%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO012-2 : 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 : n002.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 06:54:39 AM UTC 2026
% Result : Unsatisfiable 24.29s 4.49s
% Output : CNFRefutation 24.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 3 RR)
% Number of literals : 55 ( 54 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_inverse_is_an_involution,negated_conjecture,
inverse(inverse(x)) != x ).
cnf(commutativity_of_add,axiom,
add(X0,X1) = add(X1,X0) ).
cnf(commutativity_of_multiply,axiom,
multiply(X0,X1) = multiply(X1,X0) ).
cnf(distributivity2,axiom,
add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)) ).
cnf(distributivity3,axiom,
multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)) ).
cnf(distributivity4,axiom,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)) ).
cnf(additive_inverse1,axiom,
add(X0,inverse(X0)) = 'multiplicative$uidentity' ).
cnf(multiplicative_inverse1,axiom,
multiply(X0,inverse(X0)) = 'additive$uidentity' ).
cnf(multiplicative_id1,axiom,
multiply(X0,'multiplicative$uidentity') = X0 ).
cnf(multiplicative_id2,axiom,
multiply('multiplicative$uidentity',X0) = X0 ).
cnf(additive_id1,axiom,
add(X0,'additive$uidentity') = X0 ).
cnf(additive_id2,axiom,
add('additive$uidentity',X0) = X0 ).
cnf(c0,plain,
inverse(inverse(x)) != x,
inference(clausification,[status(esa)],[prove_inverse_is_an_involution]) ).
cnf(c1,plain,
add(X0,X1) = add(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_add]) ).
cnf(c2,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_multiply]) ).
cnf(c4,plain,
add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c5,plain,
multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
inference(clausification,[status(esa)],[distributivity3]) ).
cnf(c6,plain,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(clausification,[status(esa)],[distributivity4]) ).
cnf(c7,plain,
add(X0,inverse(X0)) = 'multiplicative$uidentity',
inference(clausification,[status(esa)],[additive_inverse1]) ).
cnf(c9,plain,
multiply(X0,inverse(X0)) = 'additive$uidentity',
inference(clausification,[status(esa)],[multiplicative_inverse1]) ).
cnf(c11,plain,
multiply(X0,'multiplicative$uidentity') = X0,
inference(clausification,[status(esa)],[multiplicative_id1]) ).
cnf(c12,plain,
multiply('multiplicative$uidentity',X0) = X0,
inference(clausification,[status(esa)],[multiplicative_id2]) ).
cnf(c13,plain,
add(X0,'additive$uidentity') = X0,
inference(clausification,[status(esa)],[additive_id1]) ).
cnf(c14,plain,
add('additive$uidentity',X0) = X0,
inference(clausification,[status(esa)],[additive_id2]) ).
cnf(d0,plain,
multiply(X0,add(inverse(X0),X1)) = add('additive$uidentity',multiply(X0,X1)),
inference(superposition,[status(thm)],[c9,c6]) ).
cnf(d1,plain,
multiply(X0,add(inverse(X0),X1)) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d0,c14]) ).
cnf(d2,plain,
X0 = multiply(X0,'multiplicative$uidentity'),
inference(superposition,[status(thm)],[c12,c2]) ).
cnf(d3,plain,
multiply(add(X0,X1),'multiplicative$uidentity') = add(X0,multiply(X1,'multiplicative$uidentity')),
inference(superposition,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
add(X0,X1) = add(X0,multiply(X1,'multiplicative$uidentity')),
inference(demodulation,[status(thm)],[d3,c11]) ).
cnf(d5,plain,
add(X1,X0) = add(X1,X0),
inference(demodulation,[status(thm)],[d4,c11]) ).
cnf(d6,plain,
'multiplicative$uidentity' = add(X0,inverse(X0)),
inference(superposition,[status(thm)],[c7,d5]) ).
cnf(d7,plain,
multiply(X0,'multiplicative$uidentity') = multiply(X0,inverse(inverse(X0))),
inference(superposition,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
X0 = multiply(X0,inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d7,c11]) ).
cnf(d9,plain,
add(X0,multiply(inverse(X0),X1)) = multiply('multiplicative$uidentity',add(X0,X1)),
inference(superposition,[status(thm)],[c7,c4]) ).
cnf(d10,plain,
add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(demodulation,[status(thm)],[d9,c12]) ).
cnf(d11,plain,
add(X0,inverse(X0)) = add(X0,'multiplicative$uidentity'),
inference(superposition,[status(thm)],[d2,d10]) ).
cnf(d12,plain,
'multiplicative$uidentity' = add(X0,'multiplicative$uidentity'),
inference(demodulation,[status(thm)],[d11,c7]) ).
cnf(d13,plain,
add('multiplicative$uidentity',X0) = 'multiplicative$uidentity',
inference(superposition,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
multiply(add('multiplicative$uidentity',X1),X0) = add(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c12,c5]) ).
cnf(d15,plain,
multiply('multiplicative$uidentity',X1) = add(X1,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
X0 = add(X0,multiply(X1,X0)),
inference(demodulation,[status(thm)],[d15,c12]) ).
cnf(d17,plain,
'additive$uidentity' = multiply(X0,'additive$uidentity'),
inference(superposition,[status(thm)],[d16,c14]) ).
cnf(d18,plain,
X0 = add(X0,'additive$uidentity'),
inference(superposition,[status(thm)],[c14,c1]) ).
cnf(d19,plain,
add(X0,multiply(X1,'additive$uidentity')) = multiply(add(X0,X1),X0),
inference(superposition,[status(thm)],[d18,c4]) ).
cnf(d20,plain,
add(X0,multiply(X1,'additive$uidentity')) = multiply(X0,add(X0,X1)),
inference(demodulation,[status(thm)],[d19,c2]) ).
cnf(d21,plain,
add(X1,'additive$uidentity') = multiply(X1,add(X1,X0)),
inference(demodulation,[status(thm)],[d20,d17]) ).
cnf(d22,plain,
X0 = multiply(X0,add(X0,X1)),
inference(demodulation,[status(thm)],[d21,c13]) ).
cnf(d23,plain,
X0 = multiply(X0,add(X1,X0)),
inference(superposition,[status(thm)],[c1,d22]) ).
cnf(d24,plain,
add(X0,'additive$uidentity') = add(X0,inverse(inverse(X0))),
inference(superposition,[status(thm)],[c9,d10]) ).
cnf(d25,plain,
X0 = add(X0,inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d24,c13]) ).
cnf(d26,plain,
add(X0,inverse(inverse(X0))) = X0,
inference(superposition,[status(thm)],[d25,d5]) ).
cnf(d27,plain,
inverse(inverse(X0)) = multiply(inverse(inverse(X0)),X0),
inference(superposition,[status(thm)],[d26,d23]) ).
cnf(d28,plain,
inverse(inverse(X0)) = multiply(X0,inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d27,c2]) ).
cnf(d29,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d28,d8]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[d29,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 22:37:35 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.29/4.49 % SZS status Unsatisfiable for theBenchmark.p
% 24.29/4.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------