%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL799-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 02:03:04 PM UTC 2026
% Result : Unsatisfiable 17.73s 2.76s
% Output : Proof 17.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 35
% Syntax : Number of formulae : 161 ( 125 unt; 0 def)
% Number of atoms : 217 ( 82 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 234 ( 178 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 25 ( 25 usr; 14 con; 0-5 aty)
% Number of variables : 329 ( 88 sgn 154 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f268,axiom,
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
fof(f268_nnf,plain,
! [V_e_H,V_u,V_U,V_i,V_t,V_T] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) ),
inference(nnf_transformation,[status(thm)],[f268]) ).
fof(f268_sk,plain,
! [V_e_H,V_u,V_U,V_i,V_t,V_T] :
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) ),
inference(skolemisation,[status(esa)],[f268_nnf]) ).
cnf(c268,plain,
( c_Type_Otyping(X0,c_Lambda_Osubst(X4,X1,X3),X5)
| ~ c_Type_Otyping(c_Type_Oshift(X0,X3,X2,tc_Type_Otype),X4,X5)
| ~ c_Type_Otyping(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f268_sk]) ).
cnf(t160,plain,
ifeq(c_Type_Otyping(X1,X2,X3),true,ifeq(c_Type_Otyping(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6),true,c_Type_Otyping(X1,c_Lambda_Osubst(X5,X2,X4),X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c268]) ).
cnf(t304,plain,
ifeq(c_Type_Otyping(X1,X2,X3),true,ifeq(c_Type_Otyping(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6),true,c_Type_Otyping(X1,c_Lambda_Osubst(X5,X2,X4),X6),true),true) = true,
inference(orient,[status(thm)],[t160]) ).
cnf(f261,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_argT_0) ).
fof(f261_nnf,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
inference(nnf_transformation,[status(thm)],[f261]) ).
cnf(c261,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
inference(cnf_transformation,[status(esa)],[f261_nnf]) ).
cnf(t45,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____) = true,
inference(equality_encoding,[status(esa)],[c261]) ).
cnf(t454,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____) = true,
inference(orient,[status(thm)],[t45]) ).
cnf(f262,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
fof(f262_nnf,plain,
v_n____ = v_i____,
inference(nnf_transformation,[status(thm)],[f262]) ).
cnf(c262,plain,
v_n____ = v_i____,
inference(cnf_transformation,[status(esa)],[f262_nnf]) ).
cnf(t0,plain,
v_n____ = v_i____,
inference(equality_encoding,[status(esa)],[c262]) ).
cnf(t1051,plain,
v_i____ = v_n____,
inference(orient,[status(thm)],[t0]) ).
cnf(t2302,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____) = true,
inference(step,[status(thm)],[t454,t1051]) ).
cnf(t1053,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____) = true,
inference(rw,[status(thm)],[t2302]) ).
cnf(t1130,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____) = true,
inference(orient,[status(thm)],[t1053]) ).
cnf(t1132,plain,
true = ifeq(c_Type_Otyping(v_e____,X1,v_T____),true,ifeq(true,true,c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,X1,v_n____),v_T_H_H____),true),true),
inference(cp,[status(thm)],[t304,t1130]) ).
cnf(t22,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t184,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t22]) ).
cnf(t2405,plain,
true = ifeq(c_Type_Otyping(v_e____,X1,v_T____),true,c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,X1,v_n____),v_T_H_H____),true),
inference(step,[status(thm)],[t1132,t184]) ).
cnf(t2202,plain,
ifeq(c_Type_Otyping(v_e____,X1,v_T____),true,c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,X1,v_n____),v_T_H_H____),true) = true,
inference(orient,[status(thm)],[t2405]) ).
cnf(f256,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_0) ).
fof(f256_nnf,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(nnf_transformation,[status(thm)],[f256]) ).
cnf(c256,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(cnf_transformation,[status(esa)],[f256_nnf]) ).
cnf(t8,plain,
c_Type_Otyping(v_e____,v_u____,v_T____) = true,
inference(equality_encoding,[status(esa)],[c256]) ).
cnf(t476,plain,
c_Type_Otyping(v_e____,v_u____,v_T____) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t2203,plain,
true = ifeq(true,true,c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_n____),v_T_H_H____),true),
inference(cp,[status(thm)],[t2202,t476]) ).
cnf(t2406,plain,
true = c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_n____),v_T_H_H____),
inference(step,[status(thm)],[t2203,t184]) ).
cnf(f271,negated_conjecture,
~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f271_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)],[f271]) ).
fof(f271_sk,plain,
~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
inference(skolemisation,[status(esa)],[f271_nnf]) ).
cnf(c271,plain,
~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
inference(cnf_transformation,[status(esa)],[f271_sk]) ).
cnf(t34,plain,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____) = false,
inference(equality_encoding,[status(esa)],[c271]) ).
cnf(t1000,plain,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____) = false,
inference(orient,[status(thm)],[t34]) ).
cnf(t2301,plain,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_n____),v_T_H_H____) = false,
inference(step,[status(thm)],[t1000,t1051]) ).
cnf(t1052,plain,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_n____),v_T_H_H____) = false,
inference(rw,[status(thm)],[t2301]) ).
cnf(t1087,plain,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_n____),v_T_H_H____) = false,
inference(orient,[status(thm)],[t1052]) ).
cnf(t2407,plain,
true = false,
inference(step,[status(thm)],[t2406,t1087]) ).
cnf(t2205,plain,
false = true,
inference(orient,[status(thm)],[t2407]) ).
cnf(f51,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(f51_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)],[f51]) ).
fof(f51_sk,plain,
! [V_xs,V_x,T_a] : V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c51,plain,
X0 != c_List_Olist_OCons(X1,X0,X2),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(f52,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(f52_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)],[f52]) ).
fof(f52_sk,plain,
! [V_x,V_t,T_a] : c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c52,plain,
c_List_Olist_OCons(X0,X1,X2) != X1,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(f53,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(f53_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)],[f53]) ).
fof(f53_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)],[f53_nnf]) ).
cnf(c53,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)],[f53_sk]) ).
cnf(f56,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(f56_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)],[f56]) ).
fof(f56_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)],[f56_nnf]) ).
cnf(c56,plain,
c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(f57,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(f57_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)],[f57]) ).
fof(f57_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)],[f57_nnf]) ).
cnf(c57,plain,
c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(esa)],[f57_sk]) ).
cnf(f99,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(f99_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)],[f99]) ).
fof(f99_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)],[f99_nnf]) ).
cnf(c99,plain,
~ c_ListOrder_Ostep1(X0,c_List_Olist_ONil(X1),X2,X1),
inference(cnf_transformation,[status(esa)],[f99_sk]) ).
cnf(f100,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(f100_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)],[f100]) ).
fof(f100_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)],[f100_nnf]) ).
cnf(c100,plain,
~ c_ListOrder_Ostep1(X0,X1,c_List_Olist_ONil(X2),X2),
inference(cnf_transformation,[status(esa)],[f100_sk]) ).
cnf(f112,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(f112_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)],[f112]) ).
fof(f112_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)],[f112_nnf]) ).
cnf(c112,plain,
c_List_Olist_ONil(X0) != c_List_Olist_OCons(X1,X2,X0),
inference(cnf_transformation,[status(esa)],[f112_sk]) ).
cnf(f134,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(f134_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)],[f134]) ).
fof(f134_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)],[f134_nnf]) ).
cnf(c134,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)],[f134_sk]) ).
cnf(f135,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(f135_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)],[f135]) ).
fof(f135_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)],[f135_nnf]) ).
cnf(c135,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)],[f135_sk]) ).
cnf(f136,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(f136_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)],[f136]) ).
fof(f136_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)],[f136_nnf]) ).
cnf(c136,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)],[f136_sk]) ).
cnf(f139,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(f139_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)],[f139]) ).
fof(f139_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)],[f139_nnf]) ).
cnf(c139,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)],[f139_sk]) ).
cnf(f140,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(f140_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)],[f140]) ).
fof(f140_sk,plain,
! [V_dB_H,V_nat] : c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
inference(skolemisation,[status(esa)],[f140_nnf]) ).
cnf(c140,plain,
c_Lambda_OdB_OAbs(X0) != c_Lambda_OdB_OVar(X1),
inference(cnf_transformation,[status(esa)],[f140_sk]) ).
cnf(f141,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(f141_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)],[f141]) ).
fof(f141_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)],[f141_nnf]) ).
cnf(c141,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1) != c_Lambda_OdB_OAbs(X2),
inference(cnf_transformation,[status(esa)],[f141_sk]) ).
cnf(f143,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(f143_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)],[f143]) ).
fof(f143_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)],[f143_nnf]) ).
cnf(c143,plain,
c_Lambda_OdB_OAbs(X0) != hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
inference(cnf_transformation,[status(esa)],[f143_sk]) ).
cnf(f146,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(f146_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)],[f146]) ).
fof(f146_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)],[f146_nnf]) ).
cnf(c146,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)],[f146_sk]) ).
cnf(f164,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(f164_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)],[f164]) ).
fof(f164_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)],[f164_nnf]) ).
cnf(c164,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f164_sk]) ).
cnf(f165,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(f165_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)],[f165]) ).
fof(f165_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)],[f165_nnf]) ).
cnf(c165,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f165_sk]) ).
cnf(f166,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(f166_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)],[f166]) ).
fof(f166_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)],[f166_nnf]) ).
cnf(c166,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f166_sk]) ).
cnf(f167,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(f167_nnf,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
inference(nnf_transformation,[status(thm)],[f167]) ).
fof(f167_sk,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,V_n,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(f168,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(f168_nnf,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
inference(nnf_transformation,[status(thm)],[f168]) ).
fof(f168_sk,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
inference(skolemisation,[status(esa)],[f168_nnf]) ).
cnf(c168,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f168_sk]) ).
cnf(f171,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(f171_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)],[f171]) ).
fof(f171_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)],[f171_nnf]) ).
cnf(c171,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)],[f171_sk]) ).
cnf(f174,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(f174_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)],[f174]) ).
fof(f174_sk,plain,
! [V_nat,V_dB_H] : c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
inference(skolemisation,[status(esa)],[f174_nnf]) ).
cnf(c174,plain,
c_Lambda_OdB_OVar(X0) != c_Lambda_OdB_OAbs(X1),
inference(cnf_transformation,[status(esa)],[f174_sk]) ).
cnf(f184,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(f184_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)],[f184]) ).
fof(f184_sk,plain,
! [V_m] : ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f184_nnf]) ).
cnf(c184,plain,
~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f184_sk]) ).
cnf(f185,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(f185_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)],[f185]) ).
fof(f185_sk,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f185_nnf]) ).
cnf(c185,plain,
~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f185_sk]) ).
cnf(f198,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(f198_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)],[f198]) ).
fof(f198_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)],[f198_nnf]) ).
cnf(c198,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)],[f198_sk]) ).
cnf(f201,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(f201_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)],[f201]) ).
fof(f201_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)],[f201_nnf]) ).
cnf(c201,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1) != c_Lambda_OdB_OVar(X2),
inference(cnf_transformation,[status(esa)],[f201_sk]) ).
cnf(f236,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(f236_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)],[f236]) ).
fof(f236_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)],[f236_nnf]) ).
cnf(c236,plain,
c_Lambda_OdB_OVar(X0) != hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
inference(cnf_transformation,[status(esa)],[f236_sk]) ).
cnf(f246,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(f246_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)],[f246]) ).
fof(f246_sk,plain,
! [V_i,V_t] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
inference(skolemisation,[status(esa)],[f246_nnf]) ).
cnf(c246,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X0)),X1)),
inference(cnf_transformation,[status(esa)],[f246_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c51,c52,c53,c56,c57,c99,c100,c112,c134,c135,c136,c139,c140,c141,c143,c146,c164,c165,c166,c167,c168,c171,c174,c184,c185,c198,c201,c236,c246,c271]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2205]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL799-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 00:32:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 17.73/2.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.73/2.76 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------