%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL755-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n001.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 02:08:17 PM UTC 2026
% Result : Unsatisfiable 3.41s 1.75s
% Output : CNFRefutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 13 ( 11 unt; 0 def)
% Number of atoms : 15 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 7 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 11 ( 0 sgn 11 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f115,axiom,
! [X0] : c_Suc(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
fof(f845,axiom,
! [X0] :
( ~ c_InductTermi_OIT(X0)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
fof(f860,negated_conjecture,
! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X0),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f861,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f995,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_ia,tc_nat)),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_ja,tc_nat)))),
inference(definition_unfolding,[],[f861,f115,f115]) ).
tcf(c_831,plain,
! [X0: $i,X1: $i] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),
inference(cnf_transformation,[],[f35]) ).
tcf(c_1390,plain,
! [X0: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X0))
| ~ c_InductTermi_OIT(X0) ),
inference(cnf_transformation,[],[f845]) ).
tcf(c_1404,negated_conjecture,
! [X0: $i,X1: $i] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X0),X1)),
inference(cnf_transformation,[],[f860]) ).
tcf(c_1405,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_ia,tc_nat)),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_ja,tc_nat)))),
inference(cnf_transformation,[],[f995]) ).
tcf(c_1838,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oplus__class_Oplus(v_ja,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))),
inference(demodulation,[status(thm)],[c_1405,c_831]) ).
tcf(c_1839,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oplus__class_Oplus(v_ja,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
inference(superposition,[status(thm)],[c_1390,c_1838]) ).
tcf(c_5301,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1839,c_1404]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL755-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.41 % Computer : n001.cluster.edu
% 0.18/0.41 % Model : x86_64 x86_64
% 0.18/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.41 % Memory : 8046.5625MB
% 0.18/0.41 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Thu Sep 24 00:31:52 UTC 2026
% 0.18/0.42 % CPUTime :
% 0.18/0.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.46 Running first-order theorem proving
% 0.18/0.46 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.47
% 0.18/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.18/0.47
% 0.18/0.47 % Detected problem language: tptp
% 0.18/0.48 % Proving...
% 3.41/1.75 % SZS status Started for theBenchmark.p
% 3.41/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 3.41/1.75
% 3.41/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.41/1.75
% 3.41/1.75 % ------ iProver source info
% 3.41/1.75
% 3.41/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 3.41/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.41/1.75 % git: non_committed_changes: false
% 3.41/1.75
% 3.41/1.75 % ------ Parsing...% successful
% 3.41/1.75
% 3.41/1.75
% 3.41/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.41/1.75 % ------ Proving...
% 3.41/1.75 % ------ Problem Properties
% 3.41/1.75
% 3.41/1.75 %
% 3.41/1.75 % clauses 632
% 3.41/1.75 % conjectures 3
% 3.41/1.75 % EPR 89
% 3.41/1.75 % Horn 566
% 3.41/1.75 % unary 147
% 3.41/1.75 % binary 254
% 3.41/1.75 % lits 1461
% 3.41/1.75 % lits eq 383
% 3.41/1.75 % fd_pure 0
% 3.41/1.75 % fd_pseudo 0
% 3.41/1.75 % fd_cond 25
% 3.41/1.75 % fd_pseudo_cond 56
% 3.41/1.75 % AC symbols 0
% 3.41/1.75
% 3.41/1.75 % ------ Input Options Time Limit: Unbounded
% 3.41/1.75
% 3.41/1.75
% 3.41/1.75 % ------
% 3.41/1.75 % Current options:
% 3.41/1.75 % ------
% 3.41/1.75
% 3.41/1.75
% 3.41/1.75 %
% 3.41/1.75
% 3.41/1.75 % ------ Proving...
% 3.41/1.75 %
% 3.41/1.75
% 3.41/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 3.41/1.75
% 3.41/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.41/1.75
% 3.41/1.75
%------------------------------------------------------------------------------