%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG017+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 : n019.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 1.47s 1.27s
% Output : CNFRefutation 1.47s
% 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(f11,axiom,
( e1 = op(e2,e3)
& e0 = op(e3,e3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
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(f14,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,[],[f13]) ).
fof(f16,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,[],[f14]) ).
fof(f17,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,[],[f16]) ).
fof(f22,plain,
( ~ sP2
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f23,plain,
( ~ sP1
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f208,plain,
e0 = op(e3,e3),
inference(cnf_transformation,[],[f11]) ).
fof(f209,plain,
( ~ sP2
| e1 = op(e3,e3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f210,plain,
( ~ sP2
| e1 = op(e2,e2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f211,plain,
( ~ sP2
| e1 = op(e1,e1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f212,plain,
( ~ sP2
| op(e0,e0) = e1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f213,plain,
( ~ sP1
| e2 = op(e3,e3) ),
inference(cnf_transformation,[],[f23]) ).
fof(f214,plain,
( ~ sP1
| e2 = op(e2,e2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f215,plain,
( ~ sP1
| e2 = op(e1,e1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f216,plain,
( ~ sP1
| op(e0,e0) = e2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f221,plain,
( e3 != op(e3,e3)
| e3 != op(e2,e2)
| e3 != op(e1,e1)
| op(e0,e0) != e3 ),
inference(cnf_transformation,[],[f21]) ).
fof(f222,plain,
( e2 != op(e3,e3)
| e2 != op(e2,e2)
| e2 != op(e1,e1)
| op(e0,e0) != e2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f223,plain,
( e1 != op(e3,e3)
| e1 != op(e2,e2)
| e1 != op(e1,e1)
| op(e0,e0) != e1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f224,plain,
( e0 != op(e3,e3)
| e0 != op(e2,e2)
| e0 != op(e1,e1)
| e0 != op(e0,e0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f226,plain,
( sP0
| sP1
| sP2
| e0 = op(e2,e2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f227,plain,
( sP0
| sP1
| sP2
| e0 = op(e1,e1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f228,plain,
( sP0
| sP1
| sP2
| e0 = op(e0,e0) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_227,plain,
op(e3,e3) = e0,
inference(cnf_transformation,[],[f208]) ).
tcf(c_229,plain,
( ( op(e0,e0) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_230,plain,
( ( op(e1,e1) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_231,plain,
( ( op(e2,e2) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_232,plain,
( ( op(e3,e3) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_233,plain,
( ( op(e0,e0) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_234,plain,
( ( op(e1,e1) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_235,plain,
( ( op(e2,e2) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_236,plain,
( ( op(e3,e3) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_241,negated_conjecture,
( sP0
| sP1
| sP2
| ( op(e0,e0) = e0 ) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_242,negated_conjecture,
( sP0
| sP1
| sP2
| ( op(e1,e1) = e0 ) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_243,negated_conjecture,
( sP0
| sP1
| sP2
| ( op(e2,e2) = e0 ) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_245,negated_conjecture,
( ( op(e3,e3) != e0 )
| ( op(e2,e2) != e0 )
| ( op(e1,e1) != e0 )
| ( op(e0,e0) != e0 ) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_246,negated_conjecture,
( ( op(e3,e3) != e1 )
| ( op(e2,e2) != e1 )
| ( op(e1,e1) != e1 )
| ( op(e0,e0) != e1 ) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_247,negated_conjecture,
( ( op(e3,e3) != e2 )
| ( op(e2,e2) != e2 )
| ( op(e1,e1) != e2 )
| ( op(e0,e0) != e2 ) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_248,negated_conjecture,
( ( op(e3,e3) != e3 )
| ( op(e2,e2) != e3 )
| ( op(e1,e1) != e3 )
| ( op(e0,e0) != e3 ) ),
inference(cnf_transformation,[],[f221]) ).
fof(f18,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(f19,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(f20,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(f21,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,[],[f17,f20,f19,f18]) ).
fof(f24,plain,
( ~ sP0
| ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f217,plain,
( ~ sP0
| e3 = op(e3,e3) ),
inference(cnf_transformation,[],[f24]) ).
fof(f218,plain,
( ~ sP0
| e3 = op(e2,e2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f219,plain,
( ~ sP0
| e3 = op(e1,e1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f220,plain,
( ~ sP0
| op(e0,e0) = e3 ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_237,plain,
( ( op(e0,e0) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_238,plain,
( ( op(e1,e1) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_239,plain,
( ( op(e2,e2) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_240,plain,
( ( op(e3,e3) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_249,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_245,c_246,c_247,c_248,c_241,c_242,c_243,c_229,c_230,c_231,c_232,c_233,c_234,c_235,c_236,c_237,c_238,c_239,c_240,c_227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG017+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 04:32:19 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 0.15/0.41
% 0.15/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.41
% 0.15/0.41 % Detected problem language: tptp
% 0.15/0.42 % Proving...
% 1.47/1.27 % SZS status Started for theBenchmark.p
% 1.47/1.27 % SZS status Theorem for theBenchmark.p
% 1.47/1.27
% 1.47/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.47/1.27
% 1.47/1.27 % ------ iProver source info
% 1.47/1.27
% 1.47/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.47/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.47/1.27 % git: non_committed_changes: false
% 1.47/1.27
% 1.47/1.27 % ------ Parsing...
% 1.47/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.47/1.27
% 1.47/1.27 % ------ Preprocessing...%
% 1.47/1.27
% 1.47/1.27 % SZS status Theorem for theBenchmark.p
% 1.47/1.27
% 1.47/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.47/1.27
% 1.47/1.27
%------------------------------------------------------------------------------