%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL753-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 : Sun Sep 27 07:59:38 AM UTC 2026
% Result : Unsatisfiable 10.63s 2.20s
% Output : CNFRefutation 10.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 23 unt; 0 def)
% Number of atoms : 39 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 7 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 47 ( 7 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_One__nat__def_0,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('theBenchmark.p',cls_One__nat__def_0) ).
cnf(c_419,plain,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(clausify,[status(thm)],[cls_One__nat__def_0]) ).
fof(cls_add__Suc__right_0,axiom,
! [VAR_0,VAR_1] : c_HOL_Oplus__class_Oplus(VAR_0,c_Suc(VAR_1),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(VAR_0,VAR_1,tc_nat)),
file('theBenchmark.p',cls_add__Suc__right_0) ).
cnf(c_455,plain,
c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(A,B,tc_nat)),
inference(clausify,[status(thm)],[cls_add__Suc__right_0]) ).
fof(cls_gr__implies__not0_0,axiom,
! [VAR_0] : ~ c_HOL_Oord__class_Oless(VAR_0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_gr__implies__not0_0) ).
cnf(c_521,plain,
~ c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(clausify,[status(thm)],[cls_gr__implies__not0_0]) ).
fof(cls_natgb_Oadd__r0__iff_1,axiom,
! [VAR_0] : VAR_0 = c_HOL_Oplus__class_Oplus(VAR_0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
cnf(c_589,plain,
A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(clausify,[status(thm)],[cls_natgb_Oadd__r0__iff_1]) ).
cnf(c_590,plain,
c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A,
inference(copy,[status(thm)],[c_589]) ).
fof(cls_subst__Abs_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(VAR_0),VAR_1,VAR_2) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(VAR_0,c_Lambda_Olift(VAR_1,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(VAR_2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
file('theBenchmark.p',cls_subst__Abs_0) ).
cnf(c_615,plain,
c_Lambda_Osubst(c_Lambda_OdB_OAbs(A),B,C) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(A,c_Lambda_Olift(B,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(C,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
inference(clausify,[status(thm)],[cls_subst__Abs_0]) ).
cnf(c_5993,plain,
c_Lambda_Osubst(c_Lambda_OdB_OAbs(A),B,C) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(A,c_Lambda_Olift(B,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(C,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
inference(paramod,[status(thm)],[c_419,c_615]) ).
cnf(c_5994,plain,
c_Lambda_Osubst(c_Lambda_OdB_OAbs(A),B,C) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(A,c_Lambda_Olift(B,c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Oplus__class_Oplus(C,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
inference(paramod,[status(thm)],[c_455,c_5993]) ).
cnf(c_616,plain,
c_Lambda_Osubst(c_Lambda_OdB_OAbs(A),B,C) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(A,c_Lambda_Olift(B,c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(C))),
inference(paramod,[status(thm)],[c_590,c_5994]) ).
fof(cls_lift_Osimps_I1_J_1,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Oord__class_Oless(VAR_0,VAR_1,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(VAR_0),VAR_1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(VAR_0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
file('theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
cnf(c_622,plain,
( c_HOL_Oord__class_Oless(A,B,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(A),B) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
inference(clausify,[status(thm)],[cls_lift_Osimps_I1_J_1]) ).
cnf(c_5995,plain,
( c_HOL_Oord__class_Oless(A,B,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(A),B) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) ),
inference(paramod,[status(thm)],[c_419,c_622]) ).
cnf(c_5996,plain,
( c_HOL_Oord__class_Oless(A,B,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(A),B) = c_Lambda_OdB_OVar(c_Suc(c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(paramod,[status(thm)],[c_455,c_5995]) ).
cnf(c_5997,plain,
( c_HOL_Oord__class_Oless(A,B,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(A),B) = c_Lambda_OdB_OVar(c_Suc(A)) ),
inference(paramod,[status(thm)],[c_590,c_5996]) ).
cnf(c_623,plain,
( c_HOL_Oord__class_Oless(A,B,tc_nat)
| c_Lambda_OdB_OVar(c_Suc(A)) = c_Lambda_Olift(c_Lambda_OdB_OVar(A),B) ),
inference(copy,[status(thm)],[c_5997]) ).
fof(cls_Lambda_0,axiom,
! [VAR_0] :
( ~ c_InductTermi_OIT(VAR_0)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(VAR_0)) ),
file('theBenchmark.p',cls_Lambda_0) ).
cnf(c_672,plain,
( ~ c_InductTermi_OIT(A)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(A)) ),
inference(clausify,[status(thm)],[cls_Lambda_0]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0,VAR_1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(VAR_0),VAR_1)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_676,plain,
c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(A),B)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_677,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_678,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(v_ia),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(v_ja)))),
inference(paramod,[status(thm)],[c_616,c_677]) ).
cnf(c_1997,plain,
c_Lambda_OdB_OVar(c_Suc(A)) = c_Lambda_Olift(c_Lambda_OdB_OVar(A),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(resolve,[status(thm)],[c_623,c_521]) ).
cnf(c_2406,plain,
c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(A),B))),
inference(resolve,[status(thm)],[c_676,c_672]) ).
cnf(c_5991,plain,
c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(A),c_HOL_Ozero__class_Ozero(tc_nat)),B))),
inference(paramod,[status(thm)],[c_1997,c_2406]) ).
cnf(c_5992,plain,
$false,
inference(resolve,[status(thm)],[c_5991,c_678]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL753-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 23:29:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 524341 was started by sandbox2 on n005,
% 0.10/0.37 % Fri Sep 25 23:29:31 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 10.63/2.20
% 10.63/2.20 % SZS status Unsatisfiable for theBenchmark
% 10.63/2.20
% 10.63/2.20 % Proof 1 at 1.56 (+ 0.23) seconds.
% 10.63/2.20 % Length of proof is 17.
% 10.63/2.20 % Level of proof is 5.
% 10.63/2.20 % Maximum clause weight is 15.000.
% 10.63/2.20 % Given clauses 488.
% 10.63/2.20
% 10.63/2.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------