%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL654+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 : Sun Sep 27 07:55:02 AM UTC 2026
% Result : Theorem 32.54s 8.47s
% Output : CNFRefutation 32.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of formulae : 50 ( 10 unt; 0 def)
% Number of atoms : 203 ( 0 equ)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 313 ( 160 ~; 147 |; 6 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 94 ( 0 sgn 41 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [X0] : r1(X0,X0) ).
fof(main,conjecture,
~ ? [X0] :
~ ( ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ! [X0] :
( $false
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ! [X0] :
( ~ ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( p1(X1)
& ~ ! [X0] :
( ~ ! [X1] :
( ~ p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ~ ? [X0] :
~ ( ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ! [X0] :
( $false
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ! [X0] :
( ~ ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( p1(X1)
& ~ ! [X0] :
( ~ ! [X1] :
( ~ p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) ) ),
inference(negate_conjecture,[status(cth)],[main]) ).
cnf(c0,plain,
r1(X0,X0),
inference(clausification,[status(esa)],[reflexivity]) ).
cnf(c3,plain,
( ~ r1(X0,X2)
| ~ r1(sK1,X0)
| r1(X1,sK9(X1))
| r1(X2,sK7(X2))
| ~ r1(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c4,plain,
( ~ r1(X2,X3)
| ~ r1(sK1,X2)
| p1(X1)
| r1(X3,sK7(X3))
| ~ r1(X2,X0)
| ~ r1(sK9(X0),X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c5,plain,
( ~ r1(X1,X0)
| ~ r1(sK1,X1)
| r1(X2,sK9(X2))
| ~ r1(X1,X2)
| ~ p1(sK7(X0)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c6,plain,
( ~ r1(X3,X0)
| ~ r1(sK1,X3)
| p1(X2)
| ~ r1(X3,X1)
| ~ r1(sK9(X1),X2)
| ~ p1(sK7(X0)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c7,plain,
r1(sK1,sK11),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c8,plain,
( p1(X0)
| ~ r1(sK11,X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c9,plain,
r1(sK11,sK13),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c10,plain,
r1(sK13,sK14),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c11,plain,
~ p1(sK14),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c13,plain,
( ~ r1(sK1,X3)
| ~ r1(X1,X0)
| r1(X2,sK21(X2))
| ~ r1(X3,X1)
| ~ r1(X1,X2)
| p1(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c14,plain,
( ~ r1(sK1,X3)
| ~ r1(X1,X0)
| ~ p1(sK21(X2))
| ~ r1(X3,X1)
| ~ r1(X1,X2)
| p1(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ p1(sK21(X0))
| p1(X1)
| ~ r1(sK1,sK11)
| ~ r1(sK13,X1)
| ~ r1(sK13,X0) ),
inference(resolution,[status(thm)],[c14,c9]) ).
cnf(d1,plain,
( ~ p1(sK21(X1))
| p1(X0)
| ~ r1(sK13,X1)
| ~ r1(sK13,X0) ),
inference(resolution,[status(thm)],[c7,d0]) ).
cnf(d2,plain,
( ~ p1(sK7(X0))
| ~ r1(sK1,sK11)
| ~ r1(sK11,X0)
| r1(sK13,sK9(sK13)) ),
inference(resolution,[status(thm)],[c5,c9]) ).
cnf(d3,plain,
( ~ p1(sK7(X0))
| r1(sK13,sK9(sK13))
| ~ r1(sK11,X0) ),
inference(resolution,[status(thm)],[c7,d2]) ).
cnf(d4,plain,
( ~ p1(sK7(sK11))
| r1(sK13,sK9(sK13)) ),
inference(resolution,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
( ~ r1(sK1,sK11)
| ~ r1(sK11,X0)
| r1(X0,sK7(X0))
| r1(sK13,sK9(sK13)) ),
inference(resolution,[status(thm)],[c3,c9]) ).
cnf(d6,plain,
( r1(sK13,sK9(sK13))
| ~ r1(sK11,X0)
| r1(X0,sK7(X0)) ),
inference(resolution,[status(thm)],[c7,d5]) ).
cnf(d7,plain,
( r1(sK13,sK9(sK13))
| r1(sK11,sK7(sK11)) ),
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
( p1(sK7(sK11))
| r1(sK13,sK9(sK13)) ),
inference(resolution,[status(thm)],[d7,c8]) ).
cnf(d9,plain,
( p1(sK7(sK11))
| ~ p1(sK21(sK9(sK13)))
| p1(X0)
| ~ r1(sK13,X0) ),
inference(resolution,[status(thm)],[d1,d8]) ).
cnf(d10,plain,
( ~ p1(sK21(sK9(sK13)))
| p1(sK7(sK11))
| p1(sK14) ),
inference(resolution,[status(thm)],[d9,c10]) ).
cnf(d11,plain,
( ~ p1(sK21(sK9(sK13)))
| p1(sK7(sK11)) ),
inference(resolution,[status(thm)],[c11,d10]) ).
cnf(d12,plain,
( p1(X1)
| ~ r1(sK9(sK13),X1)
| ~ r1(sK1,sK11)
| ~ r1(sK11,X0)
| r1(X0,sK7(X0)) ),
inference(resolution,[status(thm)],[c4,c9]) ).
cnf(d13,plain,
( p1(X1)
| ~ r1(sK11,X0)
| ~ r1(sK9(sK13),X1)
| r1(X0,sK7(X0)) ),
inference(resolution,[status(thm)],[c7,d12]) ).
cnf(d14,plain,
( p1(sK14)
| ~ r1(sK1,X1)
| ~ r1(X1,sK13)
| ~ r1(sK13,X0)
| r1(X0,sK21(X0)) ),
inference(resolution,[status(thm)],[c13,c10]) ).
cnf(d15,plain,
( ~ r1(sK13,X1)
| ~ r1(sK1,X0)
| r1(X1,sK21(X1))
| ~ r1(X0,sK13) ),
inference(resolution,[status(thm)],[c11,d14]) ).
cnf(d16,plain,
( ~ r1(sK13,X0)
| ~ r1(sK1,sK11)
| r1(X0,sK21(X0)) ),
inference(resolution,[status(thm)],[d15,c9]) ).
cnf(d17,plain,
( ~ r1(sK13,X0)
| r1(X0,sK21(X0)) ),
inference(resolution,[status(thm)],[c7,d16]) ).
cnf(d18,plain,
( p1(sK7(sK11))
| r1(sK9(sK13),sK21(sK9(sK13))) ),
inference(resolution,[status(thm)],[d17,d8]) ).
cnf(d19,plain,
( p1(sK21(sK9(sK13)))
| ~ r1(sK11,X0)
| r1(X0,sK7(X0))
| p1(sK7(sK11)) ),
inference(resolution,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
( p1(sK21(sK9(sK13)))
| p1(sK7(sK11))
| r1(sK11,sK7(sK11)) ),
inference(resolution,[status(thm)],[d19,c0]) ).
cnf(d21,plain,
( p1(sK7(sK11))
| p1(sK21(sK9(sK13)))
| p1(sK7(sK11)) ),
inference(resolution,[status(thm)],[d20,c8]) ).
cnf(d22,plain,
( ~ p1(sK7(X0))
| p1(X2)
| ~ r1(sK9(X1),X2)
| ~ r1(sK1,X0)
| ~ r1(X0,X1) ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(d23,plain,
( ~ p1(sK7(sK11))
| p1(X0)
| ~ r1(sK9(sK13),X0)
| ~ r1(sK1,sK11) ),
inference(resolution,[status(thm)],[d22,c9]) ).
cnf(d24,plain,
( ~ p1(sK7(sK11))
| p1(X0)
| ~ r1(sK9(sK13),X0) ),
inference(resolution,[status(thm)],[c7,d23]) ).
cnf(d25,plain,
( r1(sK13,sK9(sK13))
| p1(sK21(sK9(sK13))) ),
inference(resolution,[status(thm)],[d21,d4]) ).
cnf(d26,plain,
( r1(sK9(sK13),sK21(sK9(sK13)))
| p1(sK21(sK9(sK13))) ),
inference(resolution,[status(thm)],[d25,d17]) ).
cnf(d27,plain,
( ~ p1(sK7(sK11))
| p1(sK21(sK9(sK13)))
| p1(sK21(sK9(sK13))) ),
inference(resolution,[status(thm)],[d26,d24]) ).
cnf(d28,plain,
( p1(sK21(sK9(sK13)))
| p1(sK21(sK9(sK13))) ),
inference(resolution,[status(thm)],[d27,d21]) ).
cnf(d29,plain,
p1(sK7(sK11)),
inference(resolution,[status(thm)],[d28,d11]) ).
cnf(d30,plain,
r1(sK13,sK9(sK13)),
inference(resolution,[status(thm)],[d29,d4]) ).
cnf(d31,plain,
( ~ p1(sK21(sK9(sK13)))
| p1(X0)
| ~ r1(sK13,X0) ),
inference(resolution,[status(thm)],[d30,d1]) ).
cnf(d32,plain,
( p1(X0)
| ~ r1(sK13,X0) ),
inference(resolution,[status(thm)],[d28,d31]) ).
cnf(d33,plain,
p1(sK14),
inference(resolution,[status(thm)],[d32,c10]) ).
cnf(d34,plain,
$false,
inference(resolution,[status(thm)],[c11,d33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL654+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.43 % Computer : n003.cluster.edu
% 0.11/0.43 % Model : x86_64 x86_64
% 0.11/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.43 % Memory : 8046.5625MB
% 0.11/0.43 % OS : Linux 6.8.0-71-generic
% 0.11/0.43 % CPULimit : 300
% 0.11/0.43 % WCLimit : 300
% 0.11/0.43 % DateTime : Fri Sep 25 23:01:53 UTC 2026
% 0.11/0.43 % CPUTime :
% 0.11/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.54/8.47 % SZS status Theorem for theBenchmark.p
% 32.54/8.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------