%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG018-6 : 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 : n007.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 08:25:36 AM UTC 2026
% Result : Unsatisfiable 3.26s 16.76s
% Output : CNFRefutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 6 RR)
% Number of literals : 48 ( 47 equ; 5 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_distributivity,negated_conjecture,
multiply(add(x,y),'additive$uinverse'(z)) != add('additive$uinverse'(multiply(x,z)),'additive$uinverse'(multiply(y,z))) ).
cnf(left_additive_identity,axiom,
add('additive$uidentity',X0) = X0 ).
cnf(right_additive_identity,axiom,
add(X0,'additive$uidentity') = X0 ).
cnf(right_multiplicative_zero,axiom,
multiply(X0,'additive$uidentity') = 'additive$uidentity' ).
cnf(right_additive_inverse,axiom,
add(X0,'additive$uinverse'(X0)) = 'additive$uidentity' ).
cnf(additive_inverse_additive_inverse,axiom,
'additive$uinverse'('additive$uinverse'(X0)) = X0 ).
cnf(distribute1,axiom,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)) ).
cnf(distribute2,axiom,
multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)) ).
cnf(commutativity_for_addition,axiom,
add(X0,X1) = add(X1,X0) ).
cnf(associativity_for_addition,axiom,
add(X0,add(X1,X2)) = add(add(X0,X1),X2) ).
cnf(c0,plain,
multiply(add(x,y),'additive$uinverse'(z)) != add('additive$uinverse'(multiply(x,z)),'additive$uinverse'(multiply(y,z))),
inference(clausification,[status(esa)],[prove_distributivity]) ).
cnf(c1,plain,
add('additive$uidentity',X0) = X0,
inference(clausification,[status(esa)],[left_additive_identity]) ).
cnf(c2,plain,
add(X0,'additive$uidentity') = X0,
inference(clausification,[status(esa)],[right_additive_identity]) ).
cnf(c4,plain,
multiply(X0,'additive$uidentity') = 'additive$uidentity',
inference(clausification,[status(esa)],[right_multiplicative_zero]) ).
cnf(c6,plain,
add(X0,'additive$uinverse'(X0)) = 'additive$uidentity',
inference(clausification,[status(esa)],[right_additive_inverse]) ).
cnf(c7,plain,
'additive$uinverse'('additive$uinverse'(X0)) = X0,
inference(clausification,[status(esa)],[additive_inverse_additive_inverse]) ).
cnf(c8,plain,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(clausification,[status(esa)],[distribute1]) ).
cnf(c9,plain,
multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
inference(clausification,[status(esa)],[distribute2]) ).
cnf(c10,plain,
add(X0,X1) = add(X1,X0),
inference(clausification,[status(esa)],[commutativity_for_addition]) ).
cnf(c11,plain,
add(X0,add(X1,X2)) = add(add(X0,X1),X2),
inference(clausification,[status(esa)],[associativity_for_addition]) ).
cnf(d0,plain,
add(X0,add('additive$uinverse'(X0),X1)) = add('additive$uidentity',X1),
inference(superposition,[status(thm)],[c6,c11]) ).
cnf(d1,plain,
add(X1,add('additive$uinverse'(X1),X0)) = X0,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
add('additive$uinverse'(X0),add(X0,X1)) = X1,
inference(superposition,[status(thm)],[c7,d1]) ).
cnf(d3,plain,
add('additive$uinverse'(multiply(X0,X1)),multiply(X0,add(X1,X2))) = multiply(X0,X2),
inference(superposition,[status(thm)],[c8,d2]) ).
cnf(d4,plain,
add(X0,add(X1,'additive$uidentity')) = add(X0,X1),
inference(superposition,[status(thm)],[c11,c2]) ).
cnf(d5,plain,
add(X1,X0) = add(X1,X0),
inference(demodulation,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
'additive$uidentity' = add(X0,'additive$uinverse'(X0)),
inference(superposition,[status(thm)],[c6,d5]) ).
cnf(d7,plain,
add('additive$uinverse'(multiply(X1,X0)),multiply(X1,'additive$uidentity')) = multiply(X1,'additive$uinverse'(X0)),
inference(superposition,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
add(multiply(X0,'additive$uidentity'),'additive$uinverse'(multiply(X0,X1))) = multiply(X0,'additive$uinverse'(X1)),
inference(demodulation,[status(thm)],[d7,c10]) ).
cnf(d9,plain,
add('additive$uidentity','additive$uinverse'(multiply(X0,X1))) = multiply(X0,'additive$uinverse'(X1)),
inference(demodulation,[status(thm)],[d8,c4]) ).
cnf(d10,plain,
'additive$uinverse'(multiply(X0,X1)) = multiply(X0,'additive$uinverse'(X1)),
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(superposition,[status(thm)],[c9,d5]) ).
cnf(d12,plain,
X1 = add(X0,add('additive$uinverse'(X0),X1)),
inference(superposition,[status(thm)],[d1,d5]) ).
cnf(d13,plain,
add(X0,'additive$uidentity') = 'additive$uinverse'('additive$uinverse'(X0)),
inference(superposition,[status(thm)],[d6,d1]) ).
cnf(d14,plain,
X0 = 'additive$uinverse'('additive$uinverse'(X0)),
inference(demodulation,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
X1 = add('additive$uinverse'(X0),add(X0,X1)),
inference(superposition,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
add(X0,add(X1,'additive$uinverse'(X0))) = X1,
inference(superposition,[status(thm)],[c10,d1]) ).
cnf(d17,plain,
add('additive$uinverse'(X0),add(X1,X0)) = X1,
inference(superposition,[status(thm)],[d14,d16]) ).
cnf(d18,plain,
add('additive$uinverse'(add(X1,X0)),X1) = 'additive$uinverse'(X0),
inference(superposition,[status(thm)],[d17,d17]) ).
cnf(d19,plain,
add(X0,'additive$uinverse'(add(X0,X1))) = 'additive$uinverse'(X1),
inference(demodulation,[status(thm)],[d18,c10]) ).
cnf(d20,plain,
'additive$uinverse'(add(X0,X1)) = add('additive$uinverse'(X0),'additive$uinverse'(X1)),
inference(superposition,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
multiply(add(x,y),'additive$uinverse'(z)) != 'additive$uinverse'(add(multiply(x,z),multiply(y,z))),
inference(demodulation,[status(thm)],[c0,d20]) ).
cnf(d22,plain,
multiply(add(x,y),'additive$uinverse'(z)) != 'additive$uinverse'(multiply(add(x,y),z)),
inference(demodulation,[status(thm)],[d21,d11]) ).
cnf(d23,plain,
multiply(add(x,y),'additive$uinverse'(z)) != multiply(add(x,y),'additive$uinverse'(z)),
inference(demodulation,[status(thm)],[d22,d10]) ).
cnf(d24,plain,
multiply(X0,add('additive$uidentity',X1)) = add('additive$uidentity',multiply(X0,X1)),
inference(superposition,[status(thm)],[c4,c8]) ).
cnf(d25,plain,
multiply(X1,X0) = add('additive$uidentity',multiply(X1,X0)),
inference(demodulation,[status(thm)],[d24,c1]) ).
cnf(d26,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d25,c1]) ).
cnf(d27,plain,
$false,
inference(resolution,[status(thm)],[d26,d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG018-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n007.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sat Sep 26 05:44:38 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.26/16.76 % SZS status Unsatisfiable for theBenchmark.p
% 3.26/16.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------