%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG008-7 : 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 : n018.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 08:25:35 AM UTC 2026
% Result : Unsatisfiable 62.32s 13.80s
% Output : CNFRefutation 62.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 11
% Syntax : Number of clauses : 134 ( 134 unt; 0 nHn; 31 RR)
% Number of literals : 134 ( 133 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 : 181 ( 8 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_additive_identity,axiom,
add('additive$uidentity',X0) = X0 ).
cnf(right_additive_identity,axiom,
add(X0,'additive$uidentity') = X0 ).
cnf(right_additive_inverse,axiom,
add(X0,'additive$uinverse'(X0)) = 'additive$uidentity' ).
cnf(associativity_for_addition,axiom,
add(X0,add(X1,X2)) = add(add(X0,X1),X2) ).
cnf(commutativity_for_addition,axiom,
add(X0,X1) = add(X1,X0) ).
cnf(associativity_for_multiplication,axiom,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2) ).
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(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$uidentity',X0) = X0,
inference(clausification,[status(esa)],[left_additive_identity]) ).
cnf(c4,plain,
add(X0,'additive$uidentity') = X0,
inference(clausification,[status(esa)],[right_additive_identity]) ).
cnf(c6,plain,
add(X0,'additive$uinverse'(X0)) = 'additive$uidentity',
inference(clausification,[status(esa)],[right_additive_inverse]) ).
cnf(c7,plain,
add(X0,add(X1,X2)) = add(add(X0,X1),X2),
inference(clausification,[status(esa)],[associativity_for_addition]) ).
cnf(c8,plain,
add(X0,X1) = add(X1,X0),
inference(clausification,[status(esa)],[commutativity_for_addition]) ).
cnf(c9,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(clausification,[status(esa)],[associativity_for_multiplication]) ).
cnf(c10,plain,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(clausification,[status(esa)],[distribute1]) ).
cnf(c11,plain,
multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
inference(clausification,[status(esa)],[distribute2]) ).
cnf(d0,plain,
add(X0,add(X1,'additive$uidentity')) = add(X0,X1),
inference(superposition,[status(thm)],[c7,c4]) ).
cnf(d1,plain,
add(X1,X0) = add(X1,X0),
inference(demodulation,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
add(X0,add('additive$uinverse'(X0),X1)) = add('additive$uidentity',X1),
inference(superposition,[status(thm)],[c6,c7]) ).
cnf(d3,plain,
add(X1,add('additive$uinverse'(X1),X0)) = X0,
inference(demodulation,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
X1 = add(X0,add('additive$uinverse'(X0),X1)),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
X1 = add(X0,add(X1,'additive$uinverse'(X0))),
inference(superposition,[status(thm)],[c8,d4]) ).
cnf(d6,plain,
multiply(X0,add(X0,X1)) = add(X0,multiply(X0,X1)),
inference(superposition,[status(thm)],[c0,c10]) ).
cnf(d7,plain,
multiply(X0,X0) = add(X0,multiply(X0,'additive$uidentity')),
inference(superposition,[status(thm)],[c4,d6]) ).
cnf(d8,plain,
X0 = add(X0,multiply(X0,'additive$uidentity')),
inference(demodulation,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
multiply('additive$uinverse'(X0),'additive$uidentity') = add(X0,'additive$uinverse'(X0)),
inference(superposition,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
multiply('additive$uinverse'(X0),'additive$uidentity') = 'additive$uidentity',
inference(demodulation,[status(thm)],[d9,c6]) ).
cnf(d11,plain,
'additive$uidentity' = add(X0,'additive$uinverse'(X0)),
inference(superposition,[status(thm)],[c6,d1]) ).
cnf(d12,plain,
add(X0,'additive$uidentity') = 'additive$uinverse'('additive$uinverse'(X0)),
inference(superposition,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
X0 = 'additive$uinverse'('additive$uinverse'(X0)),
inference(demodulation,[status(thm)],[d12,c4]) ).
cnf(d14,plain,
multiply(X0,'additive$uidentity') = 'additive$uidentity',
inference(superposition,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
multiply(X0,'additive$uidentity') = add(X0,multiply(X0,'additive$uinverse'(X0))),
inference(superposition,[status(thm)],[d11,d6]) ).
cnf(d16,plain,
'additive$uidentity' = add(X0,multiply(X0,'additive$uinverse'(X0))),
inference(demodulation,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
add(X0,multiply(X0,'additive$uidentity')) = X0,
inference(superposition,[status(thm)],[d8,d1]) ).
cnf(d18,plain,
add('additive$uinverse'(X0),'additive$uidentity') = 'additive$uinverse'(X0),
inference(superposition,[status(thm)],[d10,d17]) ).
cnf(d19,plain,
'additive$uinverse'(X0) = 'additive$uinverse'(X0),
inference(demodulation,[status(thm)],[d18,c4]) ).
cnf(d20,plain,
'additive$uinverse'('additive$uinverse'(X0)) = X0,
inference(superposition,[status(thm)],[d13,d19]) ).
cnf(d21,plain,
'additive$uidentity' = add('additive$uinverse'(X0),multiply('additive$uinverse'(X0),X0)),
inference(superposition,[status(thm)],[d20,d16]) ).
cnf(d22,plain,
multiply('additive$uinverse'(X0),X0) = add(X0,'additive$uidentity'),
inference(superposition,[status(thm)],[d21,d4]) ).
cnf(d23,plain,
multiply('additive$uinverse'(X0),X0) = X0,
inference(demodulation,[status(thm)],[d22,c4]) ).
cnf(d24,plain,
multiply(add(X0,X1),X0) = add(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c0,c11]) ).
cnf(d25,plain,
multiply(X0,X0) = add(X0,multiply('additive$uidentity',X0)),
inference(superposition,[status(thm)],[c4,d24]) ).
cnf(d26,plain,
X0 = add(X0,multiply('additive$uidentity',X0)),
inference(demodulation,[status(thm)],[d25,c0]) ).
cnf(d27,plain,
multiply('additive$uidentity','additive$uinverse'(X0)) = add(X0,'additive$uinverse'(X0)),
inference(superposition,[status(thm)],[d26,d4]) ).
cnf(d28,plain,
multiply('additive$uidentity','additive$uinverse'(X0)) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d27,c6]) ).
cnf(d29,plain,
multiply('additive$uidentity',X0) = 'additive$uidentity',
inference(superposition,[status(thm)],[d20,d28]) ).
cnf(d30,plain,
multiply('additive$uidentity',X0) = add(X0,multiply('additive$uinverse'(X0),X0)),
inference(superposition,[status(thm)],[d11,d24]) ).
cnf(d31,plain,
'additive$uidentity' = add(X0,multiply('additive$uinverse'(X0),X0)),
inference(demodulation,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
'additive$uidentity' = add(X0,X0),
inference(demodulation,[status(thm)],[d31,d23]) ).
cnf(d33,plain,
'additive$uinverse'(X0) = add(X0,'additive$uidentity'),
inference(superposition,[status(thm)],[d32,d5]) ).
cnf(d34,plain,
'additive$uinverse'(X0) = X0,
inference(demodulation,[status(thm)],[d33,c4]) ).
cnf(d35,plain,
add(X0,add(X0,X1)) = X1,
inference(demodulation,[status(thm)],[d3,d34]) ).
cnf(d36,plain,
multiply(X0,add(X1,X2)) = add(multiply(X0,X2),multiply(X0,X1)),
inference(superposition,[status(thm)],[c10,c8]) ).
cnf(d37,plain,
multiply(X0,add(X1,X2)) = multiply(X0,add(X2,X1)),
inference(superposition,[status(thm)],[d36,c10]) ).
cnf(d38,plain,
multiply(X1,X0) = multiply(X1,add('additive$uidentity',X0)),
inference(superposition,[status(thm)],[c4,d37]) ).
cnf(d39,plain,
multiply(X1,X0) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d38,c3]) ).
cnf(d40,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[c9,d39]) ).
cnf(d41,plain,
multiply(add(X1,X0),X0) = add(multiply(X1,X0),X0),
inference(superposition,[status(thm)],[c0,c11]) ).
cnf(d42,plain,
multiply(add(X0,X1),X1) = add(X1,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d41,c8]) ).
cnf(d43,plain,
multiply(multiply(X0,X1),multiply(X2,X3)) = multiply(multiply(X0,multiply(X1,X2)),X3),
inference(superposition,[status(thm)],[c9,c9]) ).
cnf(d44,plain,
multiply(X0,multiply(X1,multiply(X2,X3))) = multiply(multiply(X0,multiply(X1,X2)),X3),
inference(demodulation,[status(thm)],[d43,c9]) ).
cnf(d45,plain,
multiply(X0,multiply(X1,multiply(X2,X3))) = multiply(X0,multiply(multiply(X1,X2),X3)),
inference(demodulation,[status(thm)],[d44,c9]) ).
cnf(d46,plain,
multiply(X3,multiply(X0,multiply(X1,X2))) = multiply(X3,multiply(X0,multiply(X1,X2))),
inference(demodulation,[status(thm)],[d45,c9]) ).
cnf(d47,plain,
multiply(X0,multiply(X1,multiply(X0,X1))) = multiply(X0,X1),
inference(superposition,[status(thm)],[c9,c0]) ).
cnf(d48,plain,
multiply(X0,X1) = multiply(X0,multiply(X1,multiply(X0,X1))),
inference(superposition,[status(thm)],[d47,d46]) ).
cnf(d49,plain,
multiply(add(X0,X2),X1) = add(multiply(X2,X1),multiply(X0,X1)),
inference(superposition,[status(thm)],[c11,c8]) ).
cnf(d50,plain,
multiply(add(X0,X2),X1) = multiply(add(X2,X0),X1),
inference(superposition,[status(thm)],[d49,c11]) ).
cnf(d51,plain,
multiply(X0,multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c0,c9]) ).
cnf(d52,plain,
multiply(X0,add(X2,multiply(X0,X1))) = add(multiply(X0,X2),multiply(X0,X1)),
inference(superposition,[status(thm)],[d51,c10]) ).
cnf(d53,plain,
multiply(X0,add(X1,multiply(X0,X2))) = multiply(X0,add(X1,X2)),
inference(demodulation,[status(thm)],[d52,c10]) ).
cnf(d54,plain,
multiply(a,add(b,X0)) = add(c,multiply(a,X0)),
inference(superposition,[status(thm)],[c1,c10]) ).
cnf(d55,plain,
multiply(a,'additive$uidentity') = add(c,multiply(a,'additive$uinverse'(b))),
inference(superposition,[status(thm)],[d11,d54]) ).
cnf(d56,plain,
'additive$uidentity' = add(c,multiply(a,'additive$uinverse'(b))),
inference(demodulation,[status(thm)],[d55,d14]) ).
cnf(d57,plain,
multiply(a,'additive$uidentity') = multiply(a,add(c,'additive$uinverse'(b))),
inference(superposition,[status(thm)],[d56,d53]) ).
cnf(d58,plain,
'additive$uidentity' = multiply(a,add(c,'additive$uinverse'(b))),
inference(demodulation,[status(thm)],[d57,d14]) ).
cnf(d59,plain,
multiply(a,multiply(add(c,'additive$uinverse'(b)),X0)) = multiply('additive$uidentity',X0),
inference(superposition,[status(thm)],[d58,c9]) ).
cnf(d60,plain,
multiply(a,multiply(add(c,b),X0)) = multiply('additive$uidentity',X0),
inference(demodulation,[status(thm)],[d59,d34]) ).
cnf(d61,plain,
multiply(a,multiply(add(b,c),X0)) = multiply('additive$uidentity',X0),
inference(demodulation,[status(thm)],[d60,d50]) ).
cnf(d62,plain,
multiply(a,multiply(add(b,c),X0)) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d61,d29]) ).
cnf(d63,plain,
multiply(add(b,c),a) = multiply(add(b,c),'additive$uidentity'),
inference(superposition,[status(thm)],[d62,d48]) ).
cnf(d64,plain,
multiply(add(b,c),a) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d63,d14]) ).
cnf(d65,plain,
multiply('additive$uidentity',X0) = multiply(add(b,c),multiply(a,X0)),
inference(superposition,[status(thm)],[d64,d40]) ).
cnf(d66,plain,
'additive$uidentity' = multiply(add(b,c),multiply(a,X0)),
inference(demodulation,[status(thm)],[d65,d29]) ).
cnf(d67,plain,
multiply(a,c) = multiply(a,b),
inference(superposition,[status(thm)],[c1,d51]) ).
cnf(d68,plain,
multiply(a,c) = c,
inference(demodulation,[status(thm)],[d67,c1]) ).
cnf(d69,plain,
multiply(a,multiply(c,X0)) = multiply(c,X0),
inference(superposition,[status(thm)],[d68,c9]) ).
cnf(d70,plain,
multiply(c,multiply(a,c)) = multiply(a,c),
inference(superposition,[status(thm)],[d69,d47]) ).
cnf(d71,plain,
multiply(c,c) = multiply(a,c),
inference(demodulation,[status(thm)],[d70,d68]) ).
cnf(d72,plain,
c = multiply(a,c),
inference(demodulation,[status(thm)],[d71,c0]) ).
cnf(d73,plain,
'additive$uidentity' = multiply(add(b,c),c),
inference(superposition,[status(thm)],[d72,d66]) ).
cnf(d74,plain,
'additive$uidentity' = add(c,multiply(b,c)),
inference(demodulation,[status(thm)],[d73,d42]) ).
cnf(d75,plain,
add(c,'additive$uidentity') = multiply(b,c),
inference(superposition,[status(thm)],[d74,d35]) ).
cnf(d76,plain,
c = multiply(b,c),
inference(demodulation,[status(thm)],[d75,c4]) ).
cnf(d77,plain,
multiply(c,X0) = multiply(b,multiply(c,X0)),
inference(superposition,[status(thm)],[d76,d40]) ).
cnf(d78,plain,
multiply(a,multiply(b,X0)) = multiply(c,X0),
inference(superposition,[status(thm)],[c1,c9]) ).
cnf(d79,plain,
multiply(a,multiply(c,X0)) = multiply(a,multiply(b,X0)),
inference(superposition,[status(thm)],[d78,d51]) ).
cnf(d80,plain,
multiply(c,X0) = multiply(a,multiply(b,X0)),
inference(demodulation,[status(thm)],[d79,d69]) ).
cnf(d81,plain,
multiply(b,a) = multiply(b,multiply(c,a)),
inference(superposition,[status(thm)],[d80,d48]) ).
cnf(d82,plain,
multiply(b,a) = multiply(c,a),
inference(demodulation,[status(thm)],[d81,d77]) ).
cnf(d83,plain,
multiply(a,b) = multiply(c,b),
inference(superposition,[status(thm)],[c0,d78]) ).
cnf(d84,plain,
c = multiply(c,b),
inference(demodulation,[status(thm)],[d83,c1]) ).
cnf(d85,plain,
multiply(c,add(X0,b)) = add(multiply(c,X0),c),
inference(superposition,[status(thm)],[d84,c10]) ).
cnf(d86,plain,
multiply(c,add(X0,b)) = add(c,multiply(c,X0)),
inference(demodulation,[status(thm)],[d85,c8]) ).
cnf(d87,plain,
multiply(add(multiply(X0,X1),X3),X2) = add(multiply(X0,multiply(X1,X2)),multiply(X3,X2)),
inference(superposition,[status(thm)],[c9,c11]) ).
cnf(d88,plain,
multiply(add(X2,X0),multiply(X0,X1)) = add(multiply(X2,multiply(X0,X1)),multiply(X0,X1)),
inference(superposition,[status(thm)],[d51,c11]) ).
cnf(d89,plain,
multiply(add(X0,X1),multiply(X1,X2)) = multiply(add(multiply(X0,X1),X1),X2),
inference(demodulation,[status(thm)],[d88,d87]) ).
cnf(d90,plain,
multiply(add(X0,X1),multiply(X1,X2)) = multiply(add(X1,multiply(X0,X1)),X2),
inference(demodulation,[status(thm)],[d89,c8]) ).
cnf(d91,plain,
multiply(add(X3,multiply(X0,X1)),X2) = add(multiply(X3,X2),multiply(X0,multiply(X1,X2))),
inference(superposition,[status(thm)],[c9,c11]) ).
cnf(d92,plain,
multiply(add(a,X1),multiply(c,X0)) = add(multiply(c,X0),multiply(X1,multiply(c,X0))),
inference(superposition,[status(thm)],[d69,c11]) ).
cnf(d93,plain,
multiply(add(a,X1),multiply(c,X0)) = multiply(add(c,multiply(X1,c)),X0),
inference(demodulation,[status(thm)],[d92,d91]) ).
cnf(d94,plain,
multiply(add(a,X0),multiply(c,X1)) = multiply(add(X0,c),multiply(c,X1)),
inference(demodulation,[status(thm)],[d93,d90]) ).
cnf(d95,plain,
'additive$uidentity' = multiply(add(b,c),multiply(c,X0)),
inference(superposition,[status(thm)],[d69,d66]) ).
cnf(d96,plain,
'additive$uidentity' = multiply(add(a,b),multiply(c,X0)),
inference(demodulation,[status(thm)],[d95,d94]) ).
cnf(d97,plain,
multiply(c,add(a,b)) = multiply(c,'additive$uidentity'),
inference(superposition,[status(thm)],[d96,d48]) ).
cnf(d98,plain,
add(c,multiply(c,a)) = multiply(c,'additive$uidentity'),
inference(demodulation,[status(thm)],[d97,d86]) ).
cnf(d99,plain,
add(c,multiply(b,a)) = multiply(c,'additive$uidentity'),
inference(demodulation,[status(thm)],[d98,d82]) ).
cnf(d100,plain,
add(c,multiply(b,a)) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d99,d14]) ).
cnf(d101,plain,
add(c,'additive$uidentity') = multiply(b,a),
inference(superposition,[status(thm)],[d100,d35]) ).
cnf(d102,plain,
c = multiply(b,a),
inference(demodulation,[status(thm)],[d101,c4]) ).
cnf(d103,plain,
c != c,
inference(demodulation,[status(thm)],[c2,d102]) ).
cnf(d104,plain,
X1 = add(X0,add(X0,X1)),
inference(demodulation,[status(thm)],[d4,d34]) ).
cnf(d105,plain,
add(X2,add(X0,X1)) = add(X0,add(X1,X2)),
inference(superposition,[status(thm)],[c7,c8]) ).
cnf(d106,plain,
add(X0,'additive$uidentity') = add(c,add(multiply(a,'additive$uinverse'(b)),X0)),
inference(superposition,[status(thm)],[d56,d105]) ).
cnf(d107,plain,
X0 = add(c,add(multiply(a,'additive$uinverse'(b)),X0)),
inference(demodulation,[status(thm)],[d106,c4]) ).
cnf(d108,plain,
X0 = add(c,add(multiply(a,b),X0)),
inference(demodulation,[status(thm)],[d107,d34]) ).
cnf(d109,plain,
X0 = add(c,add(c,X0)),
inference(demodulation,[status(thm)],[d108,c1]) ).
cnf(d110,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d109,d104]) ).
cnf(d111,plain,
$false,
inference(resolution,[status(thm)],[d110,d103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG008-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n018.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 05:47:21 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 62.32/13.80 % SZS status Unsatisfiable for theBenchmark.p
% 62.32/13.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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