%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG008-4 : 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 : n001.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 51.27s 8.52s
% Output : CNFRefutation 51.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 15
% Syntax : Number of clauses : 131 ( 131 unt; 0 nHn; 30 RR)
% Number of literals : 131 ( 130 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; 4 con; 0-2 aty)
% Number of variables : 180 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(boolean_ring,hypothesis,
multiply(X0,X0) = X0 ).
cnf(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c ).
cnf(prove_commutativity,negated_conjecture,
multiply(b,a) != c ).
cnf(left_identity,axiom,
add('additive$uidentity',X0) = X0 ).
cnf(left_additive_inverse,axiom,
add('additive$uinverse'(X0),X0) = 'additive$uidentity' ).
cnf(distribute1,axiom,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)) ).
cnf(distribute2,axiom,
multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)) ).
cnf(additive_inverse_additive_inverse,axiom,
'additive$uinverse'('additive$uinverse'(X0)) = X0 ).
cnf(multiply_additive_id1,axiom,
multiply(X0,'additive$uidentity') = 'additive$uidentity' ).
cnf(multiply_additive_id2,axiom,
multiply('additive$uidentity',X0) = 'additive$uidentity' ).
cnf(multiply_additive_inverse1,axiom,
multiply(X0,'additive$uinverse'(X1)) = 'additive$uinverse'(multiply(X0,X1)) ).
cnf(multiply_additive_inverse2,axiom,
multiply('additive$uinverse'(X0),X1) = 'additive$uinverse'(multiply(X0,X1)) ).
cnf(associative_addition,axiom,
add(add(X0,X1),X2) = add(X0,add(X1,X2)) ).
cnf(commutative_addition,axiom,
add(X0,X1) = add(X1,X0) ).
cnf(associative_multiplication,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c0,plain,
multiply(X0,X0) = X0,
inference(clausification,[status(esa)],[boolean_ring]) ).
cnf(c1,plain,
multiply(a,b) = c,
inference(clausification,[status(esa)],[a_times_b_is_c]) ).
cnf(c2,plain,
multiply(b,a) != c,
inference(clausification,[status(esa)],[prove_commutativity]) ).
cnf(c3,plain,
add('additive$uidentity',X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c4,plain,
add('additive$uinverse'(X0),X0) = 'additive$uidentity',
inference(clausification,[status(esa)],[left_additive_inverse]) ).
cnf(c5,plain,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(clausification,[status(esa)],[distribute1]) ).
cnf(c6,plain,
multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
inference(clausification,[status(esa)],[distribute2]) ).
cnf(c8,plain,
'additive$uinverse'('additive$uinverse'(X0)) = X0,
inference(clausification,[status(esa)],[additive_inverse_additive_inverse]) ).
cnf(c9,plain,
multiply(X0,'additive$uidentity') = 'additive$uidentity',
inference(clausification,[status(esa)],[multiply_additive_id1]) ).
cnf(c10,plain,
multiply('additive$uidentity',X0) = 'additive$uidentity',
inference(clausification,[status(esa)],[multiply_additive_id2]) ).
cnf(c12,plain,
multiply(X0,'additive$uinverse'(X1)) = 'additive$uinverse'(multiply(X0,X1)),
inference(clausification,[status(esa)],[multiply_additive_inverse1]) ).
cnf(c13,plain,
multiply('additive$uinverse'(X0),X1) = 'additive$uinverse'(multiply(X0,X1)),
inference(clausification,[status(esa)],[multiply_additive_inverse2]) ).
cnf(c14,plain,
add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(clausification,[status(esa)],[associative_addition]) ).
cnf(c15,plain,
add(X0,X1) = add(X1,X0),
inference(clausification,[status(esa)],[commutative_addition]) ).
cnf(c16,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associative_multiplication]) ).
cnf(d0,plain,
add(X0,'additive$uidentity') = X0,
inference(superposition,[status(thm)],[c15,c3]) ).
cnf(d1,plain,
multiply(X0,add(X0,X1)) = add(X0,multiply(X0,X1)),
inference(superposition,[status(thm)],[c0,c5]) ).
cnf(d2,plain,
add(multiply(X0,X2),multiply(X0,X1)) = multiply(X0,add(X1,X2)),
inference(superposition,[status(thm)],[c5,c15]) ).
cnf(d3,plain,
multiply(c,X0) = multiply(a,multiply(b,X0)),
inference(superposition,[status(thm)],[c1,c16]) ).
cnf(d4,plain,
multiply('additive$uinverse'(X0),X1) = multiply(X0,'additive$uinverse'(X1)),
inference(demodulation,[status(thm)],[c13,c12]) ).
cnf(d5,plain,
multiply(X0,'additive$uinverse'(X0)) = 'additive$uinverse'(X0),
inference(superposition,[status(thm)],[c0,c12]) ).
cnf(d6,plain,
multiply('additive$uinverse'(X0),X0) = 'additive$uinverse'('additive$uinverse'(X0)),
inference(superposition,[status(thm)],[c8,d5]) ).
cnf(d7,plain,
multiply('additive$uinverse'(X0),X0) = X0,
inference(demodulation,[status(thm)],[d6,c8]) ).
cnf(d8,plain,
multiply(X0,'additive$uinverse'(X0)) = X0,
inference(demodulation,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
X0 = 'additive$uinverse'(X0),
inference(demodulation,[status(thm)],[d5,d8]) ).
cnf(d10,plain,
'additive$uinverse'(X0) = multiply(X0,'additive$uinverse'('additive$uinverse'(X0))),
inference(superposition,[status(thm)],[c0,d4]) ).
cnf(d11,plain,
X0 = multiply(X0,'additive$uinverse'('additive$uinverse'(X0))),
inference(demodulation,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
X0 = multiply(X0,'additive$uinverse'(X0)),
inference(demodulation,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
X0 = multiply(X0,X0),
inference(demodulation,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
multiply(c,b) = multiply(a,b),
inference(superposition,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
multiply(c,b) = c,
inference(demodulation,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
add(multiply(c,X0),c) = multiply(c,add(b,X0)),
inference(superposition,[status(thm)],[d15,d2]) ).
cnf(d17,plain,
add(c,multiply(c,X0)) = multiply(c,add(b,X0)),
inference(demodulation,[status(thm)],[d16,c15]) ).
cnf(d18,plain,
multiply(c,add(c,X0)) = multiply(c,add(b,X0)),
inference(demodulation,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
add(X0,'additive$uinverse'(X0)) = 'additive$uidentity',
inference(superposition,[status(thm)],[c8,c4]) ).
cnf(d20,plain,
add(X0,X0) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d19,d9]) ).
cnf(d21,plain,
add('additive$uidentity',X1) = add(X0,add(X0,X1)),
inference(superposition,[status(thm)],[d20,c14]) ).
cnf(d22,plain,
X0 = add(X1,add(X1,X0)),
inference(demodulation,[status(thm)],[d21,c3]) ).
cnf(d23,plain,
X1 = add(X0,add(X1,X0)),
inference(superposition,[status(thm)],[c15,d22]) ).
cnf(d24,plain,
multiply(c,X0) = multiply(c,add(b,add(X0,c))),
inference(superposition,[status(thm)],[d23,d18]) ).
cnf(d25,plain,
multiply(X0,add(X1,X2)) = add(multiply(X0,X2),multiply(X0,X1)),
inference(superposition,[status(thm)],[c15,c5]) ).
cnf(d26,plain,
multiply(X0,add(X1,X2)) = multiply(X0,add(X2,X1)),
inference(superposition,[status(thm)],[d25,c5]) ).
cnf(d27,plain,
multiply(c,add(X0,c)) = multiply(c,add(b,X0)),
inference(superposition,[status(thm)],[d18,d26]) ).
cnf(d28,plain,
add(X0,add(X1,'additive$uidentity')) = add(X0,X1),
inference(superposition,[status(thm)],[c14,d0]) ).
cnf(d29,plain,
add(X1,X0) = add(X1,X0),
inference(demodulation,[status(thm)],[d28,d0]) ).
cnf(d30,plain,
multiply(X0,add(X1,X0)) = add(multiply(X0,X1),X0),
inference(superposition,[status(thm)],[c0,c5]) ).
cnf(d31,plain,
multiply(X0,add(X1,X0)) = add(X0,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d30,c15]) ).
cnf(d32,plain,
add(X0,multiply(X0,X1)) = multiply(X0,add(X1,X0)),
inference(superposition,[status(thm)],[d31,d29]) ).
cnf(d33,plain,
multiply(multiply(X0,X1),multiply(X0,'additive$uinverse'(X1))) = 'additive$uinverse'(multiply(X0,X1)),
inference(superposition,[status(thm)],[c12,d5]) ).
cnf(d34,plain,
multiply(X0,multiply(X1,multiply(X0,'additive$uinverse'(X1)))) = 'additive$uinverse'(multiply(X0,X1)),
inference(demodulation,[status(thm)],[d33,c16]) ).
cnf(d35,plain,
multiply(X1,multiply(X0,multiply(X1,X0))) = 'additive$uinverse'(multiply(X1,X0)),
inference(demodulation,[status(thm)],[d34,d9]) ).
cnf(d36,plain,
multiply(X0,multiply(X1,multiply(X0,X1))) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d35,d9]) ).
cnf(d37,plain,
multiply(add(X0,X1),X0) = add(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c0,c6]) ).
cnf(d38,plain,
'additive$uinverse'(multiply(X0,'additive$uinverse'(X1))) = multiply(X0,X1),
inference(superposition,[status(thm)],[c12,c8]) ).
cnf(d39,plain,
multiply(X0,'additive$uinverse'(X1)) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d38,d9]) ).
cnf(d40,plain,
multiply(X1,X0) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d39,d9]) ).
cnf(d41,plain,
multiply(X0,X1) = multiply(X0,multiply(X0,X1)),
inference(superposition,[status(thm)],[d13,c16]) ).
cnf(d42,plain,
c = multiply(a,b),
inference(superposition,[status(thm)],[c1,d40]) ).
cnf(d43,plain,
multiply(a,b) = multiply(a,c),
inference(superposition,[status(thm)],[d42,d41]) ).
cnf(d44,plain,
c = multiply(a,c),
inference(demodulation,[status(thm)],[d43,c1]) ).
cnf(d45,plain,
multiply(a,c) = c,
inference(superposition,[status(thm)],[d44,d40]) ).
cnf(d46,plain,
multiply(add(c,a),c) = add(c,c),
inference(superposition,[status(thm)],[d45,d37]) ).
cnf(d47,plain,
multiply(add(a,c),c) = add(c,c),
inference(demodulation,[status(thm)],[d46,c15]) ).
cnf(d48,plain,
multiply(add(a,c),c) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d47,d20]) ).
cnf(d49,plain,
multiply('additive$uidentity',X0) = multiply(add(a,c),multiply(c,X0)),
inference(superposition,[status(thm)],[d48,c16]) ).
cnf(d50,plain,
'additive$uidentity' = multiply(add(a,c),multiply(c,X0)),
inference(demodulation,[status(thm)],[d49,c10]) ).
cnf(d51,plain,
multiply(c,'additive$uidentity') = multiply(c,add(a,c)),
inference(superposition,[status(thm)],[d50,d36]) ).
cnf(d52,plain,
'additive$uidentity' = multiply(c,add(a,c)),
inference(demodulation,[status(thm)],[d51,c9]) ).
cnf(d53,plain,
add(c,'additive$uidentity') = multiply(c,add(add(a,c),c)),
inference(superposition,[status(thm)],[d52,d32]) ).
cnf(d54,plain,
c = multiply(c,add(add(a,c),c)),
inference(demodulation,[status(thm)],[d53,d0]) ).
cnf(d55,plain,
c = multiply(c,add(b,add(a,c))),
inference(demodulation,[status(thm)],[d54,d27]) ).
cnf(d56,plain,
c = multiply(c,a),
inference(demodulation,[status(thm)],[d55,d24]) ).
cnf(d57,plain,
multiply(a,multiply(b,X0)) = multiply(c,X0),
inference(superposition,[status(thm)],[d3,d40]) ).
cnf(d58,plain,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(superposition,[status(thm)],[d57,d36]) ).
cnf(d59,plain,
multiply(b,c) = multiply(b,a),
inference(demodulation,[status(thm)],[d58,d56]) ).
cnf(d60,plain,
add(X0,add(X0,X1)) = X1,
inference(superposition,[status(thm)],[d22,d29]) ).
cnf(d61,plain,
multiply(add(a,X0),c) = add(c,multiply(X0,c)),
inference(superposition,[status(thm)],[d44,c6]) ).
cnf(d62,plain,
multiply(add(a,X0),c) = multiply(add(c,X0),c),
inference(demodulation,[status(thm)],[d61,d37]) ).
cnf(d63,plain,
multiply(add(X0,a),c) = add(multiply(X0,c),c),
inference(superposition,[status(thm)],[d44,c6]) ).
cnf(d64,plain,
multiply(add(X0,a),c) = add(c,multiply(X0,c)),
inference(demodulation,[status(thm)],[d63,c15]) ).
cnf(d65,plain,
multiply(add(X0,a),c) = multiply(add(c,X0),c),
inference(demodulation,[status(thm)],[d64,d37]) ).
cnf(d66,plain,
multiply(add(X1,X0),'additive$uinverse'(X0)) = add(multiply(X1,'additive$uinverse'(X0)),'additive$uinverse'(X0)),
inference(superposition,[status(thm)],[d5,c6]) ).
cnf(d67,plain,
multiply(add(X1,X0),X0) = add(multiply(X1,'additive$uinverse'(X0)),'additive$uinverse'(X0)),
inference(demodulation,[status(thm)],[d66,d9]) ).
cnf(d68,plain,
multiply(add(X0,X1),X1) = add('additive$uinverse'(X1),multiply(X0,'additive$uinverse'(X1))),
inference(demodulation,[status(thm)],[d67,c15]) ).
cnf(d69,plain,
multiply(add(X1,X0),X0) = multiply(add('additive$uinverse'(X0),X1),'additive$uinverse'(X0)),
inference(demodulation,[status(thm)],[d68,d37]) ).
cnf(d70,plain,
multiply(add(X1,X0),X0) = multiply(add(X0,X1),'additive$uinverse'(X0)),
inference(demodulation,[status(thm)],[d69,d9]) ).
cnf(d71,plain,
multiply(add(X1,X0),X0) = multiply(add(X0,X1),X0),
inference(demodulation,[status(thm)],[d70,d9]) ).
cnf(d72,plain,
multiply(add(X0,c),c) = multiply(add(X0,a),c),
inference(superposition,[status(thm)],[d65,d71]) ).
cnf(d73,plain,
multiply(add(X1,X0),X0) = add(multiply(X1,X0),X0),
inference(superposition,[status(thm)],[c0,c6]) ).
cnf(d74,plain,
multiply(add(X0,X1),X1) = add(X1,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d73,c15]) ).
cnf(d75,plain,
multiply(add(X0,X2),X1) = add(multiply(X2,X1),multiply(X0,X1)),
inference(superposition,[status(thm)],[c6,c15]) ).
cnf(d76,plain,
multiply(add(X0,X2),X1) = multiply(add(X2,X0),X1),
inference(superposition,[status(thm)],[d75,c6]) ).
cnf(d77,plain,
multiply(multiply(X0,X1),add(X2,multiply(X0,X1))) = add(multiply(X0,X1),multiply(X0,multiply(X1,X2))),
inference(superposition,[status(thm)],[c16,d31]) ).
cnf(d78,plain,
multiply(X0,multiply(X1,add(X2,multiply(X0,X1)))) = add(multiply(X0,X1),multiply(X0,multiply(X1,X2))),
inference(demodulation,[status(thm)],[d77,c16]) ).
cnf(d79,plain,
multiply(X0,multiply(X1,add(X2,multiply(X0,X1)))) = multiply(X0,add(X1,multiply(X1,X2))),
inference(demodulation,[status(thm)],[d78,c5]) ).
cnf(d80,plain,
multiply(X2,multiply(X0,add(X1,multiply(X2,X0)))) = multiply(X2,multiply(X0,add(X0,X1))),
inference(demodulation,[status(thm)],[d79,d1]) ).
cnf(d81,plain,
multiply(multiply(X0,X1),add(X1,multiply(X0,X1))) = multiply(add(multiply(X0,X1),X0),X1),
inference(superposition,[status(thm)],[d75,d31]) ).
cnf(d82,plain,
multiply(X0,multiply(X1,add(X1,multiply(X0,X1)))) = multiply(add(multiply(X0,X1),X0),X1),
inference(demodulation,[status(thm)],[d81,c16]) ).
cnf(d83,plain,
multiply(X0,multiply(X1,add(X1,X1))) = multiply(add(multiply(X0,X1),X0),X1),
inference(demodulation,[status(thm)],[d82,d80]) ).
cnf(d84,plain,
multiply(X1,multiply(X0,'additive$uidentity')) = multiply(add(multiply(X1,X0),X1),X0),
inference(demodulation,[status(thm)],[d83,d20]) ).
cnf(d85,plain,
multiply(X1,'additive$uidentity') = multiply(add(multiply(X1,X0),X1),X0),
inference(demodulation,[status(thm)],[d84,c9]) ).
cnf(d86,plain,
'additive$uidentity' = multiply(add(multiply(X0,X1),X0),X1),
inference(demodulation,[status(thm)],[d85,c9]) ).
cnf(d87,plain,
'additive$uidentity' = multiply(add(X0,multiply(X0,X1)),X1),
inference(demodulation,[status(thm)],[d86,d76]) ).
cnf(d88,plain,
'additive$uidentity' = multiply(multiply(X0,add(X0,X1)),X1),
inference(demodulation,[status(thm)],[d87,d1]) ).
cnf(d89,plain,
'additive$uidentity' = multiply(X0,multiply(add(X0,X1),X1)),
inference(demodulation,[status(thm)],[d88,c16]) ).
cnf(d90,plain,
'additive$uidentity' = multiply(X0,multiply(add(X1,X0),X1)),
inference(superposition,[status(thm)],[d76,d89]) ).
cnf(d91,plain,
'additive$uidentity' = multiply(add(X1,X0),multiply(X1,X0)),
inference(superposition,[status(thm)],[d23,d90]) ).
cnf(d92,plain,
'additive$uidentity' = multiply(add(a,b),c),
inference(superposition,[status(thm)],[d42,d91]) ).
cnf(d93,plain,
multiply(add(add(a,b),c),c) = add(c,'additive$uidentity'),
inference(superposition,[status(thm)],[d92,d74]) ).
cnf(d94,plain,
multiply(add(add(a,b),a),c) = add(c,'additive$uidentity'),
inference(demodulation,[status(thm)],[d93,d72]) ).
cnf(d95,plain,
multiply(add(c,add(a,b)),c) = add(c,'additive$uidentity'),
inference(demodulation,[status(thm)],[d94,d65]) ).
cnf(d96,plain,
multiply(add(a,add(a,b)),c) = add(c,'additive$uidentity'),
inference(demodulation,[status(thm)],[d95,d62]) ).
cnf(d97,plain,
multiply(b,c) = add(c,'additive$uidentity'),
inference(demodulation,[status(thm)],[d96,d60]) ).
cnf(d98,plain,
multiply(b,a) = add(c,'additive$uidentity'),
inference(demodulation,[status(thm)],[d97,d59]) ).
cnf(d99,plain,
multiply(b,a) = c,
inference(demodulation,[status(thm)],[d98,d0]) ).
cnf(d100,plain,
$false,
inference(resolution,[status(thm)],[c2,d99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 05:51:12 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 51.27/8.52 % SZS status Unsatisfiable for theBenchmark.p
% 51.27/8.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------