%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG024-7 : 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 : 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 08:25:37 AM UTC 2026
% Result : Unsatisfiable 12.94s 8.67s
% Output : CNFRefutation 12.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 3 RR)
% Number of literals : 23 ( 22 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 : 45 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(inverse_product2,axiom,
multiply(X0,'additive$uinverse'(X1)) = 'additive$uinverse'(multiply(X0,X1)) ).
cnf(distributivity_of_difference2,axiom,
multiply(add(X0,'additive$uinverse'(X1)),X2) = add(multiply(X0,X2),'additive$uinverse'(multiply(X1,X2))) ).
cnf(prove_right_alternative,negated_conjecture,
associator(x,y,y) != 'additive$uidentity' ).
cnf(left_multiplicative_zero,axiom,
multiply('additive$uidentity',X0) = '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(c2,plain,
multiply(X0,'additive$uinverse'(X1)) = 'additive$uinverse'(multiply(X0,X1)),
inference(clausification,[status(esa)],[inverse_product2]) ).
cnf(c4,plain,
multiply(add(X0,'additive$uinverse'(X1)),X2) = add(multiply(X0,X2),'additive$uinverse'(multiply(X1,X2))),
inference(clausification,[status(esa)],[distributivity_of_difference2]) ).
cnf(c7,plain,
associator(x,y,y) != 'additive$uidentity',
inference(clausification,[status(esa)],[prove_right_alternative]) ).
cnf(c10,plain,
multiply('additive$uidentity',X0) = 'additive$uidentity',
inference(clausification,[status(esa)],[left_multiplicative_zero]) ).
cnf(c13,plain,
add(X0,'additive$uinverse'(X0)) = 'additive$uidentity',
inference(clausification,[status(esa)],[right_additive_inverse]) ).
cnf(c19,plain,
multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)),
inference(clausification,[status(esa)],[right_alternative]) ).
cnf(c21,plain,
associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),'additive$uinverse'(multiply(X0,multiply(X1,X2)))),
inference(clausification,[status(esa)],[associator]) ).
cnf(d0,plain,
multiply(add(X2,'additive$uinverse'(X0)),X1) = add(multiply(X2,X1),multiply(X0,'additive$uinverse'(X1))),
inference(demodulation,[status(thm)],[c4,c2]) ).
cnf(d1,plain,
multiply(add(X2,'additive$uinverse'(X3)),multiply(X0,X1)) = add(multiply(X2,multiply(X0,X1)),multiply(X3,multiply(X0,'additive$uinverse'(X1)))),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d2,plain,
associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),multiply(X0,'additive$uinverse'(multiply(X1,X2)))),
inference(demodulation,[status(thm)],[c21,c2]) ).
cnf(d3,plain,
associator(X2,X0,X1) = add(multiply(multiply(X2,X0),X1),multiply(X2,multiply(X0,'additive$uinverse'(X1)))),
inference(demodulation,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
associator(X0,X1,X1) = add(multiply(X0,multiply(X1,X1)),multiply(X0,multiply(X1,'additive$uinverse'(X1)))),
inference(superposition,[status(thm)],[c19,d3]) ).
cnf(d5,plain,
associator(X0,X1,X1) = multiply(add(X0,'additive$uinverse'(X0)),multiply(X1,X1)),
inference(demodulation,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
associator(X0,X1,X1) = multiply('additive$uidentity',multiply(X1,X1)),
inference(demodulation,[status(thm)],[d5,c13]) ).
cnf(d7,plain,
associator(X1,X0,X0) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d6,c10]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG024-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n015.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 26 05:50:33 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.94/8.67 % SZS status Unsatisfiable for theBenchmark.p
% 12.94/8.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------