%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG007-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:25:34 AM UTC 2026
% Result : Unsatisfiable 13.47s 3.70s
% Output : CNFRefutation 13.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 3 RR)
% Number of literals : 19 ( 18 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(boolean_ring,hypothesis,
multiply(X0,X0) = X0 ).
cnf(prove_inverse,negated_conjecture,
add(a,a) != 'additive$uidentity' ).
cnf(left_additive_inverse,axiom,
add('additive$uinverse'(X0),X0) = 'additive$uidentity' ).
cnf(additive_inverse_additive_inverse,axiom,
'additive$uinverse'('additive$uinverse'(X0)) = X0 ).
cnf(multiply_additive_inverse1,axiom,
multiply(X0,'additive$uinverse'(X1)) = 'additive$uinverse'(multiply(X0,X1)) ).
cnf(multiply_additive_inverse2,axiom,
multiply('additive$uinverse'(X0),X1) = 'additive$uinverse'(multiply(X0,X1)) ).
cnf(c0,plain,
multiply(X0,X0) = X0,
inference(clausification,[status(esa)],[boolean_ring]) ).
cnf(c1,plain,
add(a,a) != 'additive$uidentity',
inference(clausification,[status(esa)],[prove_inverse]) ).
cnf(c3,plain,
add('additive$uinverse'(X0),X0) = 'additive$uidentity',
inference(clausification,[status(esa)],[left_additive_inverse]) ).
cnf(c7,plain,
'additive$uinverse'('additive$uinverse'(X0)) = X0,
inference(clausification,[status(esa)],[additive_inverse_additive_inverse]) ).
cnf(c11,plain,
multiply(X0,'additive$uinverse'(X1)) = 'additive$uinverse'(multiply(X0,X1)),
inference(clausification,[status(esa)],[multiply_additive_inverse1]) ).
cnf(c12,plain,
multiply('additive$uinverse'(X0),X1) = 'additive$uinverse'(multiply(X0,X1)),
inference(clausification,[status(esa)],[multiply_additive_inverse2]) ).
cnf(d0,plain,
multiply('additive$uinverse'(X0),X1) = multiply(X0,'additive$uinverse'(X1)),
inference(demodulation,[status(thm)],[c12,c11]) ).
cnf(d1,plain,
multiply(X0,'additive$uinverse'('additive$uinverse'(X0))) = 'additive$uinverse'(X0),
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
multiply(X0,X0) = 'additive$uinverse'(X0),
inference(demodulation,[status(thm)],[d1,c7]) ).
cnf(d3,plain,
X0 = 'additive$uinverse'(X0),
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
add(X0,'additive$uinverse'(X0)) = 'additive$uidentity',
inference(superposition,[status(thm)],[c7,c3]) ).
cnf(d5,plain,
add(X0,X0) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG007-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.37 % Computer : n014.cluster.edu
% 0.07/0.37 % Model : x86_64 x86_64
% 0.07/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.37 % Memory : 8046.5625MB
% 0.07/0.37 % OS : Linux 6.8.0-71-generic
% 0.07/0.37 % CPULimit : 300
% 0.07/0.37 % WCLimit : 300
% 0.07/0.37 % DateTime : Sat Sep 26 05:44:01 UTC 2026
% 0.07/0.37 % CPUTime :
% 0.07/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.47/3.70 % SZS status Unsatisfiable for theBenchmark.p
% 13.47/3.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------