%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG036+1 : TPTP v9.3.1. Released v2.7.0.
% 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 12:53:14 PM UTC 2026
% Result : Theorem 1.38s 1.14s
% Output : CNFRefutation 1.38s
% 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(f2,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/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f4,axiom,
unit = e0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
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/sandbox2/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 ) )
& ( 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,[],[f8]) ).
fof(f14,plain,
( ~ sP2
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f15,plain,
( ~ sP1
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f40,plain,
e0 = op(e0,unit),
inference(cnf_transformation,[],[f2]) ).
fof(f74,plain,
e0 = unit,
inference(cnf_transformation,[],[f4]) ).
fof(f129,plain,
( ~ sP2
| e1 = op(e3,e3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f130,plain,
( ~ sP2
| e1 = op(e2,e2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f131,plain,
( ~ sP2
| e1 = op(e1,e1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f132,plain,
( ~ sP2
| op(e0,e0) = e1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f133,plain,
( ~ sP1
| e2 = op(e3,e3) ),
inference(cnf_transformation,[],[f15]) ).
fof(f134,plain,
( ~ sP1
| e2 = op(e2,e2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f135,plain,
( ~ sP1
| e2 = op(e1,e1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f136,plain,
( ~ sP1
| op(e0,e0) = e2 ),
inference(cnf_transformation,[],[f15]) ).
fof(f141,plain,
( sP0
| sP1
| sP2
| e0 = op(e3,e3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f142,plain,
( sP0
| sP1
| sP2
| e0 = op(e2,e2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f143,plain,
( sP0
| sP1
| sP2
| e0 = op(e1,e1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f145,plain,
( e3 != op(e3,e3)
| e3 != op(e2,e2)
| e3 != op(e1,e1)
| op(e0,e0) != e3 ),
inference(cnf_transformation,[],[f13]) ).
fof(f146,plain,
( e2 != op(e3,e3)
| e2 != op(e2,e2)
| e2 != op(e1,e1)
| op(e0,e0) != e2 ),
inference(cnf_transformation,[],[f13]) ).
fof(f147,plain,
( e1 != op(e3,e3)
| e1 != op(e2,e2)
| e1 != op(e1,e1)
| op(e0,e0) != e1 ),
inference(cnf_transformation,[],[f13]) ).
fof(f148,plain,
( e0 != op(e3,e3)
| e0 != op(e2,e2)
| e0 != op(e1,e1)
| e0 != op(e0,e0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f166,plain,
unit = op(unit,unit),
inference(definition_unfolding,[],[f40,f74,f74]) ).
fof(f233,plain,
( ~ sP2
| e1 = op(unit,unit) ),
inference(definition_unfolding,[],[f132,f74,f74]) ).
fof(f234,plain,
( ~ sP1
| e2 = op(unit,unit) ),
inference(definition_unfolding,[],[f136,f74,f74]) ).
fof(f236,plain,
( op(e3,e3) != unit
| op(e2,e2) != unit
| op(e1,e1) != unit
| unit != op(unit,unit) ),
inference(definition_unfolding,[],[f148,f74,f74,f74,f74,f74,f74]) ).
fof(f237,plain,
( e1 != op(e3,e3)
| e1 != op(e2,e2)
| e1 != op(e1,e1)
| e1 != op(unit,unit) ),
inference(definition_unfolding,[],[f147,f74,f74]) ).
fof(f238,plain,
( e2 != op(e3,e3)
| e2 != op(e2,e2)
| e2 != op(e1,e1)
| e2 != op(unit,unit) ),
inference(definition_unfolding,[],[f146,f74,f74]) ).
fof(f239,plain,
( e3 != op(e3,e3)
| e3 != op(e2,e2)
| e3 != op(e1,e1)
| e3 != op(unit,unit) ),
inference(definition_unfolding,[],[f145,f74,f74]) ).
fof(f241,plain,
( sP0
| sP1
| sP2
| op(e1,e1) = unit ),
inference(definition_unfolding,[],[f143,f74]) ).
fof(f242,plain,
( sP0
| sP1
| sP2
| op(e2,e2) = unit ),
inference(definition_unfolding,[],[f142,f74]) ).
fof(f243,plain,
( sP0
| sP1
| sP2
| op(e3,e3) = unit ),
inference(definition_unfolding,[],[f141,f74]) ).
tcf(c_66,plain,
op(unit,unit) = unit,
inference(cnf_transformation,[],[f166]) ).
tcf(c_159,plain,
( ( op(unit,unit) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_160,plain,
( ( op(e1,e1) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_161,plain,
( ( op(e2,e2) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_162,plain,
( ( op(e3,e3) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_163,plain,
( ( op(unit,unit) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_164,plain,
( ( op(e1,e1) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_165,plain,
( ( op(e2,e2) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_166,plain,
( ( op(e3,e3) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_171,negated_conjecture,
( ( op(e3,e3) != unit )
| ( op(e2,e2) != unit )
| ( op(e1,e1) != unit )
| ( op(unit,unit) != unit ) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_172,negated_conjecture,
( ( op(e3,e3) != e1 )
| ( op(e2,e2) != e1 )
| ( op(e1,e1) != e1 )
| ( op(unit,unit) != e1 ) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_173,negated_conjecture,
( ( op(e3,e3) != e2 )
| ( op(e2,e2) != e2 )
| ( op(e1,e1) != e2 )
| ( op(unit,unit) != e2 ) ),
inference(cnf_transformation,[],[f238]) ).
tcf(c_174,negated_conjecture,
( ( op(e3,e3) != e3 )
| ( op(e2,e2) != e3 )
| ( op(e1,e1) != e3 )
| ( op(unit,unit) != e3 ) ),
inference(cnf_transformation,[],[f239]) ).
tcf(c_176,negated_conjecture,
( sP0
| sP1
| sP2
| ( op(e1,e1) = unit ) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_177,negated_conjecture,
( sP0
| sP1
| sP2
| ( op(e2,e2) = unit ) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_178,negated_conjecture,
( sP0
| sP1
| sP2
| ( op(e3,e3) = unit ) ),
inference(cnf_transformation,[],[f243]) ).
fof(f10,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(f11,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(f12,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(f13,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,[],[f9,f12,f11,f10]) ).
fof(f16,plain,
( ~ sP0
| ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f137,plain,
( ~ sP0
| e3 = op(e3,e3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f138,plain,
( ~ sP0
| e3 = op(e2,e2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f139,plain,
( ~ sP0
| e3 = op(e1,e1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f140,plain,
( ~ sP0
| op(e0,e0) = e3 ),
inference(cnf_transformation,[],[f16]) ).
fof(f235,plain,
( ~ sP0
| e3 = op(unit,unit) ),
inference(definition_unfolding,[],[f140,f74,f74]) ).
tcf(c_167,plain,
( ( op(unit,unit) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_168,plain,
( ( op(e1,e1) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_169,plain,
( ( op(e2,e2) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_170,plain,
( ( op(e3,e3) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_179,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_171,c_172,c_173,c_174,c_176,c_177,c_178,c_159,c_160,c_161,c_162,c_163,c_164,c_165,c_166,c_167,c_168,c_169,c_170,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG036+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.34 % Computer : n014.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 04:35:32 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.39 % Detected problem language: tptp
% 0.13/0.40 % Proving...
% 1.38/1.14 % SZS status Started for theBenchmark.p
% 1.38/1.14 % SZS status Theorem for theBenchmark.p
% 1.38/1.14
% 1.38/1.14 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.38/1.14
% 1.38/1.14 % ------ iProver source info
% 1.38/1.14
% 1.38/1.14 % git: date: 2026-07-19 20:42:38 +0200
% 1.38/1.14 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.38/1.14 % git: non_committed_changes: false
% 1.38/1.14
% 1.38/1.14 % ------ Parsing...
% 1.38/1.14 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.38/1.14
% 1.38/1.14 % ------ Preprocessing...%
% 1.38/1.14
% 1.38/1.14 % SZS status Theorem for theBenchmark.p
% 1.38/1.14
% 1.38/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.38/1.14
% 1.38/1.14
%------------------------------------------------------------------------------