%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO013-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 06:54:40 AM UTC 2026
% Result : Unsatisfiable 41.97s 5.89s
% Output : CNFRefutation 41.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of clauses : 83 ( 83 unt; 0 nHn; 20 RR)
% Number of literals : 83 ( 82 equ; 2 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 : 102 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_a_multiplicative_identity,hypothesis,
add(a,b) = 'multiplicative$uidentity' ).
cnf(b_an_additive_identity,hypothesis,
multiply(a,b) = 'additive$uidentity' ).
cnf(prove_a_inverse_is_b,negated_conjecture,
b != inverse(a) ).
cnf(commutativity_of_add,axiom,
add(X0,X1) = add(X1,X0) ).
cnf(commutativity_of_multiply,axiom,
multiply(X0,X1) = multiply(X1,X0) ).
cnf(distributivity1,axiom,
add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)) ).
cnf(distributivity2,axiom,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)) ).
cnf(additive_id1,axiom,
add(X0,'additive$uidentity') = X0 ).
cnf(multiplicative_id1,axiom,
multiply(X0,'multiplicative$uidentity') = X0 ).
cnf(additive_inverse1,axiom,
add(X0,inverse(X0)) = 'multiplicative$uidentity' ).
cnf(multiplicative_inverse1,axiom,
multiply(X0,inverse(X0)) = 'additive$uidentity' ).
cnf(c0,plain,
add(a,b) = 'multiplicative$uidentity',
inference(clausification,[status(esa)],[b_a_multiplicative_identity]) ).
cnf(c1,plain,
multiply(a,b) = 'additive$uidentity',
inference(clausification,[status(esa)],[b_an_additive_identity]) ).
cnf(c2,plain,
b != inverse(a),
inference(clausification,[status(esa)],[prove_a_inverse_is_b]) ).
cnf(c3,plain,
add(X0,X1) = add(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_add]) ).
cnf(c4,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_multiply]) ).
cnf(c5,plain,
add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c6,plain,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c7,plain,
add(X0,'additive$uidentity') = X0,
inference(clausification,[status(esa)],[additive_id1]) ).
cnf(c8,plain,
multiply(X0,'multiplicative$uidentity') = X0,
inference(clausification,[status(esa)],[multiplicative_id1]) ).
cnf(c9,plain,
add(X0,inverse(X0)) = 'multiplicative$uidentity',
inference(clausification,[status(esa)],[additive_inverse1]) ).
cnf(c10,plain,
multiply(X0,inverse(X0)) = 'additive$uidentity',
inference(clausification,[status(esa)],[multiplicative_inverse1]) ).
cnf(d0,plain,
add('additive$uidentity',X0) = X0,
inference(superposition,[status(thm)],[c3,c7]) ).
cnf(d1,plain,
multiply(X0,add(inverse(X0),X1)) = add('additive$uidentity',multiply(X0,X1)),
inference(superposition,[status(thm)],[c10,c6]) ).
cnf(d2,plain,
multiply(X0,add(inverse(X0),X1)) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
multiply(X0,'multiplicative$uidentity') = multiply(X0,inverse(inverse(X0))),
inference(superposition,[status(thm)],[c9,d2]) ).
cnf(d4,plain,
X0 = multiply(X0,inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d3,c8]) ).
cnf(d5,plain,
multiply(a,add(b,X0)) = add('additive$uidentity',multiply(a,X0)),
inference(superposition,[status(thm)],[c1,c6]) ).
cnf(d6,plain,
multiply(a,add(b,X0)) = multiply(a,X0),
inference(demodulation,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
multiply(a,'multiplicative$uidentity') = multiply(a,inverse(b)),
inference(superposition,[status(thm)],[c9,d6]) ).
cnf(d8,plain,
a = multiply(a,inverse(b)),
inference(demodulation,[status(thm)],[d7,c8]) ).
cnf(d9,plain,
multiply('multiplicative$uidentity',X0) = X0,
inference(superposition,[status(thm)],[c4,c8]) ).
cnf(d10,plain,
add(X0,multiply(inverse(X0),X1)) = multiply('multiplicative$uidentity',add(X0,X1)),
inference(superposition,[status(thm)],[c9,c5]) ).
cnf(d11,plain,
add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(demodulation,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
add(X0,inverse(X0)) = add(X0,'multiplicative$uidentity'),
inference(superposition,[status(thm)],[c8,d11]) ).
cnf(d13,plain,
'multiplicative$uidentity' = add(X0,'multiplicative$uidentity'),
inference(demodulation,[status(thm)],[d12,c9]) ).
cnf(d14,plain,
'multiplicative$uidentity' = add('multiplicative$uidentity',X0),
inference(superposition,[status(thm)],[d13,c3]) ).
cnf(d15,plain,
multiply(X0,add('multiplicative$uidentity',X1)) = add(X0,multiply(X0,X1)),
inference(superposition,[status(thm)],[c8,c6]) ).
cnf(d16,plain,
multiply(X1,'multiplicative$uidentity') = add(X1,multiply(X1,X0)),
inference(demodulation,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
X0 = add(X0,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d16,c8]) ).
cnf(d18,plain,
X0 = add('additive$uidentity',X0),
inference(superposition,[status(thm)],[c7,c3]) ).
cnf(d19,plain,
multiply('additive$uidentity',X0) = 'additive$uidentity',
inference(superposition,[status(thm)],[d17,d18]) ).
cnf(d20,plain,
X0 = add(X0,'additive$uidentity'),
inference(superposition,[status(thm)],[d0,c3]) ).
cnf(d21,plain,
add(X0,multiply('additive$uidentity',X1)) = multiply(X0,add(X0,X1)),
inference(superposition,[status(thm)],[d20,c5]) ).
cnf(d22,plain,
multiply(X0,add(X2,add(X0,X1))) = add(multiply(X0,X2),add(X0,multiply('additive$uidentity',X1))),
inference(superposition,[status(thm)],[d21,c6]) ).
cnf(d23,plain,
multiply(X1,add(X2,add(X1,X0))) = add(multiply(X1,X2),add(X1,'additive$uidentity')),
inference(demodulation,[status(thm)],[d22,d19]) ).
cnf(d24,plain,
multiply(X0,add(X1,add(X0,X2))) = add(add(X0,'additive$uidentity'),multiply(X0,X1)),
inference(demodulation,[status(thm)],[d23,c3]) ).
cnf(d25,plain,
multiply(X0,add(X1,add(X0,X2))) = add(X0,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d24,c7]) ).
cnf(d26,plain,
multiply(X0,add(X1,add(X0,X2))) = X0,
inference(demodulation,[status(thm)],[d25,d17]) ).
cnf(d27,plain,
add(X0,multiply(X1,inverse(X0))) = multiply(add(X0,X1),'multiplicative$uidentity'),
inference(superposition,[status(thm)],[c9,c5]) ).
cnf(d28,plain,
add(X0,multiply(X1,inverse(X0))) = add(X0,X1),
inference(demodulation,[status(thm)],[d27,c8]) ).
cnf(d29,plain,
add('additive$uidentity',multiply(X0,X1)) = multiply(X0,add('additive$uidentity',X1)),
inference(superposition,[status(thm)],[d18,c5]) ).
cnf(d30,plain,
multiply(X0,X1) = multiply(X0,add('additive$uidentity',X1)),
inference(demodulation,[status(thm)],[d29,d0]) ).
cnf(d31,plain,
multiply(X1,X0) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d30,d0]) ).
cnf(d32,plain,
'additive$uidentity' = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[c10,d31]) ).
cnf(d33,plain,
add(X0,'additive$uidentity') = add(X0,X0),
inference(superposition,[status(thm)],[d32,d28]) ).
cnf(d34,plain,
X0 = add(X0,X0),
inference(demodulation,[status(thm)],[d33,c7]) ).
cnf(d35,plain,
multiply(X0,add(X1,X0)) = X0,
inference(superposition,[status(thm)],[d34,d26]) ).
cnf(d36,plain,
add(a,multiply(b,X0)) = multiply('multiplicative$uidentity',add(a,X0)),
inference(superposition,[status(thm)],[c0,c5]) ).
cnf(d37,plain,
add(a,multiply(b,X0)) = add(a,X0),
inference(demodulation,[status(thm)],[d36,d9]) ).
cnf(d38,plain,
add(a,multiply(X0,b)) = add(a,X0),
inference(superposition,[status(thm)],[c4,d37]) ).
cnf(d39,plain,
add(a,multiply(X0,b)) = multiply(add(a,X0),'multiplicative$uidentity'),
inference(superposition,[status(thm)],[c0,c5]) ).
cnf(d40,plain,
add(a,X0) = multiply(add(a,X0),'multiplicative$uidentity'),
inference(demodulation,[status(thm)],[d39,d38]) ).
cnf(d41,plain,
add(a,X0) = add(a,X0),
inference(demodulation,[status(thm)],[d40,c8]) ).
cnf(d42,plain,
add(a,'additive$uidentity') = add(a,inverse(b)),
inference(superposition,[status(thm)],[c10,d37]) ).
cnf(d43,plain,
a = add(a,inverse(b)),
inference(demodulation,[status(thm)],[d42,c7]) ).
cnf(d44,plain,
add(a,inverse(b)) = a,
inference(superposition,[status(thm)],[d43,d41]) ).
cnf(d45,plain,
multiply(inverse(b),a) = inverse(b),
inference(superposition,[status(thm)],[d44,d35]) ).
cnf(d46,plain,
multiply(a,inverse(b)) = inverse(b),
inference(demodulation,[status(thm)],[d45,c4]) ).
cnf(d47,plain,
a = inverse(b),
inference(demodulation,[status(thm)],[d46,d8]) ).
cnf(d48,plain,
b = multiply(b,inverse(a)),
inference(superposition,[status(thm)],[d47,d4]) ).
cnf(d49,plain,
X0 = multiply('multiplicative$uidentity',X0),
inference(superposition,[status(thm)],[c8,c4]) ).
cnf(d50,plain,
multiply('multiplicative$uidentity',add(X0,X1)) = add(X0,multiply('multiplicative$uidentity',X1)),
inference(superposition,[status(thm)],[d49,c6]) ).
cnf(d51,plain,
add(X0,X1) = add(X0,multiply('multiplicative$uidentity',X1)),
inference(demodulation,[status(thm)],[d50,d9]) ).
cnf(d52,plain,
add(X1,X0) = add(X1,X0),
inference(demodulation,[status(thm)],[d51,d9]) ).
cnf(d53,plain,
add(X0,'additive$uidentity') = add(X0,inverse(inverse(X0))),
inference(superposition,[status(thm)],[c10,d11]) ).
cnf(d54,plain,
X0 = add(X0,inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d53,c7]) ).
cnf(d55,plain,
add(X0,inverse(inverse(X0))) = X0,
inference(superposition,[status(thm)],[d54,d52]) ).
cnf(d56,plain,
add(b,inverse(a)) = b,
inference(superposition,[status(thm)],[d47,d55]) ).
cnf(d57,plain,
multiply(inverse(a),b) = inverse(a),
inference(superposition,[status(thm)],[d56,d35]) ).
cnf(d58,plain,
multiply(b,inverse(a)) = inverse(a),
inference(demodulation,[status(thm)],[d57,c4]) ).
cnf(d59,plain,
b = inverse(a),
inference(demodulation,[status(thm)],[d58,d48]) ).
cnf(d60,plain,
$false,
inference(resolution,[status(thm)],[c2,d59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO013-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n009.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 22:35:30 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.97/5.89 % SZS status Unsatisfiable for theBenchmark.p
% 41.97/5.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------