%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG039+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 12:53:15 PM UTC 2026
% Result : Theorem 0.47s 1.28s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 3 unt; 3 def)
% Number of atoms : 322 ( 270 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 384 ( 116 ~; 135 |; 133 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
( e2 = op(e3,e1)
& e0 = op(e1,e1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(f7,conjecture,
~ ( ~ ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) )
& ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f8,negated_conjecture,
~ ~ ( ~ ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) )
& ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
( ~ ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) )
& ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
( ( e3 != op(e3,e3)
| e3 != op(e2,e2)
| e3 != op(e1,e1)
| op(e0,e0) != e3 )
& ( e2 != op(e3,e3)
| e2 != op(e2,e2)
| e2 != op(e1,e1)
| op(e0,e0) != e2 )
& ( e1 != op(e3,e3)
| e1 != op(e2,e2)
| e1 != op(e1,e1)
| op(e0,e0) != e1 )
& ( e0 != op(e3,e3)
| e0 != op(e2,e2)
| e0 != op(e1,e1)
| e0 != op(e0,e0) )
& ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f11,plain,
( ( e3 != op(e3,e3)
| e3 != op(e2,e2)
| e3 != op(e1,e1)
| op(e0,e0) != e3 )
& ( e2 != op(e3,e3)
| e2 != op(e2,e2)
| e2 != op(e1,e1)
| op(e0,e0) != e2 )
& ( e1 != op(e3,e3)
| e1 != op(e2,e2)
| e1 != op(e1,e1)
| op(e0,e0) != e1 )
& ( e0 != op(e3,e3)
| e0 != op(e2,e2)
| e0 != op(e1,e1)
| e0 != op(e0,e0) )
& ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ) ),
inference(flattening,[],[f10]) ).
fof(f16,plain,
( ~ sP2
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f17,plain,
( ~ sP1
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f131,plain,
e0 = op(e1,e1),
inference(cnf_transformation,[],[f6]) ).
fof(f132,plain,
( ~ sP2
| e1 = op(e3,e3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f133,plain,
( ~ sP2
| e1 = op(e2,e2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f134,plain,
( ~ sP2
| e1 = op(e1,e1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f135,plain,
( ~ sP2
| op(e0,e0) = e1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f136,plain,
( ~ sP1
| e2 = op(e3,e3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f137,plain,
( ~ sP1
| e2 = op(e2,e2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f138,plain,
( ~ sP1
| e2 = op(e1,e1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f139,plain,
( ~ sP1
| op(e0,e0) = e2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f144,plain,
( e3 != op(e3,e3)
| e3 != op(e2,e2)
| e3 != op(e1,e1)
| op(e0,e0) != e3 ),
inference(cnf_transformation,[],[f15]) ).
fof(f145,plain,
( e2 != op(e3,e3)
| e2 != op(e2,e2)
| e2 != op(e1,e1)
| op(e0,e0) != e2 ),
inference(cnf_transformation,[],[f15]) ).
fof(f146,plain,
( e1 != op(e3,e3)
| e1 != op(e2,e2)
| e1 != op(e1,e1)
| op(e0,e0) != e1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f147,plain,
( e0 != op(e3,e3)
| e0 != op(e2,e2)
| e0 != op(e1,e1)
| e0 != op(e0,e0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f148,plain,
( sP0
| sP1
| sP2
| e0 = op(e3,e3) ),
inference(cnf_transformation,[],[f15]) ).
fof(f149,plain,
( sP0
| sP1
| sP2
| e0 = op(e2,e2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f151,plain,
( sP0
| sP1
| sP2
| e0 = op(e0,e0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_160,plain,
op(e1,e1) = e0,
inference(cnf_transformation,[],[f131]) ).
tcf(c_162,plain,
( ( op(e0,e0) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_163,plain,
( ( op(e1,e1) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_164,plain,
( ( op(e2,e2) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_165,plain,
( ( op(e3,e3) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_166,plain,
( ( op(e0,e0) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_167,plain,
( ( op(e1,e1) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_168,plain,
( ( op(e2,e2) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_169,plain,
( ( op(e3,e3) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_174,negated_conjecture,
( sP0
| sP1
| sP2
| ( op(e0,e0) = e0 ) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_176,negated_conjecture,
( sP0
| sP1
| sP2
| ( op(e2,e2) = e0 ) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_177,negated_conjecture,
( sP0
| sP1
| sP2
| ( op(e3,e3) = e0 ) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_178,negated_conjecture,
( ( op(e3,e3) != e0 )
| ( op(e2,e2) != e0 )
| ( op(e1,e1) != e0 )
| ( op(e0,e0) != e0 ) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_179,negated_conjecture,
( ( op(e3,e3) != e1 )
| ( op(e2,e2) != e1 )
| ( op(e1,e1) != e1 )
| ( op(e0,e0) != e1 ) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_180,negated_conjecture,
( ( op(e3,e3) != e2 )
| ( op(e2,e2) != e2 )
| ( op(e1,e1) != e2 )
| ( op(e0,e0) != e2 ) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_181,negated_conjecture,
( ( op(e3,e3) != e3 )
| ( op(e2,e2) != e3 )
| ( op(e1,e1) != e3 )
| ( op(e0,e0) != e3 ) ),
inference(cnf_transformation,[],[f144]) ).
fof(f12,definition,
( ~ sP0
| ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f13,definition,
( ~ sP1
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f14,definition,
( ~ sP2
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f15,plain,
( ( e3 != op(e3,e3)
| e3 != op(e2,e2)
| e3 != op(e1,e1)
| op(e0,e0) != e3 )
& ( e2 != op(e3,e3)
| e2 != op(e2,e2)
| e2 != op(e1,e1)
| op(e0,e0) != e2 )
& ( e1 != op(e3,e3)
| e1 != op(e2,e2)
| e1 != op(e1,e1)
| op(e0,e0) != e1 )
& ( e0 != op(e3,e3)
| e0 != op(e2,e2)
| e0 != op(e1,e1)
| e0 != op(e0,e0) )
& ( sP0
| sP1
| sP2
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ) ),
inference(definition_folding,[],[f11,f14,f13,f12]) ).
fof(f18,plain,
( ~ sP0
| ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f140,plain,
( ~ sP0
| e3 = op(e3,e3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f141,plain,
( ~ sP0
| e3 = op(e2,e2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f142,plain,
( ~ sP0
| e3 = op(e1,e1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f143,plain,
( ~ sP0
| op(e0,e0) = e3 ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_170,plain,
( ( op(e0,e0) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_171,plain,
( ( op(e1,e1) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_172,plain,
( ( op(e2,e2) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_173,plain,
( ( op(e3,e3) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_182,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_178,c_179,c_180,c_181,c_174,c_176,c_177,c_162,c_163,c_164,c_165,c_166,c_167,c_168,c_169,c_170,c_171,c_172,c_173,c_160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG039+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.42 % Computer : n014.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 04:36:32 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.48 Running first-order theorem proving
% 0.16/0.48 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
% 0.23/0.50
% 0.23/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.50
% 0.23/0.50 % Detected problem language: tptp
% 0.23/0.51 % Proving...
% 0.47/1.28 % SZS status Started for theBenchmark.p
% 0.47/1.28 % SZS status Theorem for theBenchmark.p
% 0.47/1.28
% 0.47/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.47/1.28
% 0.47/1.28 % ------ iProver source info
% 0.47/1.28
% 0.47/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.47/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.47/1.28 % git: non_committed_changes: false
% 0.47/1.28
% 0.47/1.28 % ------ Parsing...
% 0.47/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.47/1.28
% 0.47/1.28 % ------ Preprocessing...%
% 0.47/1.28
% 0.47/1.28 % SZS status Theorem for theBenchmark.p
% 0.47/1.28
% 0.47/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.47/1.28
% 0.47/1.28
%------------------------------------------------------------------------------