%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL756-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 02:08:18 PM UTC 2026
% Result : Unsatisfiable 2.58s 1.38s
% Output : CNFRefutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 7 ( 7 unt; 0 def)
% Number of atoms : 7 ( 1 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 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 : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 5 ( 0 sgn 5 !; 0 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
fof(f118,axiom,
! [X0] : c_Suc(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
fof(f860,negated_conjecture,
! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X0),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f861,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f995,plain,
~ c_InductTermi_OIT(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,f118,f118]) ).
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_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_3254,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1405,c_1404]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL756-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.41 % Computer : n014.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Thu Sep 24 00:26:33 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.49
% 0.16/0.49 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.49
% 0.16/0.49 % Detected problem language: tptp
% 0.22/0.51 % Proving...
% 2.58/1.38 % SZS status Started for theBenchmark.p
% 2.58/1.38 % SZS status Unsatisfiable for theBenchmark.p
% 2.58/1.38
% 2.58/1.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.58/1.38
% 2.58/1.38 % ------ iProver source info
% 2.58/1.38
% 2.58/1.38 % git: date: 2026-07-19 20:42:38 +0200
% 2.58/1.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.58/1.38 % git: non_committed_changes: false
% 2.58/1.38
% 2.58/1.38 % ------ Parsing...% successful
% 2.58/1.38
% 2.58/1.38
% 2.58/1.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.58/1.38
% 2.58/1.38 % ------ Preprocessing...%
% 2.58/1.38
% 2.58/1.38 % SZS status Unsatisfiable for theBenchmark.p
% 2.58/1.38
% 2.58/1.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.58/1.38
% 2.58/1.38
%------------------------------------------------------------------------------