%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL798-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 11.47s 2.66s
% Output : Proof 11.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 30
% Syntax : Number of formulae : 130 ( 90 unt; 0 def)
% Number of atoms : 194 ( 49 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 225 ( 161 ~; 64 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-4 aty)
% Number of variables : 223 ( 55 sgn 106 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f65,axiom,
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
fof(f65_nnf,plain,
! [V_r] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r)) ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [V_r] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r)) ),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c65,plain,
( ~ c_InductTermi_OIT(X0)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X0)) ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(hi43,axiom,
ifeq(c_InductTermi_OIT(X0),true,c_InductTermi_OIT(c_Lambda_OdB_OAbs(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(f64,axiom,
c_InductTermi_OIT(v_ua______),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).
fof(f64_nnf,plain,
c_InductTermi_OIT(v_ua______),
inference(nnf_transformation,[status(thm)],[f64]) ).
cnf(c64,plain,
c_InductTermi_OIT(v_ua______),
inference(cnf_transformation,[status(esa)],[f64_nnf]) ).
cnf(hi42,axiom,
c_InductTermi_OIT(v_ua______) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t14,plain,
c_InductTermi_OIT(c_Lambda_OdB_OAbs(v_ua______)) = true,
inference(hyper_resolution,[status(thm)],[hi43,hi42]) ).
cnf(t496,plain,
c_InductTermi_OIT(c_Lambda_OdB_OAbs(v_ua______)) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(f69,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),v_a____,V_T_H)
| ~ c_InductTermi_OIT(V_u)
| ~ c_Type_Otyping(V_e,V_u,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_u,V_i)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f69_nnf,plain,
! [V_u,V_i,V_e,V_T_H] :
( ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),v_a____,V_T_H)
| ~ c_InductTermi_OIT(V_u)
| ~ c_Type_Otyping(V_e,V_u,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_u,V_i)) ),
inference(nnf_transformation,[status(thm)],[f69]) ).
fof(f69_sk,plain,
! [V_u,V_i,V_e,V_T_H] :
( ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),v_a____,V_T_H)
| ~ c_InductTermi_OIT(V_u)
| ~ c_Type_Otyping(V_e,V_u,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_u,V_i)) ),
inference(skolemisation,[status(esa)],[f69_nnf]) ).
cnf(c69,plain,
( ~ c_Type_Otyping(c_Type_Oshift(X2,X1,v_T____,tc_Type_Otype),v_a____,X3)
| ~ c_InductTermi_OIT(X0)
| ~ c_Type_Otyping(X2,X0,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_a____,X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f69_sk]) ).
cnf(hi47,axiom,
ifeq(c_Type_Otyping(X0,X1,v_T____),true,ifeq(c_InductTermi_OIT(X1),true,ifeq(c_Type_Otyping(c_Type_Oshift(X0,X2,v_T____,tc_Type_Otype),v_a____,X3),true,c_InductTermi_OIT(c_Lambda_Osubst(v_a____,X1,X2)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c69]) ).
cnf(f70,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f70_nnf,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(nnf_transformation,[status(thm)],[f70]) ).
cnf(c70,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(cnf_transformation,[status(esa)],[f70_nnf]) ).
cnf(hi48,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____) = true,
inference(equality_encoding,[status(esa)],[c70]) ).
cnf(f71,axiom,
c_InductTermi_OIT(v_u____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
fof(f71_nnf,plain,
c_InductTermi_OIT(v_u____),
inference(nnf_transformation,[status(thm)],[f71]) ).
cnf(c71,plain,
c_InductTermi_OIT(v_u____),
inference(cnf_transformation,[status(esa)],[f71_nnf]) ).
cnf(hi49,axiom,
c_InductTermi_OIT(v_u____) = true,
inference(equality_encoding,[status(esa)],[c71]) ).
cnf(f72,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/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_03) ).
fof(f72_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)],[f72]) ).
cnf(c72,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)],[f72_nnf]) ).
cnf(hi50,axiom,
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)],[c72]) ).
cnf(t44,plain,
c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)) = true,
inference(hyper_resolution,[status(thm)],[hi47,hi48,hi49,hi50]) ).
cnf(t602,plain,
c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)) = true,
inference(orient,[status(thm)],[t44]) ).
cnf(t49,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t217,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t49]) ).
cnf(f0,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(f0_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)],[f0]) ).
fof(f0_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)],[f0_nnf]) ).
cnf(c0,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)],[f0_sk]) ).
cnf(f5,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(f5_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)],[f5]) ).
fof(f5_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)],[f5_nnf]) ).
cnf(c5,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)],[f5_sk]) ).
cnf(f6,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(f6_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)],[f6]) ).
fof(f6_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)],[f6_nnf]) ).
cnf(c6,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)],[f6_sk]) ).
cnf(f7,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(f7_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)],[f7]) ).
fof(f7_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)],[f7_nnf]) ).
cnf(c7,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)],[f7_sk]) ).
cnf(f8,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(f8_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)],[f8]) ).
fof(f8_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)],[f8_nnf]) ).
cnf(c8,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)],[f8_sk]) ).
cnf(f9,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(f9_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)],[f9]) ).
fof(f9_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)],[f9_nnf]) ).
cnf(c9,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)],[f9_sk]) ).
cnf(f20,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(f20_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)],[f20]) ).
fof(f20_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)],[f20_nnf]) ).
cnf(c20,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(f21,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(f21_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)],[f21]) ).
fof(f21_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)],[f21_nnf]) ).
cnf(c21,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(f22,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(f22_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)],[f22]) ).
fof(f22_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)],[f22_nnf]) ).
cnf(c22,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(f23,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(f23_nnf,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(f24,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(f24_nnf,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(f27,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(f27_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)],[f27]) ).
fof(f27_sk,plain,
! [V_m] : ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(f28,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(f28_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)],[f28]) ).
fof(f28_sk,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(f29,axiom,
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(f29_nnf,plain,
! [V_dB1_H,V_dB2_H,V_nat] : c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [V_dB1_H,V_dB2_H,V_nat] : c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
c_Lambda_OdB_OApp(X0,X1) != c_Lambda_OdB_OVar(X2),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(f33,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(f33_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)],[f33]) ).
fof(f33_sk,plain,
! [V_xs,V_x,T_a] : V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c33,plain,
X0 != c_List_Olist_OCons(X1,X0,X2),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(f34,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(f34_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)],[f34]) ).
fof(f34_sk,plain,
! [V_x,V_t,T_a] : c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c34,plain,
c_List_Olist_OCons(X0,X1,X2) != X1,
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(f42,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(f42_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)],[f42]) ).
fof(f42_sk,plain,
! [V_nat,V_dB_H] : c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
c_Lambda_OdB_OVar(X0) != c_Lambda_OdB_OAbs(X1),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(f44,axiom,
c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
fof(f44_nnf,plain,
! [V_nat,V_dB1_H,V_dB2_H] : c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [V_nat,V_dB1_H,V_dB2_H] : c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
c_Lambda_OdB_OVar(X0) != c_Lambda_OdB_OApp(X1,X2),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(f48,axiom,
~ 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(f48_nnf,plain,
! [V_i,V_t] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [V_i,V_t] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c48,plain,
~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X0),X1),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(f53,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
fof(f53_nnf,plain,
! [V_dB_H,V_dB1,V_dB2] : c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2),
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
! [V_dB_H,V_dB1,V_dB2] : c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2),
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c53,plain,
c_Lambda_OdB_OAbs(X0) != c_Lambda_OdB_OApp(X1,X2),
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
cnf(f55,axiom,
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(f55_nnf,plain,
! [V_dB1,V_dB2,V_dB_H] : c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [V_dB1,V_dB2,V_dB_H] : c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c55,plain,
c_Lambda_OdB_OApp(X0,X1) != c_Lambda_OdB_OAbs(X2),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(f56,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(f56_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)],[f56]) ).
fof(f56_sk,plain,
! [V_dB_H,V_nat] : c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
c_Lambda_OdB_OAbs(X0) != c_Lambda_OdB_OVar(X1),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(f73,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f73_nnf,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c5,c6,c7,c8,c9,c20,c21,c22,c23,c24,c27,c28,c29,c33,c34,c42,c44,c48,c53,c55,c56,c73]) ).
cnf(g0_0,plain,
true != ifeq(c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),true,false,c_InductTermi_OIT(c_Lambda_OdB_OAbs(v_ua______))),
inference(rw,[status(thm)],[g0_0,t496]) ).
cnf(g0_2,plain,
true != ifeq(c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),false,c_InductTermi_OIT(c_Lambda_OdB_OAbs(v_ua______))),
inference(rw,[status(thm)],[g0_1,t602]) ).
cnf(g0_3,plain,
true != false,
inference(rw,[status(thm)],[g0_2,t217]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL798-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/1.01 % Computer : n011.cluster.edu
% 0.06/1.01 % Model : x86_64 x86_64
% 0.06/1.01 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/1.01 % Memory : 8046.5625MB
% 0.06/1.01 % OS : Linux 6.8.0-71-generic
% 0.06/1.01 % CPULimit : 300
% 0.06/1.01 % WCLimit : 300
% 0.06/1.01 % DateTime : Thu Sep 24 00:30:58 UTC 2026
% 0.06/1.01 % CPUTime :
% 0.06/1.02 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 11.47/2.66 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.47/2.66 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------