%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : ALG039+1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Jul 24 09:45:45 AM UTC 2025
% Result : Theorem 9.37s 1.47s
% Output : CNFRefutation 9.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 88 ( 1 unt; 0 def)
% Number of atoms : 285 ( 200 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 330 ( 133 ~; 147 |; 50 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% 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 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,plain,
~ ( ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) )
& ~ ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(co1_negated,plain,
~ ~ ( ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) )
& ~ ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(113,plain,
( op(e0,e0) = e0
| sP0
| sP1
| sP2 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l0,plain,
( op(e0,e0) = e0
| sP0
| sP1
| sP2 ),
inference(instantiation,[status(thm)],[113]) ).
cnf(123,plain,
( op(e1,e1) = e3
| ~ sP2 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l8,plain,
( op(e1,e1) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[123]) ).
cnf(125,plain,
( op(e3,e3) = e2
| ~ sP1 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l3,plain,
( op(e3,e3) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[125]) ).
cnf(119,plain,
( op(e2,e2) != e2
| op(e3,e3) != e2
| op(e0,e0) != e2
| op(e1,e1) != e2 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l5,plain,
( op(e2,e2) != e2
| op(e3,e3) != e2
| op(e0,e0) != e2
| op(e1,e1) != e2 ),
inference(instantiation,[status(thm)],[119]) ).
cnf(117,plain,
( op(e2,e2) != e0
| op(e3,e3) != e0
| op(e0,e0) != e0
| op(e1,e1) != e0 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l2,plain,
( op(e2,e2) != e0
| op(e3,e3) != e0
| op(e0,e0) != e0
| op(e1,e1) != e0 ),
inference(instantiation,[status(thm)],[117]) ).
cnf(132,plain,
( op(e0,e0) = e1
| ~ sP0 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l1,plain,
( op(e0,e0) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[132]) ).
cnf(128,plain,
( op(e0,e0) = e2
| ~ sP1 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l20,plain,
( op(e0,e0) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[128]) ).
cnf(116,plain,
( op(e3,e3) = e0
| sP0
| sP1
| sP2 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l4,plain,
( op(e3,e3) = e0
| sP0
| sP1
| sP2 ),
inference(instantiation,[status(thm)],[116]) ).
cnf(l918,plain,
( op(e0,e0) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[128]) ).
cnf(126,plain,
( op(e2,e2) = e2
| ~ sP1 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l15,plain,
( op(e2,e2) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[126]) ).
cnf(114,plain,
( op(e1,e1) = e0
| sP0
| sP1
| sP2 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l63,plain,
( op(e1,e1) = e0
| sP0
| sP1
| sP2 ),
inference(instantiation,[status(thm)],[114]) ).
cnf(122,plain,
( op(e2,e2) = e3
| ~ sP2 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l121,plain,
( op(e2,e2) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[122]) ).
cnf(120,plain,
( op(e2,e2) != e3
| op(e3,e3) != e3
| op(e0,e0) != e3
| op(e1,e1) != e3 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l16,plain,
( op(e2,e2) != e3
| op(e3,e3) != e3
| op(e0,e0) != e3
| op(e1,e1) != e3 ),
inference(instantiation,[status(thm)],[120]) ).
cnf(124,plain,
( op(e0,e0) = e3
| ~ sP2 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l65,plain,
( op(e0,e0) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[124]) ).
cnf(131,plain,
( op(e1,e1) = e1
| ~ sP0 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l64,plain,
( op(e1,e1) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[131]) ).
cnf(129,plain,
( op(e3,e3) = e1
| ~ sP0 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l79,plain,
( op(e3,e3) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[129]) ).
cnf(l80,plain,
( op(e2,e2) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[126]) ).
cnf(121,plain,
( op(e3,e3) = e3
| ~ sP2 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l19,plain,
( op(e3,e3) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[121]) ).
cnf(127,plain,
( op(e1,e1) = e2
| ~ sP1 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l860,plain,
( op(e1,e1) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[127]) ).
cnf(l146,plain,
( op(e2,e2) != e3
| op(e3,e3) != e3
| op(e0,e0) != e3
| op(e1,e1) != e3 ),
inference(instantiation,[status(thm)],[120]) ).
cnf(l337,plain,
( op(e2,e2) != e2
| op(e3,e3) != e2
| op(e0,e0) != e2
| op(e1,e1) != e2 ),
inference(instantiation,[status(thm)],[119]) ).
cnf(118,plain,
( op(e2,e2) != e1
| op(e3,e3) != e1
| op(e0,e0) != e1
| op(e1,e1) != e1 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l193,plain,
( op(e2,e2) != e1
| op(e3,e3) != e1
| op(e0,e0) != e1
| op(e1,e1) != e1 ),
inference(instantiation,[status(thm)],[118]) ).
cnf(l89,plain,
( op(e2,e2) != e1
| op(e3,e3) != e1
| op(e0,e0) != e1
| op(e1,e1) != e1 ),
inference(instantiation,[status(thm)],[118]) ).
cnf(l213,plain,
( op(e0,e0) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[132]) ).
cnf(130,plain,
( op(e2,e2) = e1
| ~ sP0 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l169,plain,
( op(e2,e2) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[130]) ).
cnf(l82,plain,
( op(e2,e2) != e3
| op(e3,e3) != e3
| op(e0,e0) != e3
| op(e1,e1) != e3 ),
inference(instantiation,[status(thm)],[120]) ).
cnf(l314,plain,
( op(e2,e2) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[130]) ).
cnf(l208,plain,
( op(e3,e3) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[129]) ).
cnf(l241,plain,
( op(e1,e1) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[131]) ).
cnf(l340,plain,
( op(e0,e0) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[128]) ).
cnf(l939,plain,
( op(e2,e2) != e2
| op(e3,e3) != e2
| op(e0,e0) != e2
| op(e1,e1) != e2 ),
inference(instantiation,[status(thm)],[119]) ).
cnf(l236,plain,
( op(e0,e0) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[124]) ).
cnf(l6,plain,
( op(e2,e2) != e1
| op(e3,e3) != e1
| op(e0,e0) != e1
| op(e1,e1) != e1 ),
inference(instantiation,[status(thm)],[118]) ).
cnf(l152,plain,
( op(e1,e1) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[123]) ).
cnf(l92,plain,
( op(e3,e3) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[121]) ).
cnf(l1274,plain,
( op(e3,e3) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[125]) ).
cnf(l52,plain,
( op(e0,e0) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[124]) ).
cnf(l18,plain,
( op(e2,e2) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[122]) ).
cnf(l165,plain,
( op(e1,e1) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[123]) ).
cnf(l57,plain,
( op(e2,e2) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[130]) ).
cnf(l412,plain,
( op(e1,e1) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[127]) ).
cnf(l99,plain,
( op(e2,e2) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[122]) ).
cnf(l28,plain,
( op(e3,e3) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[129]) ).
cnf(l25,plain,
( op(e1,e1) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[131]) ).
cnf(l151,plain,
( op(e3,e3) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[121]) ).
cnf(l1275,plain,
( op(e2,e2) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[126]) ).
cnf(l411,plain,
( op(e3,e3) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[125]) ).
cnf(l1279,plain,
( op(e1,e1) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[127]) ).
cnf(115,plain,
( op(e2,e2) = e0
| sP0
| sP1
| sP2 ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l58,plain,
( op(e2,e2) = e0
| sP0
| sP1
| sP2 ),
inference(instantiation,[status(thm)],[115]) ).
cnf(l60,plain,
( op(e0,e0) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[132]) ).
cnf(l168,plain,
( op(e0,e0) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[132]) ).
cnf(l59,plain,
( op(e0,e0) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[124]) ).
cnf(l66,plain,
( op(e2,e2) != e1
| op(e3,e3) != e1
| op(e0,e0) != e1
| op(e1,e1) != e1 ),
inference(instantiation,[status(thm)],[118]) ).
cnf(l62,plain,
( op(e2,e2) != e3
| op(e3,e3) != e3
| op(e0,e0) != e3
| op(e1,e1) != e3 ),
inference(instantiation,[status(thm)],[120]) ).
cnf(l67,plain,
( op(e2,e2) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[126]) ).
cnf(l104,plain,
( op(e1,e1) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[131]) ).
cnf(l68,plain,
( op(e2,e2) != e2
| op(e3,e3) != e2
| op(e0,e0) != e2
| op(e1,e1) != e2 ),
inference(instantiation,[status(thm)],[119]) ).
cnf(l1233,plain,
( op(e3,e3) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[121]) ).
cnf(l199,plain,
( op(e1,e1) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[127]) ).
cnf(l200,plain,
( op(e3,e3) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[125]) ).
cnf(l108,plain,
( op(e1,e1) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[123]) ).
cnf(l102,plain,
( op(e2,e2) = e3
| ~ sP2 ),
inference(instantiation,[status(thm)],[122]) ).
cnf(l154,plain,
( op(e0,e0) = e2
| ~ sP1 ),
inference(instantiation,[status(thm)],[128]) ).
cnf(l100,plain,
( op(e3,e3) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[129]) ).
cnf(l1048,plain,
( op(e2,e2) = e1
| ~ sP0 ),
inference(instantiation,[status(thm)],[130]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l8,l3,l5,l2,l1,l20,l4,l918,l15,l63,l121,l16,l65,l64,l79,l80,l19,l860,l146,l337,l193,l89,l213,l169,l82,l314,l208,l241,l340,l939,l236,l6,l152,l92,l1274,l52,l18,l165,l57,l412,l99,l28,l25,l151,l1275,l411,l1279,l58,l60,l168,l59,l66,l62,l67,l104,l68,l1233,l199,l200,l108,l102,l154,l100,l1048]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.08 % Problem : ALG039+1 : TPTP v9.0.0. Released v2.7.0.
% 0.05/0.09 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.28 % Computer : n026.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Sun Jul 20 02:02:04 EDT 2025
% 0.08/0.28 % CPUTime :
% 0.08/0.29 % launching worker at depth: 1
% 0.08/0.29 % launching worker at depth: 3
% 0.08/0.29 % launching worker at depth: 4
% 0.08/0.29 % launching worker at depth: 5
% 0.08/0.29 % launching worker at depth: 6
% 0.08/0.29 % launching worker at depth: 2
% 0.08/0.29 % launching worker at depth: 7
% 0.08/0.29 % launching worker at depth: 8
% 9.37/1.47 % SZS status Theorem for theBenchmark
% 9.37/1.47 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------