%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG014+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 : 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 : Fri Sep 25 12:53:10 PM UTC 2026
% Result : Theorem 1.43s 1.49s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 65 ( 6 unt; 3 def)
% Number of atoms : 305 ( 241 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 356 ( 116 ~; 143 |; 97 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( ( unit = e3
| unit = e2
| unit = e1
| unit = e0 )
& op(e3,unit) = e3
& op(unit,e3) = e3
& op(e2,unit) = e2
& op(unit,e2) = e2
& op(e1,unit) = e1
& op(unit,e1) = e1
& op(e0,unit) = e0
& op(unit,e0) = e0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f5,axiom,
unit = e0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
fof(f12,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(f13,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)],[f12]) ).
fof(f15,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 ) )
& ( 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) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f20,plain,
( ~ sP2
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f21,plain,
( ~ sP1
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f110,plain,
e0 = op(e0,unit),
inference(cnf_transformation,[],[f3]) ).
fof(f124,plain,
e0 = unit,
inference(cnf_transformation,[],[f5]) ).
fof(f206,plain,
( ~ sP2
| e1 = op(e3,e3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f207,plain,
( ~ sP2
| e1 = op(e2,e2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f208,plain,
( ~ sP2
| e1 = op(e1,e1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f209,plain,
( ~ sP2
| op(e0,e0) = e1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f210,plain,
( ~ sP1
| e2 = op(e3,e3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f211,plain,
( ~ sP1
| e2 = op(e2,e2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f212,plain,
( ~ sP1
| e2 = op(e1,e1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f213,plain,
( ~ sP1
| op(e0,e0) = e2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f218,plain,
( sP0
| sP1
| sP2
| e0 = op(e3,e3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f219,plain,
( sP0
| sP1
| sP2
| e0 = op(e2,e2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f220,plain,
( sP0
| sP1
| sP2
| e0 = op(e1,e1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f222,plain,
( e3 != op(e3,e3)
| e3 != op(e2,e2)
| e3 != op(e1,e1)
| op(e0,e0) != e3 ),
inference(cnf_transformation,[],[f19]) ).
fof(f223,plain,
( e2 != op(e3,e3)
| e2 != op(e2,e2)
| e2 != op(e1,e1)
| op(e0,e0) != e2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f224,plain,
( e1 != op(e3,e3)
| e1 != op(e2,e2)
| e1 != op(e1,e1)
| op(e0,e0) != e1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f225,plain,
( e0 != op(e3,e3)
| e0 != op(e2,e2)
| e0 != op(e1,e1)
| e0 != op(e0,e0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f280,plain,
unit = op(unit,unit),
inference(definition_unfolding,[],[f110,f124,f124]) ).
fof(f332,plain,
( ~ sP2
| e1 = op(unit,unit) ),
inference(definition_unfolding,[],[f209,f124,f124]) ).
fof(f333,plain,
( ~ sP1
| e2 = op(unit,unit) ),
inference(definition_unfolding,[],[f213,f124,f124]) ).
fof(f335,plain,
( op(e3,e3) != unit
| op(e2,e2) != unit
| op(e1,e1) != unit
| unit != op(unit,unit) ),
inference(definition_unfolding,[],[f225,f124,f124,f124,f124,f124,f124]) ).
fof(f336,plain,
( e1 != op(e3,e3)
| e1 != op(e2,e2)
| e1 != op(e1,e1)
| e1 != op(unit,unit) ),
inference(definition_unfolding,[],[f224,f124,f124]) ).
fof(f337,plain,
( e2 != op(e3,e3)
| e2 != op(e2,e2)
| e2 != op(e1,e1)
| e2 != op(unit,unit) ),
inference(definition_unfolding,[],[f223,f124,f124]) ).
fof(f338,plain,
( e3 != op(e3,e3)
| e3 != op(e2,e2)
| e3 != op(e1,e1)
| e3 != op(unit,unit) ),
inference(definition_unfolding,[],[f222,f124,f124]) ).
fof(f340,plain,
( sP0
| sP1
| sP2
| op(e1,e1) = unit ),
inference(definition_unfolding,[],[f220,f124]) ).
fof(f341,plain,
( sP0
| sP1
| sP2
| op(e2,e2) = unit ),
inference(definition_unfolding,[],[f219,f124]) ).
fof(f342,plain,
( sP0
| sP1
| sP2
| op(e3,e3) = unit ),
inference(definition_unfolding,[],[f218,f124]) ).
tcf(c_130,plain,
op(unit,unit) = unit,
inference(cnf_transformation,[],[f280]) ).
tcf(c_226,plain,
( ( op(unit,unit) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f332]) ).
tcf(c_227,plain,
( ( op(e1,e1) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_228,plain,
( ( op(e2,e2) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_229,plain,
( ( op(e3,e3) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_230,plain,
( ( op(unit,unit) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f333]) ).
tcf(c_231,plain,
( ( op(e1,e1) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_232,plain,
( ( op(e2,e2) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_233,plain,
( ( op(e3,e3) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_238,negated_conjecture,
( ( op(e3,e3) != unit )
| ( op(e2,e2) != unit )
| ( op(e1,e1) != unit )
| ( op(unit,unit) != unit ) ),
inference(cnf_transformation,[],[f335]) ).
tcf(c_239,negated_conjecture,
( ( op(e3,e3) != e1 )
| ( op(e2,e2) != e1 )
| ( op(e1,e1) != e1 )
| ( op(unit,unit) != e1 ) ),
inference(cnf_transformation,[],[f336]) ).
tcf(c_240,negated_conjecture,
( ( op(e3,e3) != e2 )
| ( op(e2,e2) != e2 )
| ( op(e1,e1) != e2 )
| ( op(unit,unit) != e2 ) ),
inference(cnf_transformation,[],[f337]) ).
tcf(c_241,negated_conjecture,
( ( op(e3,e3) != e3 )
| ( op(e2,e2) != e3 )
| ( op(e1,e1) != e3 )
| ( op(unit,unit) != e3 ) ),
inference(cnf_transformation,[],[f338]) ).
tcf(c_243,negated_conjecture,
( sP0
| sP1
| sP2
| ( op(e1,e1) = unit ) ),
inference(cnf_transformation,[],[f340]) ).
tcf(c_244,negated_conjecture,
( sP0
| sP1
| sP2
| ( op(e2,e2) = unit ) ),
inference(cnf_transformation,[],[f341]) ).
tcf(c_245,negated_conjecture,
( sP0
| sP1
| sP2
| ( op(e3,e3) = unit ) ),
inference(cnf_transformation,[],[f342]) ).
fof(f16,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(f17,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(f18,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(f19,plain,
( ( sP0
| sP1
| sP2
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) )
& ( 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) ) ),
inference(definition_folding,[],[f15,f18,f17,f16]) ).
fof(f22,plain,
( ~ sP0
| ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f214,plain,
( ~ sP0
| e3 = op(e3,e3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f215,plain,
( ~ sP0
| e3 = op(e2,e2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f216,plain,
( ~ sP0
| e3 = op(e1,e1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f217,plain,
( ~ sP0
| op(e0,e0) = e3 ),
inference(cnf_transformation,[],[f22]) ).
fof(f334,plain,
( ~ sP0
| e3 = op(unit,unit) ),
inference(definition_unfolding,[],[f217,f124,f124]) ).
tcf(c_234,plain,
( ( op(unit,unit) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f334]) ).
tcf(c_235,plain,
( ( op(e1,e1) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_236,plain,
( ( op(e2,e2) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_237,plain,
( ( op(e3,e3) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_246,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_238,c_239,c_240,c_241,c_243,c_244,c_245,c_226,c_227,c_228,c_229,c_230,c_231,c_232,c_233,c_234,c_235,c_236,c_237,c_130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG014+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.57 % Computer : n005.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Fri Sep 25 04:31:48 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.60 Running first-order theorem proving
% 0.10/0.60 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
% 0.10/0.62
% 0.10/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.62
% 0.10/0.62 % Detected problem language: tptp
% 0.15/0.63 % Proving...
% 1.43/1.49 % SZS status Started for theBenchmark.p
% 1.43/1.49 % SZS status Theorem for theBenchmark.p
% 1.43/1.49
% 1.43/1.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.43/1.49
% 1.43/1.49 % ------ iProver source info
% 1.43/1.49
% 1.43/1.49 % git: date: 2026-07-19 20:42:38 +0200
% 1.43/1.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.43/1.49 % git: non_committed_changes: false
% 1.43/1.49
% 1.43/1.49 % ------ Parsing...
% 1.43/1.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.43/1.49
% 1.43/1.49 % ------ Preprocessing...%
% 1.43/1.49
% 1.43/1.49 % SZS status Theorem for theBenchmark.p
% 1.43/1.49
% 1.43/1.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.43/1.49
% 1.43/1.49
%------------------------------------------------------------------------------