%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 06:47:02 AM UTC 2026
% Result : Unsatisfiable 10.35s 2.09s
% Output : CNFRefutation 10.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 46 ( 11 unt; 13 nHn; 34 RR)
% Number of literals : 107 ( 0 equ; 50 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 61 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
product(X0,'multiplicative$uidentity',X0) ).
cnf(not_abelian,axiom,
~ product('multiplicative$uidentity','multiplicative$uidentity','additive$uidentity') ).
cnf(product_of_inverses2,axiom,
( ~ product('additive$uinverse'(X0),'additive$uinverse'(X1),X2)
| product(X0,X1,X2) ) ).
cnf(product_to_inverse,axiom,
( product(X0,'additive$uinverse'(X1),'additive$uinverse'(X2))
| ~ product(X0,X1,X2) ) ).
cnf(inverse_and_identity,axiom,
( product(X0,X0,'additive$uidentity')
| product(X0,'multiplicative$uinverse'(X0),'multiplicative$uidentity') ) ).
cnf(inverse_greater_than_0,axiom,
( ~ 'greater$uthan$u0'('additive$uinverse'(X0))
| ~ 'greater$uthan$u0'(X0) ) ).
cnf(greater_than_0_square,axiom,
( ~ product(X0,X0,'additive$uidentity')
| ~ 'greater$uthan$u0'(X0) ) ).
cnf(commutativity_of_product,axiom,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ) ).
cnf(product_and_inverse,axiom,
( 'greater$uthan$u0'('additive$uinverse'(X0))
| product(X0,X0,'additive$uidentity')
| 'greater$uthan$u0'(X0) ) ).
cnf(square_to_0,axiom,
( product(X2,X2,'additive$uidentity')
| ~ product(X0,X0,'additive$uidentity')
| ~ product(X0,X1,X2) ) ).
cnf(product_and_greater_than_0,axiom,
( 'greater$uthan$u0'(X2)
| ~ 'greater$uthan$u0'(X1)
| ~ 'greater$uthan$u0'(X0)
| ~ product(X0,X1,X2) ) ).
cnf(a_greater_than_0,hypothesis,
'greater$uthan$u0'(a) ).
cnf(prove_a_inverse_greater_than_0,negated_conjecture,
~ 'greater$uthan$u0'('multiplicative$uinverse'(a)) ).
cnf(c0,plain,
product(X0,'multiplicative$uidentity',X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c1,plain,
~ product('multiplicative$uidentity','multiplicative$uidentity','additive$uidentity'),
inference(clausification,[status(esa)],[not_abelian]) ).
cnf(c3,plain,
( ~ product('additive$uinverse'(X0),'additive$uinverse'(X1),X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_of_inverses2]) ).
cnf(c4,plain,
( product(X0,'additive$uinverse'(X1),'additive$uinverse'(X2))
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_to_inverse]) ).
cnf(c5,plain,
( product(X0,X0,'additive$uidentity')
| product(X0,'multiplicative$uinverse'(X0),'multiplicative$uidentity') ),
inference(clausification,[status(esa)],[inverse_and_identity]) ).
cnf(c6,plain,
( ~ 'greater$uthan$u0'('additive$uinverse'(X0))
| ~ 'greater$uthan$u0'(X0) ),
inference(clausification,[status(esa)],[inverse_greater_than_0]) ).
cnf(c7,plain,
( ~ product(X0,X0,'additive$uidentity')
| ~ 'greater$uthan$u0'(X0) ),
inference(clausification,[status(esa)],[greater_than_0_square]) ).
cnf(c8,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_product]) ).
cnf(c9,plain,
( 'greater$uthan$u0'('additive$uinverse'(X0))
| product(X0,X0,'additive$uidentity')
| 'greater$uthan$u0'(X0) ),
inference(clausification,[status(esa)],[product_and_inverse]) ).
cnf(c10,plain,
( product(X2,X2,'additive$uidentity')
| ~ product(X0,X0,'additive$uidentity')
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[square_to_0]) ).
cnf(c11,plain,
( 'greater$uthan$u0'(X2)
| ~ 'greater$uthan$u0'(X1)
| ~ 'greater$uthan$u0'(X0)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_and_greater_than_0]) ).
cnf(c12,plain,
'greater$uthan$u0'(a),
inference(clausification,[status(esa)],[a_greater_than_0]) ).
cnf(c13,plain,
~ 'greater$uthan$u0'('multiplicative$uinverse'(a)),
inference(clausification,[status(esa)],[prove_a_inverse_greater_than_0]) ).
cnf(d0,plain,
( product('multiplicative$uinverse'(X0),X0,'multiplicative$uidentity')
| product(X0,X0,'additive$uidentity') ),
inference(resolution,[status(thm)],[c5,c8]) ).
cnf(d1,plain,
( 'greater$uthan$u0'('additive$uinverse'(X1))
| 'greater$uthan$u0'(X1)
| ~ product(X1,X2,X0)
| product(X0,X0,'additive$uidentity') ),
inference(resolution,[status(thm)],[c10,c9]) ).
cnf(d2,plain,
( product(X0,X0,'additive$uidentity')
| 'greater$uthan$u0'('additive$uinverse'('multiplicative$uinverse'(X0)))
| 'greater$uthan$u0'('multiplicative$uinverse'(X0))
| product('multiplicative$uidentity','multiplicative$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( 'greater$uthan$u0'('multiplicative$uinverse'(X0))
| 'greater$uthan$u0'('additive$uinverse'('multiplicative$uinverse'(X0)))
| product(X0,X0,'additive$uidentity') ),
inference(resolution,[status(thm)],[c1,d2]) ).
cnf(d4,plain,
( ~ product(X2,X1,X0)
| ~ 'greater$uthan$u0'(X2)
| ~ 'greater$uthan$u0'('additive$uinverse'(X1))
| 'greater$uthan$u0'('additive$uinverse'(X0)) ),
inference(resolution,[status(thm)],[c11,c4]) ).
cnf(d5,plain,
( product(X0,X0,'additive$uidentity')
| 'greater$uthan$u0'('additive$uinverse'('multiplicative$uidentity'))
| ~ 'greater$uthan$u0'('additive$uinverse'('multiplicative$uinverse'(X0)))
| ~ 'greater$uthan$u0'(X0) ),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
( product(X0,X0,'additive$uidentity')
| 'greater$uthan$u0'('additive$uinverse'('additive$uinverse'(X0)))
| 'greater$uthan$u0'('additive$uinverse'(X0)) ),
inference(resolution,[status(thm)],[c9,c3]) ).
cnf(d7,plain,
( product(X0,X0,'additive$uidentity')
| 'greater$uthan$u0'('additive$uinverse'('additive$uinverse'('additive$uinverse'(X0))))
| 'greater$uthan$u0'('additive$uinverse'('additive$uinverse'(X0))) ),
inference(resolution,[status(thm)],[d6,c3]) ).
cnf(d8,plain,
( 'greater$uthan$u0'('additive$uinverse'('additive$uinverse'('additive$uinverse'('multiplicative$uidentity'))))
| 'greater$uthan$u0'('additive$uinverse'('additive$uinverse'('multiplicative$uidentity'))) ),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
( product(X0,X1,'additive$uinverse'(X2))
| ~ product('additive$uinverse'(X0),X1,X2) ),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(d10,plain,
product(X0,'multiplicative$uidentity','additive$uinverse'('additive$uinverse'(X0))),
inference(resolution,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
( 'greater$uthan$u0'('additive$uinverse'('additive$uinverse'('additive$uinverse'(X0))))
| ~ 'greater$uthan$u0'('additive$uinverse'('multiplicative$uidentity'))
| ~ 'greater$uthan$u0'(X0) ),
inference(resolution,[status(thm)],[d4,d10]) ).
cnf(d12,plain,
( ~ 'greater$uthan$u0'('additive$uinverse'('additive$uinverse'(X0)))
| ~ 'greater$uthan$u0'('additive$uinverse'('multiplicative$uidentity'))
| ~ 'greater$uthan$u0'(X0) ),
inference(resolution,[status(thm)],[d11,c6]) ).
cnf(d13,plain,
( 'greater$uthan$u0'('additive$uinverse'('additive$uinverse'('multiplicative$uidentity')))
| ~ 'greater$uthan$u0'('additive$uinverse'('multiplicative$uidentity'))
| ~ 'greater$uthan$u0'('additive$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( ~ 'greater$uthan$u0'('additive$uinverse'('multiplicative$uidentity'))
| ~ 'greater$uthan$u0'('additive$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d13,c6]) ).
cnf(d15,plain,
( ~ 'greater$uthan$u0'('additive$uinverse'('multiplicative$uinverse'(X0)))
| ~ 'greater$uthan$u0'(X0)
| product(X0,X0,'additive$uidentity') ),
inference(resolution,[status(thm)],[d14,d5]) ).
cnf(d16,plain,
( 'greater$uthan$u0'('multiplicative$uinverse'(X0))
| product(X0,X0,'additive$uidentity')
| ~ 'greater$uthan$u0'(X0)
| product(X0,X0,'additive$uidentity') ),
inference(resolution,[status(thm)],[d15,d3]) ).
cnf(d17,plain,
( ~ 'greater$uthan$u0'(X0)
| 'greater$uthan$u0'('multiplicative$uinverse'(X0))
| ~ 'greater$uthan$u0'(X0) ),
inference(resolution,[status(thm)],[d16,c7]) ).
cnf(d18,plain,
~ 'greater$uthan$u0'(a),
inference(resolution,[status(thm)],[d17,c13]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[c12,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 20:57:14 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.35/2.09 % SZS status Unsatisfiable for theBenchmark.p
% 10.35/2.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------