%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL818-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 02:03:08 PM UTC 2026
% Result : Unsatisfiable 98.18s 12.86s
% Output : Proof 98.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 43
% Syntax : Number of formulae : 194 ( 146 unt; 0 def)
% Number of atoms : 262 ( 103 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 286 ( 218 ~; 68 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 30 ( 30 usr; 16 con; 0-5 aty)
% Number of variables : 414 ( 104 sgn 190 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f328,axiom,
( ~ c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))
| ~ c_Type_Otyping(V_env,V_t,V_T)
| c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).
fof(f328_nnf,plain,
! [V_env,V_s,V_t,V_U,V_T] :
( ~ c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))
| ~ c_Type_Otyping(V_env,V_t,V_T)
| c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U) ),
inference(nnf_transformation,[status(thm)],[f328]) ).
fof(f328_sk,plain,
! [V_env,V_s,V_t,V_U,V_T] :
( ~ c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))
| ~ c_Type_Otyping(V_env,V_t,V_T)
| c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U) ),
inference(skolemisation,[status(esa)],[f328_nnf]) ).
cnf(c328,plain,
( ~ c_Type_Otyping(X0,X1,hAPP(hAPP(c_Type_Otype_OFun,X4),X3))
| ~ c_Type_Otyping(X0,X2,X4)
| c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3) ),
inference(cnf_transformation,[status(esa)],[f328_sk]) ).
cnf(t183,plain,
ifeq(c_Type_Otyping(X1,X2,X3),true,ifeq(c_Type_Otyping(X1,X4,hAPP(hAPP(c_Type_Otype_OFun,X3),X5)),true,c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2),X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c328]) ).
cnf(t335,plain,
ifeq(c_Type_Otyping(X1,X2,X3),true,ifeq(c_Type_Otyping(X1,X4,hAPP(hAPP(c_Type_Otype_OFun,X3),X5)),true,c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2),X5),true),true) = true,
inference(orient,[status(thm)],[t183]) ).
cnf(f372,axiom,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f372_nnf,plain,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
inference(nnf_transformation,[status(thm)],[f372]) ).
cnf(c372,plain,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
inference(cnf_transformation,[status(esa)],[f372_nnf]) ).
cnf(t28,plain,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____) = true,
inference(equality_encoding,[status(esa)],[c372]) ).
cnf(t497,plain,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____) = true,
inference(orient,[status(thm)],[t28]) ).
cnf(t502,plain,
true = ifeq(true,true,ifeq(c_Type_Otyping(v_e____,X1,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),X2)),true,c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_Osubst(v_a____,v_u____,v_i____)),X2),true),true),
inference(cp,[status(thm)],[t335,t497]) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t189,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t19]) ).
cnf(t10212,plain,
true = ifeq(c_Type_Otyping(v_e____,X1,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),X2)),true,c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_Osubst(v_a____,v_u____,v_i____)),X2),true),
inference(step,[status(thm)],[t502,t189]) ).
cnf(t9724,plain,
ifeq(c_Type_Otyping(v_e____,X1,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),X2)),true,c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_Osubst(v_a____,v_u____,v_i____)),X2),true) = true,
inference(orient,[status(thm)],[t10212]) ).
cnf(f374,negated_conjecture,
~ c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,v_u____),c_Lambda_Osubst(v_a____,v_u____,v_i____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f374_nnf,plain,
~ c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,v_u____),c_Lambda_Osubst(v_a____,v_u____,v_i____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(nnf_transformation,[status(thm)],[f374]) ).
fof(f374_sk,plain,
~ c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,v_u____),c_Lambda_Osubst(v_a____,v_u____,v_i____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(skolemisation,[status(esa)],[f374_nnf]) ).
cnf(c374,plain,
~ c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,v_u____),c_Lambda_Osubst(v_a____,v_u____,v_i____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(cnf_transformation,[status(esa)],[f374_sk]) ).
cnf(t145,plain,
c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,v_u____),c_Lambda_Osubst(v_a____,v_u____,v_i____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) = false,
inference(equality_encoding,[status(esa)],[c374]) ).
cnf(t663,plain,
c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,v_u____),c_Lambda_Osubst(v_a____,v_u____,v_i____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) = false,
inference(orient,[status(thm)],[t145]) ).
cnf(t9730,plain,
true = ifeq(c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),true,false,true),
inference(cp,[status(thm)],[t9724,t663]) ).
cnf(f324,axiom,
c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
fof(f324_nnf,plain,
! [V_f,V_x,V_xs,T_b,V_a,T_a] : c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)),
inference(nnf_transformation,[status(thm)],[f324]) ).
fof(f324_sk,plain,
! [V_f,V_x,V_xs,T_b,V_a,T_a] : c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)),
inference(skolemisation,[status(esa)],[f324_nnf]) ).
cnf(c324,plain,
c_List_Ofoldr(X0,c_List_Olist_OCons(X1,X2,X3),X4,X3,X5) = hAPP(hAPP(X0,X1),c_List_Ofoldr(X0,X2,X4,X3,X5)),
inference(cnf_transformation,[status(esa)],[f324_sk]) ).
cnf(t161,plain,
hAPP(hAPP(X1,X2),c_List_Ofoldr(X1,X3,X4,X5,X6)) = c_List_Ofoldr(X1,c_List_Olist_OCons(X2,X3,X5),X4,X5,X6),
inference(equality_encoding,[status(esa)],[c324]) ).
cnf(t239,plain,
c_List_Ofoldr(X1,c_List_Olist_OCons(X2,X3,X4),X5,X4,X6) = hAPP(hAPP(X1,X2),c_List_Ofoldr(X1,X3,X5,X4,X6)),
inference(orient,[status(thm)],[t161]) ).
cnf(t10213,plain,
true = ifeq(c_Type_Otyping(v_e____,v_u____,c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype)),true,false,true),
inference(step,[status(thm)],[t9730,t239]) ).
cnf(f353,axiom,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_T_0) ).
fof(f353_nnf,plain,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(nnf_transformation,[status(thm)],[f353]) ).
cnf(c353,plain,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(cnf_transformation,[status(esa)],[f353_nnf]) ).
cnf(t64,plain,
hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) = v_T____,
inference(equality_encoding,[status(esa)],[c353]) ).
cnf(t9977,plain,
c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype) = v_T____,
inference(step,[status(thm)],[t64,t239]) ).
cnf(t260,plain,
c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype) = v_T____,
inference(orient,[status(thm)],[t9977]) ).
cnf(t10214,plain,
true = ifeq(c_Type_Otyping(v_e____,v_u____,v_T____),true,false,true),
inference(step,[status(thm)],[t10213,t260]) ).
cnf(f373,axiom,
c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f373_nnf,plain,
c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(nnf_transformation,[status(thm)],[f373]) ).
cnf(c373,plain,
c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(cnf_transformation,[status(esa)],[f373_nnf]) ).
cnf(t100,plain,
c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) = true,
inference(equality_encoding,[status(esa)],[c373]) ).
cnf(t9978,plain,
c_Type_Otyping(v_e____,v_u____,c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype)) = true,
inference(step,[status(thm)],[t100,t239]) ).
cnf(t9979,plain,
c_Type_Otyping(v_e____,v_u____,v_T____) = true,
inference(step,[status(thm)],[t9978,t260]) ).
cnf(t507,plain,
c_Type_Otyping(v_e____,v_u____,v_T____) = true,
inference(orient,[status(thm)],[t9979]) ).
cnf(t10215,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t10214,t507]) ).
cnf(t10216,plain,
true = false,
inference(step,[status(thm)],[t10215,t189]) ).
cnf(t9737,plain,
false = true,
inference(orient,[status(thm)],[t10216]) ).
cnf(f6,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/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f6_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)],[f6]) ).
fof(f6_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)],[f6_nnf]) ).
cnf(c6,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)],[f6_sk]) ).
cnf(f7,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/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f7_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)],[f7]) ).
fof(f7_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)],[f7_nnf]) ).
cnf(c7,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)],[f7_sk]) ).
cnf(f10,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/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f10_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)],[f10]) ).
fof(f10_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)],[f10_nnf]) ).
cnf(c10,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)],[f10_sk]) ).
cnf(f29,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
fof(f29_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)],[f29]) ).
fof(f29_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)],[f29_nnf]) ).
cnf(c29,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)],[f29_sk]) ).
cnf(f72,axiom,
~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
fof(f72_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)],[f72]) ).
fof(f72_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)],[f72_nnf]) ).
cnf(c72,plain,
~ c_ListOrder_Ostep1(X0,c_List_Olist_ONil(X1),X2,X1),
inference(cnf_transformation,[status(esa)],[f72_sk]) ).
cnf(f73,axiom,
~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
fof(f73_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)],[f73]) ).
fof(f73_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)],[f73_nnf]) ).
cnf(c73,plain,
~ c_ListOrder_Ostep1(X0,X1,c_List_Olist_ONil(X2),X2),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(f83,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/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f83_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)],[f83]) ).
fof(f83_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)],[f83_nnf]) ).
cnf(c83,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)],[f83_sk]) ).
cnf(f84,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/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f84_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)],[f84]) ).
fof(f84_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)],[f84_nnf]) ).
cnf(c84,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)],[f84_sk]) ).
cnf(f138,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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f138_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)],[f138]) ).
fof(f138_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)],[f138_nnf]) ).
cnf(c138,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)],[f138_sk]) ).
cnf(f139,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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f139_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)],[f139]) ).
fof(f139_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)],[f139_nnf]) ).
cnf(c139,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)],[f139_sk]) ).
cnf(f140,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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f140_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)],[f140]) ).
fof(f140_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)],[f140_nnf]) ).
cnf(c140,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)],[f140_sk]) ).
cnf(f141,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f141_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)],[f141]) ).
fof(f141_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)],[f141_nnf]) ).
cnf(c141,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)],[f141_sk]) ).
cnf(f150,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/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
fof(f150_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)],[f150]) ).
fof(f150_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)],[f150_nnf]) ).
cnf(c150,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)],[f150_sk]) ).
cnf(f163,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f163_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)],[f163]) ).
fof(f163_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)],[f163_nnf]) ).
cnf(c163,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f163_sk]) ).
cnf(f164,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f164_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)],[f164]) ).
fof(f164_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)],[f164_nnf]) ).
cnf(c164,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f164_sk]) ).
cnf(f165,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f165_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)],[f165]) ).
fof(f165_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)],[f165_nnf]) ).
cnf(c165,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f165_sk]) ).
cnf(f166,axiom,
~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
fof(f166_nnf,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
inference(nnf_transformation,[status(thm)],[f166]) ).
fof(f166_sk,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
inference(skolemisation,[status(esa)],[f166_nnf]) ).
cnf(c166,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f166_sk]) ).
cnf(f167,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f167_nnf,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
inference(nnf_transformation,[status(thm)],[f167]) ).
fof(f167_sk,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
inference(skolemisation,[status(esa)],[f167_nnf]) ).
cnf(c167,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f167_sk]) ).
cnf(f193,axiom,
~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
fof(f193_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)],[f193]) ).
fof(f193_sk,plain,
! [V_m] : ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f193_nnf]) ).
cnf(c193,plain,
~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f193_sk]) ).
cnf(f194,axiom,
~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
fof(f194_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)],[f194]) ).
fof(f194_sk,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f194_nnf]) ).
cnf(c194,plain,
~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f194_sk]) ).
cnf(f228,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/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
fof(f228_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)],[f228]) ).
fof(f228_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)],[f228_nnf]) ).
cnf(c228,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)],[f228_sk]) ).
cnf(f232,axiom,
V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
fof(f232_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)],[f232]) ).
fof(f232_sk,plain,
! [V_xs,V_x,T_a] : V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
inference(skolemisation,[status(esa)],[f232_nnf]) ).
cnf(c232,plain,
X0 != c_List_Olist_OCons(X1,X0,X2),
inference(cnf_transformation,[status(esa)],[f232_sk]) ).
cnf(f233,axiom,
c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
fof(f233_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)],[f233]) ).
fof(f233_sk,plain,
! [V_x,V_t,T_a] : c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
inference(skolemisation,[status(esa)],[f233_nnf]) ).
cnf(c233,plain,
c_List_Olist_OCons(X0,X1,X2) != X1,
inference(cnf_transformation,[status(esa)],[f233_sk]) ).
cnf(f239,axiom,
c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
fof(f239_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)],[f239]) ).
fof(f239_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)],[f239_nnf]) ).
cnf(c239,plain,
c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(esa)],[f239_sk]) ).
cnf(f240,axiom,
c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
fof(f240_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)],[f240]) ).
fof(f240_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)],[f240_nnf]) ).
cnf(c240,plain,
c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(esa)],[f240_sk]) ).
cnf(f262,axiom,
c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
fof(f262_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)],[f262]) ).
fof(f262_sk,plain,
! [V_nat,V_dB_H] : c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
inference(skolemisation,[status(esa)],[f262_nnf]) ).
cnf(c262,plain,
c_Lambda_OdB_OVar(X0) != c_Lambda_OdB_OAbs(X1),
inference(cnf_transformation,[status(esa)],[f262_sk]) ).
cnf(f267,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/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
fof(f267_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)],[f267]) ).
fof(f267_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)],[f267_nnf]) ).
cnf(c267,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)],[f267_sk]) ).
cnf(f281,axiom,
c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
fof(f281_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)],[f281]) ).
fof(f281_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)],[f281_nnf]) ).
cnf(c281,plain,
c_List_Olist_ONil(X0) != c_List_Olist_OCons(X1,X2,X0),
inference(cnf_transformation,[status(esa)],[f281_sk]) ).
cnf(f282,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
fof(f282_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)],[f282]) ).
fof(f282_sk,plain,
! [V_i,V_t] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
inference(skolemisation,[status(esa)],[f282_nnf]) ).
cnf(c282,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X0)),X1)),
inference(cnf_transformation,[status(esa)],[f282_sk]) ).
cnf(f303,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
fof(f303_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)],[f303]) ).
fof(f303_sk,plain,
! [V_dB_H,V_nat] : c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
inference(skolemisation,[status(esa)],[f303_nnf]) ).
cnf(c303,plain,
c_Lambda_OdB_OAbs(X0) != c_Lambda_OdB_OVar(X1),
inference(cnf_transformation,[status(esa)],[f303_sk]) ).
cnf(f312,axiom,
hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) != c_Type_Otype_OAtom(V_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).
fof(f312_nnf,plain,
! [V_type1_H,V_type2_H,V_nat] : hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) != c_Type_Otype_OAtom(V_nat),
inference(nnf_transformation,[status(thm)],[f312]) ).
fof(f312_sk,plain,
! [V_type1_H,V_type2_H,V_nat] : hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) != c_Type_Otype_OAtom(V_nat),
inference(skolemisation,[status(esa)],[f312_nnf]) ).
cnf(c312,plain,
hAPP(hAPP(c_Type_Otype_OFun,X0),X1) != c_Type_Otype_OAtom(X2),
inference(cnf_transformation,[status(esa)],[f312_sk]) ).
cnf(f315,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
fof(f315_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)],[f315]) ).
fof(f315_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)],[f315_nnf]) ).
cnf(c315,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1) != c_Lambda_OdB_OAbs(X2),
inference(cnf_transformation,[status(esa)],[f315_sk]) ).
cnf(f317,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
fof(f317_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)],[f317]) ).
fof(f317_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)],[f317_nnf]) ).
cnf(c317,plain,
c_Lambda_OdB_OAbs(X0) != hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
inference(cnf_transformation,[status(esa)],[f317_sk]) ).
cnf(f334,axiom,
c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
fof(f334_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)],[f334]) ).
fof(f334_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)],[f334_nnf]) ).
cnf(c334,plain,
c_Lambda_OdB_OVar(X0) != hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
inference(cnf_transformation,[status(esa)],[f334_sk]) ).
cnf(f360,axiom,
c_Type_Otype_OAtom(V_nat) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I3_J_0) ).
fof(f360_nnf,plain,
! [V_nat,V_type1_H,V_type2_H] : c_Type_Otype_OAtom(V_nat) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H),
inference(nnf_transformation,[status(thm)],[f360]) ).
fof(f360_sk,plain,
! [V_nat,V_type1_H,V_type2_H] : c_Type_Otype_OAtom(V_nat) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H),
inference(skolemisation,[status(esa)],[f360_nnf]) ).
cnf(c360,plain,
c_Type_Otype_OAtom(X0) != hAPP(hAPP(c_Type_Otype_OFun,X1),X2),
inference(cnf_transformation,[status(esa)],[f360_sk]) ).
cnf(f371,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
fof(f371_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)],[f371]) ).
fof(f371_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)],[f371_nnf]) ).
cnf(c371,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1) != c_Lambda_OdB_OVar(X2),
inference(cnf_transformation,[status(esa)],[f371_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c6,c7,c10,c29,c72,c73,c83,c84,c138,c139,c140,c141,c150,c163,c164,c165,c166,c167,c193,c194,c228,c232,c233,c239,c240,c262,c267,c281,c282,c303,c312,c315,c317,c334,c360,c371,c374]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t9737]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL818-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n009.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 00:32:43 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 98.18/12.86 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 98.18/12.86 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------