%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG008-3 : 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 : n017.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 57.98s 10.14s
% Output : CNFRefutation 57.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 16
% Syntax : Number of clauses : 131 ( 131 unt; 0 nHn; 33 RR)
% Number of literals : 131 ( 130 equ; 3 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 : 175 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
add(X0,'additive$uidentity') = X0 ).
cnf(right_inverse,axiom,
add(X0,'additive$uinverse'(X0)) = 'additive$uidentity' ).
cnf(boolean_ring,hypothesis,
multiply(X0,X0) = X0 ).
cnf(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c ).
cnf(prove_commutativity,negated_conjecture,
multiply(b,a) != c ).
cnf(left_identity,axiom,
add('additive$uidentity',X0) = X0 ).
cnf(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,
add(X0,'additive$uidentity') = X0,
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c1,plain,
add(X0,'additive$uinverse'(X0)) = 'additive$uidentity',
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c2,plain,
multiply(X0,X0) = X0,
inference(clausification,[status(esa)],[boolean_ring]) ).
cnf(c3,plain,
multiply(a,b) = c,
inference(clausification,[status(esa)],[a_times_b_is_c]) ).
cnf(c4,plain,
multiply(b,a) != c,
inference(clausification,[status(esa)],[prove_commutativity]) ).
cnf(c5,plain,
add('additive$uidentity',X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c7,plain,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(clausification,[status(esa)],[distribute1]) ).
cnf(c8,plain,
multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
inference(clausification,[status(esa)],[distribute2]) ).
cnf(c10,plain,
'additive$uinverse'('additive$uinverse'(X0)) = X0,
inference(clausification,[status(esa)],[additive_inverse_additive_inverse]) ).
cnf(c11,plain,
multiply(X0,'additive$uidentity') = 'additive$uidentity',
inference(clausification,[status(esa)],[multiply_additive_id1]) ).
cnf(c12,plain,
multiply('additive$uidentity',X0) = 'additive$uidentity',
inference(clausification,[status(esa)],[multiply_additive_id2]) ).
cnf(c14,plain,
multiply(X0,'additive$uinverse'(X1)) = 'additive$uinverse'(multiply(X0,X1)),
inference(clausification,[status(esa)],[multiply_additive_inverse1]) ).
cnf(c15,plain,
multiply('additive$uinverse'(X0),X1) = 'additive$uinverse'(multiply(X0,X1)),
inference(clausification,[status(esa)],[multiply_additive_inverse2]) ).
cnf(c16,plain,
add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(clausification,[status(esa)],[associative_addition]) ).
cnf(c17,plain,
add(X0,X1) = add(X1,X0),
inference(clausification,[status(esa)],[commutative_addition]) ).
cnf(c18,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associative_multiplication]) ).
cnf(d0,plain,
X0 = add(X0,'additive$uidentity'),
inference(superposition,[status(thm)],[c5,c17]) ).
cnf(d1,plain,
add(X0,X1) = add(X0,add(X1,'additive$uidentity')),
inference(superposition,[status(thm)],[c16,d0]) ).
cnf(d2,plain,
add(X1,X0) = add(X1,X0),
inference(demodulation,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
multiply('additive$uinverse'(X0),X1) = multiply(X0,'additive$uinverse'(X1)),
inference(demodulation,[status(thm)],[c15,c14]) ).
cnf(d4,plain,
multiply(X0,'additive$uinverse'(X0)) = 'additive$uinverse'(X0),
inference(superposition,[status(thm)],[c2,c14]) ).
cnf(d5,plain,
multiply('additive$uinverse'(X0),X0) = 'additive$uinverse'('additive$uinverse'(X0)),
inference(superposition,[status(thm)],[c10,d4]) ).
cnf(d6,plain,
multiply('additive$uinverse'(X0),X0) = X0,
inference(demodulation,[status(thm)],[d5,c10]) ).
cnf(d7,plain,
multiply(X0,'additive$uinverse'(X0)) = X0,
inference(demodulation,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
X0 = 'additive$uinverse'(X0),
inference(demodulation,[status(thm)],[d4,d7]) ).
cnf(d9,plain,
add(X0,X0) = 'additive$uidentity',
inference(demodulation,[status(thm)],[c1,d8]) ).
cnf(d10,plain,
'additive$uidentity' = add(X0,X0),
inference(superposition,[status(thm)],[d9,c17]) ).
cnf(d11,plain,
add('additive$uidentity',X1) = add(X0,add(X0,X1)),
inference(superposition,[status(thm)],[d10,c16]) ).
cnf(d12,plain,
X0 = add(X1,add(X1,X0)),
inference(demodulation,[status(thm)],[d11,c5]) ).
cnf(d13,plain,
add(X0,add(X0,X1)) = X1,
inference(superposition,[status(thm)],[d12,d2]) ).
cnf(d14,plain,
multiply(add(X0,X1),X0) = add(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c2,c8]) ).
cnf(d15,plain,
multiply(X0,X1) = multiply(X0,multiply(X0,X1)),
inference(superposition,[status(thm)],[c2,c18]) ).
cnf(d16,plain,
'additive$uinverse'(multiply(X0,'additive$uinverse'(X1))) = multiply(X0,X1),
inference(superposition,[status(thm)],[c14,c10]) ).
cnf(d17,plain,
multiply(X0,'additive$uinverse'(X1)) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
multiply(X1,X0) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d17,d8]) ).
cnf(d19,plain,
c = multiply(a,b),
inference(superposition,[status(thm)],[c3,d18]) ).
cnf(d20,plain,
multiply(a,b) = multiply(a,c),
inference(superposition,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
c = multiply(a,c),
inference(demodulation,[status(thm)],[d20,c3]) ).
cnf(d22,plain,
multiply(add(a,X0),c) = add(c,multiply(X0,c)),
inference(superposition,[status(thm)],[d21,c8]) ).
cnf(d23,plain,
multiply(add(a,X0),c) = multiply(add(c,X0),c),
inference(demodulation,[status(thm)],[d22,d14]) ).
cnf(d24,plain,
multiply(add(X0,a),c) = add(multiply(X0,c),c),
inference(superposition,[status(thm)],[d21,c8]) ).
cnf(d25,plain,
multiply(add(X0,a),c) = add(c,multiply(X0,c)),
inference(demodulation,[status(thm)],[d24,c17]) ).
cnf(d26,plain,
multiply(add(X0,a),c) = multiply(add(c,X0),c),
inference(demodulation,[status(thm)],[d25,d14]) ).
cnf(d27,plain,
multiply(add(X1,X0),'additive$uinverse'(X0)) = add(multiply(X1,'additive$uinverse'(X0)),'additive$uinverse'(X0)),
inference(superposition,[status(thm)],[d4,c8]) ).
cnf(d28,plain,
multiply(add(X1,X0),X0) = add(multiply(X1,'additive$uinverse'(X0)),'additive$uinverse'(X0)),
inference(demodulation,[status(thm)],[d27,d8]) ).
cnf(d29,plain,
multiply(add(X0,X1),X1) = add('additive$uinverse'(X1),multiply(X0,'additive$uinverse'(X1))),
inference(demodulation,[status(thm)],[d28,c17]) ).
cnf(d30,plain,
multiply(add(X1,X0),X0) = multiply(add('additive$uinverse'(X0),X1),'additive$uinverse'(X0)),
inference(demodulation,[status(thm)],[d29,d14]) ).
cnf(d31,plain,
multiply(add(X1,X0),X0) = multiply(add(X0,X1),'additive$uinverse'(X0)),
inference(demodulation,[status(thm)],[d30,d8]) ).
cnf(d32,plain,
multiply(add(X1,X0),X0) = multiply(add(X0,X1),X0),
inference(demodulation,[status(thm)],[d31,d8]) ).
cnf(d33,plain,
multiply(add(X0,c),c) = multiply(add(X0,a),c),
inference(superposition,[status(thm)],[d26,d32]) ).
cnf(d34,plain,
add(multiply(X2,X1),multiply(X0,X1)) = multiply(add(X0,X2),X1),
inference(superposition,[status(thm)],[c8,c17]) ).
cnf(d35,plain,
add(X0,multiply(X1,X0)) = multiply(add(X1,X0),X0),
inference(superposition,[status(thm)],[c2,d34]) ).
cnf(d36,plain,
multiply(add(X0,X2),X1) = add(multiply(X2,X1),multiply(X0,X1)),
inference(superposition,[status(thm)],[c8,c17]) ).
cnf(d37,plain,
multiply(add(X0,X2),X1) = multiply(add(X2,X0),X1),
inference(superposition,[status(thm)],[d36,c8]) ).
cnf(d38,plain,
multiply(X0,add(X0,X1)) = add(X0,multiply(X0,X1)),
inference(superposition,[status(thm)],[c2,c7]) ).
cnf(d39,plain,
multiply(X0,add(X1,X0)) = add(multiply(X0,X1),X0),
inference(superposition,[status(thm)],[c2,c7]) ).
cnf(d40,plain,
multiply(X0,add(X1,X0)) = add(X0,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d39,c17]) ).
cnf(d41,plain,
multiply(multiply(X0,X1),add(X2,multiply(X0,X1))) = add(multiply(X0,X1),multiply(X0,multiply(X1,X2))),
inference(superposition,[status(thm)],[c18,d40]) ).
cnf(d42,plain,
multiply(X0,multiply(X1,add(X2,multiply(X0,X1)))) = add(multiply(X0,X1),multiply(X0,multiply(X1,X2))),
inference(demodulation,[status(thm)],[d41,c18]) ).
cnf(d43,plain,
multiply(X0,multiply(X1,add(X2,multiply(X0,X1)))) = multiply(X0,add(X1,multiply(X1,X2))),
inference(demodulation,[status(thm)],[d42,c7]) ).
cnf(d44,plain,
multiply(X2,multiply(X0,add(X1,multiply(X2,X0)))) = multiply(X2,multiply(X0,add(X0,X1))),
inference(demodulation,[status(thm)],[d43,d38]) ).
cnf(d45,plain,
multiply(multiply(X0,X1),add(X1,multiply(X0,X1))) = multiply(add(multiply(X0,X1),X0),X1),
inference(superposition,[status(thm)],[d36,d40]) ).
cnf(d46,plain,
multiply(X0,multiply(X1,add(X1,multiply(X0,X1)))) = multiply(add(multiply(X0,X1),X0),X1),
inference(demodulation,[status(thm)],[d45,c18]) ).
cnf(d47,plain,
multiply(X0,multiply(X1,add(X1,X1))) = multiply(add(multiply(X0,X1),X0),X1),
inference(demodulation,[status(thm)],[d46,d44]) ).
cnf(d48,plain,
multiply(X1,multiply(X0,'additive$uidentity')) = multiply(add(multiply(X1,X0),X1),X0),
inference(demodulation,[status(thm)],[d47,d9]) ).
cnf(d49,plain,
multiply(X1,'additive$uidentity') = multiply(add(multiply(X1,X0),X1),X0),
inference(demodulation,[status(thm)],[d48,c11]) ).
cnf(d50,plain,
'additive$uidentity' = multiply(add(multiply(X0,X1),X0),X1),
inference(demodulation,[status(thm)],[d49,c11]) ).
cnf(d51,plain,
'additive$uidentity' = multiply(add(X0,multiply(X0,X1)),X1),
inference(demodulation,[status(thm)],[d50,d37]) ).
cnf(d52,plain,
'additive$uidentity' = multiply(multiply(X0,add(X0,X1)),X1),
inference(demodulation,[status(thm)],[d51,d38]) ).
cnf(d53,plain,
'additive$uidentity' = multiply(X0,multiply(add(X0,X1),X1)),
inference(demodulation,[status(thm)],[d52,c18]) ).
cnf(d54,plain,
'additive$uidentity' = multiply(X0,multiply(add(X1,X0),X1)),
inference(superposition,[status(thm)],[d37,d53]) ).
cnf(d55,plain,
X1 = add(X0,add(X1,X0)),
inference(superposition,[status(thm)],[c17,d12]) ).
cnf(d56,plain,
'additive$uidentity' = multiply(add(X1,X0),multiply(X1,X0)),
inference(superposition,[status(thm)],[d55,d54]) ).
cnf(d57,plain,
multiply(c,X0) = multiply(a,multiply(b,X0)),
inference(superposition,[status(thm)],[c3,c18]) ).
cnf(d58,plain,
multiply(c,b) = multiply(a,b),
inference(superposition,[status(thm)],[c2,d57]) ).
cnf(d59,plain,
multiply(c,b) = c,
inference(demodulation,[status(thm)],[d58,c3]) ).
cnf(d60,plain,
'additive$uidentity' = multiply(add(c,b),c),
inference(superposition,[status(thm)],[d59,d56]) ).
cnf(d61,plain,
'additive$uidentity' = multiply(add(b,a),c),
inference(demodulation,[status(thm)],[d60,d26]) ).
cnf(d62,plain,
'additive$uidentity' = multiply(add(a,b),c),
inference(demodulation,[status(thm)],[d61,d37]) ).
cnf(d63,plain,
add(c,'additive$uidentity') = multiply(add(add(a,b),c),c),
inference(superposition,[status(thm)],[d62,d35]) ).
cnf(d64,plain,
c = multiply(add(add(a,b),c),c),
inference(demodulation,[status(thm)],[d63,c0]) ).
cnf(d65,plain,
c = multiply(add(add(a,b),a),c),
inference(demodulation,[status(thm)],[d64,d33]) ).
cnf(d66,plain,
c = multiply(add(c,add(a,b)),c),
inference(demodulation,[status(thm)],[d65,d26]) ).
cnf(d67,plain,
c = multiply(add(a,add(a,b)),c),
inference(demodulation,[status(thm)],[d66,d23]) ).
cnf(d68,plain,
c = multiply(b,c),
inference(demodulation,[status(thm)],[d67,d13]) ).
cnf(d69,plain,
add(X0,add(X1,X0)) = X1,
inference(superposition,[status(thm)],[c17,d13]) ).
cnf(d70,plain,
add(multiply(X0,add(X1,X0)),X2) = add(X0,add(multiply(X0,X1),X2)),
inference(superposition,[status(thm)],[d40,c16]) ).
cnf(d71,plain,
multiply(X0,X1) = multiply(X0,multiply(X1,multiply(X0,X1))),
inference(superposition,[status(thm)],[c2,c18]) ).
cnf(d72,plain,
multiply(a,c) = c,
inference(superposition,[status(thm)],[d21,d18]) ).
cnf(d73,plain,
multiply(add(c,a),c) = add(c,c),
inference(superposition,[status(thm)],[d72,d14]) ).
cnf(d74,plain,
multiply(add(a,c),c) = add(c,c),
inference(demodulation,[status(thm)],[d73,c17]) ).
cnf(d75,plain,
multiply(add(a,c),c) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d74,d9]) ).
cnf(d76,plain,
multiply('additive$uidentity',X0) = multiply(add(a,c),multiply(c,X0)),
inference(superposition,[status(thm)],[d75,c18]) ).
cnf(d77,plain,
'additive$uidentity' = multiply(add(a,c),multiply(c,X0)),
inference(demodulation,[status(thm)],[d76,c12]) ).
cnf(d78,plain,
multiply(c,add(a,c)) = multiply(c,'additive$uidentity'),
inference(superposition,[status(thm)],[d77,d71]) ).
cnf(d79,plain,
multiply(c,add(a,c)) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d78,c11]) ).
cnf(d80,plain,
add('additive$uidentity',X0) = add(c,add(multiply(c,a),X0)),
inference(superposition,[status(thm)],[d79,d70]) ).
cnf(d81,plain,
X0 = add(c,add(multiply(c,a),X0)),
inference(demodulation,[status(thm)],[d80,c5]) ).
cnf(d82,plain,
c = multiply(c,a),
inference(superposition,[status(thm)],[d81,d69]) ).
cnf(d83,plain,
multiply(multiply(X0,X1),multiply(X0,'additive$uinverse'(X1))) = 'additive$uinverse'(multiply(X0,X1)),
inference(superposition,[status(thm)],[c14,d4]) ).
cnf(d84,plain,
multiply(X0,multiply(X1,multiply(X0,'additive$uinverse'(X1)))) = 'additive$uinverse'(multiply(X0,X1)),
inference(demodulation,[status(thm)],[d83,c18]) ).
cnf(d85,plain,
multiply(X1,multiply(X0,multiply(X1,X0))) = 'additive$uinverse'(multiply(X1,X0)),
inference(demodulation,[status(thm)],[d84,d8]) ).
cnf(d86,plain,
multiply(X0,multiply(X1,multiply(X0,X1))) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d85,d8]) ).
cnf(d87,plain,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(superposition,[status(thm)],[d57,d86]) ).
cnf(d88,plain,
multiply(b,c) = multiply(b,a),
inference(demodulation,[status(thm)],[d87,d82]) ).
cnf(d89,plain,
c = multiply(b,a),
inference(demodulation,[status(thm)],[d88,d68]) ).
cnf(d90,plain,
c != c,
inference(demodulation,[status(thm)],[c4,d89]) ).
cnf(d91,plain,
multiply(c,add(b,c)) = add(c,c),
inference(superposition,[status(thm)],[d59,d40]) ).
cnf(d92,plain,
multiply(c,add(b,c)) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d91,d9]) ).
cnf(d93,plain,
'additive$uidentity' = multiply(c,add(b,c)),
inference(superposition,[status(thm)],[d92,d18]) ).
cnf(d94,plain,
add('additive$uidentity',X0) = add(c,add(multiply(c,b),X0)),
inference(superposition,[status(thm)],[d93,d70]) ).
cnf(d95,plain,
X0 = add(c,add(multiply(c,b),X0)),
inference(demodulation,[status(thm)],[d94,c5]) ).
cnf(d96,plain,
X0 = add(c,add(c,X0)),
inference(demodulation,[status(thm)],[d95,d59]) ).
cnf(d97,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d96,d13]) ).
cnf(d98,plain,
$false,
inference(resolution,[status(thm)],[d97,d90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 05:39:48 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 57.98/10.14 % SZS status Unsatisfiable for theBenchmark.p
% 57.98/10.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------