)],[f479_sk]) ).
cnf(f496,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
fof(f496_nnf,plain,
! [V_n,V_ts,V_r,V_ss] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
inference(nnf_transformation,[status(thm)],[f496]) ).
fof(f496_sk,plain,
! [V_n,V_ts,V_r,V_ss] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
inference(skolemisation,[status(esa)],[f496_nnf]) ).
cnf(c496,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),
inference(cnf_transformation,[status(esa)],[f496_sk]) ).
cnf(f499,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
fof(f499_nnf,plain,
! [V_s,V_t,V_n,V_ss] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
inference(nnf_transformation,[status(thm)],[f499]) ).
fof(f499_sk,plain,
! [V_s,V_t,V_n,V_ss] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
inference(skolemisation,[status(esa)],[f499_nnf]) ).
cnf(c499,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),
inference(cnf_transformation,[status(esa)],[f499_sk]) ).
cnf(f511,axiom,
c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
fof(f511_nnf,plain,
! [V_nat,V_dB1_H,V_dB2_H] : c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H),
inference(nnf_transformation,[status(thm)],[f511]) ).
fof(f511_sk,plain,
! [V_nat,V_dB1_H,V_dB2_H] : c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H),
inference(skolemisation,[status(esa)],[f511_nnf]) ).
cnf(c511,plain,
c_Lambda_OdB_OVar(X0) != hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
inference(cnf_transformation,[status(esa)],[f511_sk]) ).
cnf(f514,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
fof(f514_nnf,plain,
! [V_dB1_H,V_dB2_H,V_nat] : hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
inference(nnf_transformation,[status(thm)],[f514]) ).
fof(f514_sk,plain,
! [V_dB1_H,V_dB2_H,V_nat] : hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
inference(skolemisation,[status(esa)],[f514_nnf]) ).
cnf(c514,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1) != c_Lambda_OdB_OVar(X2),
inference(cnf_transformation,[status(esa)],[f514_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c30,c62,c89,c91,c93,c95,c97,c98,c211,c212,c222,c223,c261,c268,c269,c305,c313,c314,c328,c329,c330,c331,c332,c353,c373,c374,c407,c410,c412,c414,c427,c428,c464,c467,c469,c479,c496,c499,c511,c514,c519]) ).
cnf(g0_0,plain,
sF1 != false,
inference(rw,[status(thm)],[goal_0,t241]) ).
cnf(g0_1,plain,
sF1 != sF1,
inference(rw,[status(thm)],[g0_0,t3496]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL778-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n026.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 00:31:30 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 21.17/8.14 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.17/8.14 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------