%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG024-6 : 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 : 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 08:25:37 AM UTC 2026
% Result : Unsatisfiable 14.10s 3.60s
% Output : CNFRefutation 14.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 3 RR)
% Number of literals : 11 ( 10 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 16 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_right_alternative,negated_conjecture,
associator(x,y,y) != 'additive$uidentity' ).
cnf(right_additive_inverse,axiom,
add(X0,'additive$uinverse'(X0)) = 'additive$uidentity' ).
cnf(right_alternative,axiom,
multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)) ).
cnf(associator,axiom,
associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),'additive$uinverse'(multiply(X0,multiply(X1,X2)))) ).
cnf(c0,plain,
associator(x,y,y) != 'additive$uidentity',
inference(clausification,[status(esa)],[prove_right_alternative]) ).
cnf(c6,plain,
add(X0,'additive$uinverse'(X0)) = 'additive$uidentity',
inference(clausification,[status(esa)],[right_additive_inverse]) ).
cnf(c12,plain,
multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)),
inference(clausification,[status(esa)],[right_alternative]) ).
cnf(c14,plain,
associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),'additive$uinverse'(multiply(X0,multiply(X1,X2)))),
inference(clausification,[status(esa)],[associator]) ).
cnf(d0,plain,
associator(X0,X1,X1) = add(multiply(X0,multiply(X1,X1)),'additive$uinverse'(multiply(X0,multiply(X1,X1)))),
inference(superposition,[status(thm)],[c12,c14]) ).
cnf(d1,plain,
associator(X0,X1,X1) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d0,c6]) ).
cnf(d2,plain,
$false,
inference(resolution,[status(thm)],[d1,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG024-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n003.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 05:48:54 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.10/3.60 % SZS status Unsatisfiable for theBenchmark.p
% 14.10/3.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------