%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : LCL688+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 : Mon Sep 7 12:14:23 PM UTC 2026
% Result : Theorem 70.13s 9.28s
% Output : CNFRefutation 70.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 14 unt; 0 def)
% Number of atoms : 169 ( 0 equ)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 295 ( 163 ~; 120 |; 11 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 83 ( 3 sgn 58 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(main,plain,
~ ? [X] :
~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ p4(Y) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| p3(X) )
| ~ p2(Y) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ! [X] :
( ~ r1(Y,X)
| p3(X) )
| ~ p2(Y) ) )
& p2(X)
& ~ ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ p2(Y) ) ) ) ) ) ) )
| ( ~ p1(X)
& ~ ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| p1(X) ) )
& ! [Y] :
( ~ r1(X,Y)
| p1(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ ! [Y] :
( ~ r1(X,Y)
| p1(Y) )
& p1(X) ) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| p1(Y) ) )
| ! [X] :
( ~ r1(Y,X)
| p1(X) ) )
| ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| p2(Y) ) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ~ p1(Y) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ p1(X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(main_negated,plain,
~ ~ ? [X] :
~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ p4(Y) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| p3(X) )
| ~ p2(Y) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ! [X] :
( ~ r1(Y,X)
| p3(X) )
| ~ p2(Y) ) )
& p2(X)
& ~ ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ p2(Y) ) ) ) ) ) ) )
| ( ~ p1(X)
& ~ ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| p1(X) ) )
& ! [Y] :
( ~ r1(X,Y)
| p1(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ ! [Y] :
( ~ r1(X,Y)
| p1(Y) )
& p1(X) ) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| p1(Y) ) )
| ! [X] :
( ~ r1(Y,X)
| p1(X) ) )
| ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| p2(Y) ) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ~ p1(Y) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ p1(X) ) ) ),
inference(negate_conjecture,[status(cth)],[main]) ).
cnf(3,plain,
( ~ r1(X0,X1)
| ~ r1(sK1,X0)
| r1(X1,sK2(X0,X1)) ),
inference(cnf,[status(esa)],[main_negated]) ).
cnf(l0,plain,
( ~ r1(sK1,sK11)
| ~ r1(sK1,sK1)
| r1(sK11,sK2(sK1,sK11)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(17,plain,
r1(sK1,sK11),
inference(cnf,[status(esa)],[main_negated]) ).
cnf(l1,plain,
r1(sK1,sK11),
inference(instantiation,[status(thm)],[17]) ).
fof(reflexivity,plain,
! [X] : r1(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
cnf(0,plain,
r1(X0,X0),
inference(cnf,[status(esa)],[reflexivity]) ).
cnf(l2,plain,
r1(sK1,sK1),
inference(instantiation,[status(thm)],[0]) ).
cnf(9,plain,
( ~ p2(X0)
| ~ r1(X1,X0)
| ~ r1(X0,X2)
| ~ r1(sK1,X1)
| sP0(X0,X3,X4,X1)
| p2(X2) ),
inference(cnf,[status(esa)],[main_negated]) ).
cnf(l3,plain,
( ~ p2(sK2(sK1,sK11))
| ~ r1(sK11,sK2(sK1,sK11))
| ~ r1(sK2(sK1,sK11),sK12(sK2(sK1,sK11)))
| ~ r1(sK1,sK11)
| sP0(sK2(sK1,sK11),sK2(sK1,sK11),sK2(sK2(sK1,sK11),sK5(sK11,sK2(sK1,sK11),sK2(sK1,sK11))),sK11)
| p2(sK12(sK2(sK1,sK11))) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l16,plain,
r1(sK1,sK11),
inference(instantiation,[status(thm)],[17]) ).
cnf(6,plain,
( ~ r1(X0,X1)
| ~ r1(sK1,X0)
| p2(sK2(X0,X1)) ),
inference(cnf,[status(esa)],[main_negated]) ).
cnf(l76,plain,
( ~ r1(sK1,sK11)
| ~ r1(sK1,sK1)
| p2(sK2(sK1,sK11)) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(19,plain,
( ~ p2(sK12(X0))
| ~ r1(sK11,X0) ),
inference(cnf,[status(esa)],[main_negated]) ).
cnf(l126,plain,
( ~ p2(sK12(sK2(sK1,sK11)))
| ~ r1(sK11,sK2(sK1,sK11)) ),
inference(instantiation,[status(thm)],[19]) ).
cnf(l80,plain,
r1(sK1,sK1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l146,plain,
r1(sK1,sK11),
inference(instantiation,[status(thm)],[17]) ).
cnf(25,plain,
( ~ p2(X0)
| ~ r1(X1,X2)
| ~ r1(sK5(X3,X1,X2),X0)
| ~ sP0(X1,X2,X0,X3) ),
inference(cnf,[status(esa)],[main_negated]) ).
cnf(l104,plain,
( ~ p2(sK2(sK2(sK1,sK11),sK5(sK11,sK2(sK1,sK11),sK2(sK1,sK11))))
| ~ r1(sK2(sK1,sK11),sK2(sK1,sK11))
| ~ r1(sK5(sK11,sK2(sK1,sK11),sK2(sK1,sK11)),sK2(sK2(sK1,sK11),sK5(sK11,sK2(sK1,sK11),sK2(sK1,sK11))))
| ~ sP0(sK2(sK1,sK11),sK2(sK1,sK11),sK2(sK2(sK1,sK11),sK5(sK11,sK2(sK1,sK11),sK2(sK1,sK11))),sK11) ),
inference(instantiation,[status(thm)],[25]) ).
cnf(18,plain,
( ~ r1(sK11,X0)
| r1(X0,sK12(X0)) ),
inference(cnf,[status(esa)],[main_negated]) ).
cnf(l9,plain,
( ~ r1(sK11,sK2(sK1,sK11))
| r1(sK2(sK1,sK11),sK12(sK2(sK1,sK11))) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(l161,plain,
r1(sK2(sK1,sK11),sK2(sK1,sK11)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l152,plain,
( ~ r1(sK2(sK1,sK11),sK5(sK11,sK2(sK1,sK11),sK2(sK1,sK11)))
| ~ r1(sK1,sK2(sK1,sK11))
| p2(sK2(sK2(sK1,sK11),sK5(sK11,sK2(sK1,sK11),sK2(sK1,sK11)))) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l154,plain,
( ~ r1(sK2(sK1,sK11),sK5(sK11,sK2(sK1,sK11),sK2(sK1,sK11)))
| ~ r1(sK1,sK2(sK1,sK11))
| r1(sK5(sK11,sK2(sK1,sK11),sK2(sK1,sK11)),sK2(sK2(sK1,sK11),sK5(sK11,sK2(sK1,sK11),sK2(sK1,sK11)))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(26,plain,
( ~ r1(X0,X1)
| r1(X1,sK5(X2,X0,X1))
| ~ sP0(X0,X1,X3,X2) ),
inference(cnf,[status(esa)],[main_negated]) ).
cnf(l155,plain,
( ~ r1(sK2(sK1,sK11),sK2(sK1,sK11))
| r1(sK2(sK1,sK11),sK5(sK11,sK2(sK1,sK11),sK2(sK1,sK11)))
| ~ sP0(sK2(sK1,sK11),sK2(sK1,sK11),sK2(sK2(sK1,sK11),sK5(sK11,sK2(sK1,sK11),sK2(sK1,sK11))),sK11) ),
inference(instantiation,[status(thm)],[26]) ).
fof(transitivity,plain,
! [X,Y,Z] :
( ( r1(X,Y)
& r1(Y,Z) )
=> r1(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
cnf(1,plain,
( ~ r1(X0,X1)
| ~ r1(X1,X2)
| r1(X0,X2) ),
inference(cnf,[status(esa)],[transitivity]) ).
cnf(l165,plain,
( ~ r1(sK1,sK11)
| ~ r1(sK11,sK2(sK1,sK11))
| r1(sK1,sK2(sK1,sK11)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l516,plain,
( ~ r1(sK1,sK11)
| ~ r1(sK11,sK2(sK1,sK11))
| r1(sK1,sK2(sK1,sK11)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l528,plain,
r1(sK1,sK11),
inference(instantiation,[status(thm)],[17]) ).
cnf(l311,plain,
( ~ r1(sK2(sK1,sK11),sK2(sK1,sK11))
| r1(sK2(sK1,sK11),sK5(sK11,sK2(sK1,sK11),sK2(sK1,sK11)))
| ~ sP0(sK2(sK1,sK11),sK2(sK1,sK11),sK2(sK2(sK1,sK11),sK5(sK11,sK2(sK1,sK11),sK2(sK1,sK11))),sK11) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(l693,plain,
r1(sK2(sK1,sK11),sK2(sK1,sK11)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l156,plain,
r1(sK2(sK1,sK11),sK2(sK1,sK11)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l545,plain,
r1(sK1,sK11),
inference(instantiation,[status(thm)],[17]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l16,l76,l126,l80,l146,l104,l9,l161,l152,l154,l155,l165,l516,l528,l311,l693,l156,l545]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL688+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 4 17:58:23 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % launching worker at depth: 1
% 0.08/0.35 % launching worker at depth: 2
% 0.08/0.35 % launching worker at depth: 3
% 0.08/0.35 % launching worker at depth: 4
% 0.08/0.35 % launching worker at depth: 6
% 0.08/0.35 % launching worker at depth: 5
% 0.08/0.35 % launching worker at depth: 7
% 0.08/0.35 % launching worker at depth: 8
% 0.12/0.36 % launching worker at depth: 9
% 0.12/0.45 % launching worker at depth: 10
% 11.45/1.83 % launching worker at depth: 11
% 70.13/9.28 % SZS status Theorem for theBenchmark
% 70.13/9.28 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------