%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HWV021-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:32:56 AM UTC 2026
% Result : Unsatisfiable 13.41s 4.19s
% Output : CNFRefutation 13.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of clauses : 72 ( 29 unt; 19 nHn; 61 RR)
% Number of literals : 145 ( 52 equ; 66 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quest_1,negated_conjecture,
'p$uRd$uerror'(plus('t$u139',n1)) ).
cnf(quest_2,negated_conjecture,
'p$uRd'('t$u139') ).
cnf(quest_3,negated_conjecture,
~ 'p$uReset'('t$u139') ).
cnf(quest_4,negated_conjecture,
~ 'p$uEmpty'('t$u139') ).
cnf(axiom_1,axiom,
plus(X0,n1) != n0 ).
cnf(axiom_2,axiom,
gt(plus(X0,n1),n0) ).
cnf(axiom_3,axiom,
( gt(X0,minus(X0,n1))
| ~ gt(X0,n0) ) ).
cnf(axiom_4,axiom,
( 'def$u10'(X1,X0)
| plus(X2,X1) = X0
| minus(X0,X1) != X2 ) ).
cnf(axiom_7,axiom,
( X1 != X0
| ~ 'def$u10'(X0,X1) ) ).
cnf(axiom_9,axiom,
( ~ gt(plus(X0,n1),plus(X1,n1))
| gt(X0,X1) ) ).
cnf(axiom_13,axiom,
( ~ gt(X1,X2)
| gt(X0,X2)
| ~ gt(X0,X1) ) ).
cnf(axiom_14,axiom,
( gt(X0,plus(X1,n1))
| plus(X1,n1) = X0
| ~ gt(X0,X1) ) ).
cnf(axiom_15,axiom,
( gt(X0,n0)
| X0 = n0 ) ).
cnf(axiom_16,axiom,
( X0 = plus('y$u27'(X0),n1)
| X0 = n0 ) ).
cnf(axiom_17,axiom,
~ gt(X0,X0) ).
cnf(axiom_18,axiom,
( X0 = X1
| plus(X0,n1) != plus(X1,n1) ) ).
cnf(axiom_19,axiom,
plus(n0,X0) = X0 ).
cnf(axiom_20,axiom,
n1 = plus(n0,n1) ).
cnf(axiom_24,axiom,
( 'p$uEmpty'(X0)
| 'int$ulevel'(X0) != n0 ) ).
cnf(axiom_52,axiom,
( ~ 'p$uRd$uerror'(plus(X0,n1))
| ~ gt('int$ulevel'(X0),n0)
| ~ 'p$uRd'(X0)
| ~ 'p$uWr'(X0)
| 'p$uReset'(X0) ) ).
cnf(axiom_70,axiom,
( ~ 'p$uRd$uerror'(plus(X0,n1))
| ~ gt('int$ulevel'(X0),n0)
| ~ 'p$uRd'(X0)
| 'p$uWr'(X0)
| 'p$uReset'(X0) ) ).
cnf(c0,plain,
'p$uRd$uerror'(plus('t$u139',n1)),
inference(clausification,[status(esa)],[quest_1]) ).
cnf(c1,plain,
'p$uRd'('t$u139'),
inference(clausification,[status(esa)],[quest_2]) ).
cnf(c2,plain,
~ 'p$uReset'('t$u139'),
inference(clausification,[status(esa)],[quest_3]) ).
cnf(c3,plain,
~ 'p$uEmpty'('t$u139'),
inference(clausification,[status(esa)],[quest_4]) ).
cnf(c4,plain,
plus(X0,n1) != n0,
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c5,plain,
gt(plus(X0,n1),n0),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c6,plain,
( gt(X0,minus(X0,n1))
| ~ gt(X0,n0) ),
inference(clausification,[status(esa)],[axiom_3]) ).
cnf(c7,plain,
( 'def$u10'(X1,X0)
| plus(X2,X1) = X0
| minus(X0,X1) != X2 ),
inference(clausification,[status(esa)],[axiom_4]) ).
cnf(c10,plain,
( X1 != X0
| ~ 'def$u10'(X0,X1) ),
inference(clausification,[status(esa)],[axiom_7]) ).
cnf(c12,plain,
( ~ gt(plus(X0,n1),plus(X1,n1))
| gt(X0,X1) ),
inference(clausification,[status(esa)],[axiom_9]) ).
cnf(c16,plain,
( ~ gt(X1,X2)
| gt(X0,X2)
| ~ gt(X0,X1) ),
inference(clausification,[status(esa)],[axiom_13]) ).
cnf(c17,plain,
( gt(X0,plus(X1,n1))
| plus(X1,n1) = X0
| ~ gt(X0,X1) ),
inference(clausification,[status(esa)],[axiom_14]) ).
cnf(c18,plain,
( gt(X0,n0)
| X0 = n0 ),
inference(clausification,[status(esa)],[axiom_15]) ).
cnf(c19,plain,
( X0 = plus('y$u27'(X0),n1)
| X0 = n0 ),
inference(clausification,[status(esa)],[axiom_16]) ).
cnf(c20,plain,
~ gt(X0,X0),
inference(clausification,[status(esa)],[axiom_17]) ).
cnf(c21,plain,
( X0 = X1
| plus(X0,n1) != plus(X1,n1) ),
inference(clausification,[status(esa)],[axiom_18]) ).
cnf(c22,plain,
plus(n0,X0) = X0,
inference(clausification,[status(esa)],[axiom_19]) ).
cnf(c23,plain,
n1 = plus(n0,n1),
inference(clausification,[status(esa)],[axiom_20]) ).
cnf(c27,plain,
( 'p$uEmpty'(X0)
| 'int$ulevel'(X0) != n0 ),
inference(clausification,[status(esa)],[axiom_24]) ).
cnf(c55,plain,
( ~ gt('int$ulevel'(X0),n0)
| ~ 'p$uRd'(X0)
| 'p$uReset'(X0)
| ~ 'p$uWr'(X0)
| ~ 'p$uRd$uerror'(plus(X0,n1)) ),
inference(clausification,[status(esa)],[axiom_52]) ).
cnf(c73,plain,
( 'p$uWr'(X0)
| 'p$uReset'(X0)
| ~ 'p$uRd$uerror'(plus(X0,n1))
| ~ 'p$uRd'(X0)
| ~ gt('int$ulevel'(X0),n0) ),
inference(clausification,[status(esa)],[axiom_70]) ).
cnf(d0,plain,
( 'int$ulevel'(X0) = n0
| ~ 'p$uWr'(X0)
| 'p$uReset'(X0)
| ~ 'p$uRd'(X0)
| ~ 'p$uRd$uerror'(plus(X0,n1)) ),
inference(resolution,[status(thm)],[c55,c18]) ).
cnf(d1,plain,
( ~ 'p$uWr'('t$u139')
| 'p$uReset'('t$u139')
| ~ 'p$uRd'('t$u139')
| 'int$ulevel'('t$u139') = n0 ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( ~ 'p$uWr'('t$u139')
| 'p$uReset'('t$u139')
| 'int$ulevel'('t$u139') = n0 ),
inference(resolution,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
( ~ 'p$uWr'('t$u139')
| 'int$ulevel'('t$u139') = n0 ),
inference(resolution,[status(thm)],[c2,d2]) ).
cnf(d4,plain,
( 'int$ulevel'(X0) = n0
| 'p$uWr'(X0)
| 'p$uReset'(X0)
| ~ 'p$uRd'(X0)
| ~ 'p$uRd$uerror'(plus(X0,n1)) ),
inference(resolution,[status(thm)],[c73,c18]) ).
cnf(d5,plain,
( 'p$uWr'('t$u139')
| 'p$uReset'('t$u139')
| ~ 'p$uRd'('t$u139')
| 'int$ulevel'('t$u139') = n0 ),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
( 'p$uWr'('t$u139')
| 'p$uReset'('t$u139')
| 'int$ulevel'('t$u139') = n0 ),
inference(resolution,[status(thm)],[c1,d5]) ).
cnf(d7,plain,
( 'p$uWr'('t$u139')
| 'int$ulevel'('t$u139') = n0 ),
inference(resolution,[status(thm)],[c2,d6]) ).
cnf(d8,plain,
( 'int$ulevel'('t$u139') = n0
| 'int$ulevel'('t$u139') = n0 ),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( 'p$uEmpty'('t$u139')
| n0 != n0 ),
inference(superposition,[status(thm)],[d8,c27]) ).
cnf(d10,plain,
n0 != n0,
inference(resolution,[status(thm)],[c3,d9]) ).
cnf(d11,plain,
( gt(n0,X0)
| ~ gt(n1,plus(X0,n1)) ),
inference(superposition,[status(thm)],[c22,c12]) ).
cnf(d12,plain,
( gt(plus(X1,n1),X0)
| ~ gt(n0,X0) ),
inference(resolution,[status(thm)],[c16,c5]) ).
cnf(d13,plain,
~ gt(n0,plus(X0,n1)),
inference(resolution,[status(thm)],[d12,c20]) ).
cnf(d14,plain,
( ~ gt(n0,X0)
| plus(X0,n1) = n0 ),
inference(resolution,[status(thm)],[d13,c17]) ).
cnf(d15,plain,
~ gt(n0,X0),
inference(resolution,[status(thm)],[c4,d14]) ).
cnf(d16,plain,
~ gt(n1,plus(X0,n1)),
inference(resolution,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
( X0 = n0
| ~ gt(n1,X0) ),
inference(superposition,[status(thm)],[c19,d16]) ).
cnf(d18,plain,
( ~ gt(n1,n0)
| minus(n1,n1) = n0 ),
inference(resolution,[status(thm)],[d17,c6]) ).
cnf(d19,plain,
gt(n1,n0),
inference(superposition,[status(thm)],[c22,c5]) ).
cnf(d20,plain,
minus(n1,n1) = n0,
inference(resolution,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
( X0 = n0
| plus(X0,n1) != n1 ),
inference(superposition,[status(thm)],[c22,c21]) ).
cnf(d22,plain,
~ 'def$u10'(X0,X0),
inference(equality_resolution,[status(thm)],[c10]) ).
cnf(d23,plain,
( 'def$u10'(X1,X0)
| plus(minus(X0,X1),X1) = X0 ),
inference(equality_resolution,[status(thm)],[c7]) ).
cnf(d24,plain,
plus(minus(X0,X0),X0) = X0,
inference(resolution,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
( minus(n1,n1) = n0
| n1 != n1 ),
inference(superposition,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
( n0 = n0
| n1 != n1 ),
inference(demodulation,[status(thm)],[d25,d20]) ).
cnf(d27,plain,
n1 = n1,
inference(demodulation,[status(thm)],[c23,c22]) ).
cnf(d28,plain,
n0 = n0,
inference(resolution,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
$false,
inference(resolution,[status(thm)],[d28,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV021-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % Computer : n015.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Fri Sep 25 16:05:13 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.41/4.19 % SZS status Unsatisfiable for theBenchmark.p
% 13.41/4.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------