%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL834-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 02:03:11 PM UTC 2026
% Result : Unsatisfiable 37.18s 5.12s
% Output : Proof 37.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 39
% Syntax : Number of formulae : 167 ( 115 unt; 0 def)
% Number of atoms : 247 ( 78 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 306 ( 226 ~; 80 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 10 con; 0-5 aty)
% Number of variables : 356 ( 94 sgn 170 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f435,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
fof(f435_nnf,plain,
! [V_r,V_ss,V_s] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(nnf_transformation,[status(thm)],[f435]) ).
fof(f435_sk,plain,
! [V_r,V_ss,V_s] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(skolemisation,[status(esa)],[f435_nnf]) ).
cnf(c435,plain,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(cnf_transformation,[status(esa)],[f435_sk]) ).
cnf(t114,plain,
ifeq(hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)),true,hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB))),true) = true,
inference(equality_encoding,[status(esa)],[c435]) ).
cnf(t206,plain,
ifeq(hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)),true,hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB))),true) = true,
inference(orient,[status(thm)],[t114]) ).
cnf(f443,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f443_nnf,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(nnf_transformation,[status(thm)],[f443]) ).
fof(f443_sk,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(skolemisation,[status(esa)],[f443_nnf]) ).
cnf(c443,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(cnf_transformation,[status(esa)],[f443_sk]) ).
cnf(t117,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) = false,
inference(equality_encoding,[status(esa)],[c443]) ).
cnf(t348,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) = false,
inference(orient,[status(thm)],[t117]) ).
cnf(t351,plain,
true = ifeq(hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____)),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)))),true,false,true),
inference(cp,[status(thm)],[t206,t348]) ).
cnf(f434,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
fof(f434_nnf,plain,
! [V_s,V_t] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(nnf_transformation,[status(thm)],[f434]) ).
fof(f434_sk,plain,
! [V_s,V_t] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(skolemisation,[status(esa)],[f434_nnf]) ).
cnf(c434,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(cnf_transformation,[status(esa)],[f434_sk]) ).
cnf(t106,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))) = true,
inference(equality_encoding,[status(esa)],[c434]) ).
cnf(t180,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))) = true,
inference(orient,[status(thm)],[t106]) ).
cnf(t449,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t351,t180]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t123,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t450,plain,
true = false,
inference(step,[status(thm)],[t449,t123]) ).
cnf(t402,plain,
false = true,
inference(orient,[status(thm)],[t450]) ).
cnf(f33,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(f33_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)],[f33]) ).
fof(f33_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)],[f33_nnf]) ).
cnf(c33,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)],[f33_sk]) ).
cnf(f35,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(f35_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)],[f35]) ).
fof(f35_sk,plain,
! [V_m] : ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c35,plain,
~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(f36,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(f36_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)],[f36]) ).
fof(f36_sk,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c36,plain,
~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(f44,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(f44_nnf,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(f45,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(f45_nnf,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c45,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(f46,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(f46_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)],[f46]) ).
fof(f46_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)],[f46_nnf]) ).
cnf(c46,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(f47,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(f47_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)],[f47]) ).
fof(f47_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)],[f47_nnf]) ).
cnf(c47,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(f48,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(f48_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)],[f48]) ).
fof(f48_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)],[f48_nnf]) ).
cnf(c48,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(f71,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(f71_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)],[f71]) ).
fof(f71_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)],[f71_nnf]) ).
cnf(c71,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)],[f71_sk]) ).
cnf(f72,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(f72_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)],[f72]) ).
fof(f72_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)],[f72_nnf]) ).
cnf(c72,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)],[f72_sk]) ).
cnf(f86,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(f86_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)],[f86]) ).
fof(f86_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)],[f86_nnf]) ).
cnf(c86,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)],[f86_sk]) ).
cnf(f87,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(f87_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)],[f87]) ).
fof(f87_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)],[f87_nnf]) ).
cnf(c87,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)],[f87_sk]) ).
cnf(f88,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(f88_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)],[f88]) ).
fof(f88_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)],[f88_nnf]) ).
cnf(c88,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)],[f88_sk]) ).
cnf(f89,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(f89_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)],[f89]) ).
fof(f89_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)],[f89_nnf]) ).
cnf(c89,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)],[f89_sk]) ).
cnf(f104,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(f104_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)],[f104]) ).
fof(f104_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)],[f104_nnf]) ).
cnf(c104,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)],[f104_sk]) ).
cnf(f107,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(f107_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)],[f107]) ).
fof(f107_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)],[f107_nnf]) ).
cnf(c107,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)],[f107_sk]) ).
cnf(f197,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(f197_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)],[f197]) ).
fof(f197_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)],[f197_nnf]) ).
cnf(c197,plain,
c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(esa)],[f197_sk]) ).
cnf(f198,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(f198_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)],[f198]) ).
fof(f198_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)],[f198_nnf]) ).
cnf(c198,plain,
c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(esa)],[f198_sk]) ).
cnf(f202,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(f202_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)],[f202]) ).
fof(f202_sk,plain,
! [V_x,V_t,T_a] : c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
inference(skolemisation,[status(esa)],[f202_nnf]) ).
cnf(c202,plain,
c_List_Olist_OCons(X0,X1,X2) != X1,
inference(cnf_transformation,[status(esa)],[f202_sk]) ).
cnf(f203,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(f203_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)],[f203]) ).
fof(f203_sk,plain,
! [V_xs,V_x,T_a] : V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
inference(skolemisation,[status(esa)],[f203_nnf]) ).
cnf(c203,plain,
X0 != c_List_Olist_OCons(X1,X0,X2),
inference(cnf_transformation,[status(esa)],[f203_sk]) ).
cnf(f217,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(f217_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)],[f217]) ).
fof(f217_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)],[f217_nnf]) ).
cnf(c217,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)],[f217_sk]) ).
cnf(f221,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(f221_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)],[f221]) ).
fof(f221_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)],[f221_nnf]) ).
cnf(c221,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)],[f221_sk]) ).
cnf(f242,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(f242_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)],[f242]) ).
fof(f242_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)],[f242_nnf]) ).
cnf(c242,plain,
c_Lambda_OdB_OVar(X0) != hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
inference(cnf_transformation,[status(esa)],[f242_sk]) ).
cnf(f292,axiom,
~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_ONil(T_a)),V_xs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
fof(f292_nnf,plain,
! [V_r,T_a,V_xs] : ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_ONil(T_a)),V_xs)),
inference(nnf_transformation,[status(thm)],[f292]) ).
fof(f292_sk,plain,
! [V_r,T_a,V_xs] : ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_ONil(T_a)),V_xs)),
inference(skolemisation,[status(esa)],[f292_nnf]) ).
cnf(c292,plain,
~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(X0,X1),c_List_Olist_ONil(X1)),X2)),
inference(cnf_transformation,[status(esa)],[f292_sk]) ).
cnf(f293,axiom,
~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_xs),c_List_Olist_ONil(T_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
fof(f293_nnf,plain,
! [V_r,T_a,V_xs] : ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_xs),c_List_Olist_ONil(T_a))),
inference(nnf_transformation,[status(thm)],[f293]) ).
fof(f293_sk,plain,
! [V_r,T_a,V_xs] : ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_xs),c_List_Olist_ONil(T_a))),
inference(skolemisation,[status(esa)],[f293_nnf]) ).
cnf(c293,plain,
~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(X0,X1),X2),c_List_Olist_ONil(X1))),
inference(cnf_transformation,[status(esa)],[f293_sk]) ).
cnf(f307,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(f307_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)],[f307]) ).
fof(f307_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)],[f307_nnf]) ).
cnf(c307,plain,
c_List_Olist_ONil(X0) != c_List_Olist_OCons(X1,X2,X0),
inference(cnf_transformation,[status(esa)],[f307_sk]) ).
cnf(f348,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(f348_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)],[f348]) ).
fof(f348_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)],[f348_nnf]) ).
cnf(c348,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1) != c_Lambda_OdB_OVar(X2),
inference(cnf_transformation,[status(esa)],[f348_sk]) ).
cnf(f355,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(f355_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)],[f355]) ).
fof(f355_sk,plain,
! [V_i,V_t] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
inference(skolemisation,[status(esa)],[f355_nnf]) ).
cnf(c355,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X0)),X1)),
inference(cnf_transformation,[status(esa)],[f355_sk]) ).
cnf(f360,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(f360_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)],[f360]) ).
fof(f360_sk,plain,
! [V_dB_H,V_nat] : c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
inference(skolemisation,[status(esa)],[f360_nnf]) ).
cnf(c360,plain,
c_Lambda_OdB_OAbs(X0) != c_Lambda_OdB_OVar(X1),
inference(cnf_transformation,[status(esa)],[f360_sk]) ).
cnf(f364,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(f364_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)],[f364]) ).
fof(f364_sk,plain,
! [V_nat,V_dB_H] : c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
inference(skolemisation,[status(esa)],[f364_nnf]) ).
cnf(c364,plain,
c_Lambda_OdB_OVar(X0) != c_Lambda_OdB_OAbs(X1),
inference(cnf_transformation,[status(esa)],[f364_sk]) ).
cnf(f396,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(f396_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)],[f396]) ).
fof(f396_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)],[f396_nnf]) ).
cnf(c396,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)],[f396_sk]) ).
cnf(f419,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(f419_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)],[f419]) ).
fof(f419_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)],[f419_nnf]) ).
cnf(c419,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)],[f419_sk]) ).
cnf(f423,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(f423_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)],[f423]) ).
fof(f423_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)],[f423_nnf]) ).
cnf(c423,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)],[f423_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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c33,c35,c36,c44,c45,c46,c47,c48,c71,c72,c86,c87,c88,c89,c104,c107,c197,c198,c202,c203,c217,c221,c242,c292,c293,c307,c348,c355,c360,c364,c396,c419,c423,c427,c428,c443]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t402]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL834-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 00:36:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 37.18/5.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.18/5.12 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------