%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO012-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 28.09s 11.65s
% Output : CNFRefutation 28.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 3 RR)
% Number of literals : 48 ( 47 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 : 71 ( 7 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(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,
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(c3,plain,
add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c4,plain,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c5,plain,
add(X0,'additive$uidentity') = X0,
inference(clausification,[status(esa)],[additive_id1]) ).
cnf(c6,plain,
multiply(X0,'multiplicative$uidentity') = X0,
inference(clausification,[status(esa)],[multiplicative_id1]) ).
cnf(c7,plain,
add(X0,inverse(X0)) = 'multiplicative$uidentity',
inference(clausification,[status(esa)],[additive_inverse1]) ).
cnf(c8,plain,
multiply(X0,inverse(X0)) = 'additive$uidentity',
inference(clausification,[status(esa)],[multiplicative_inverse1]) ).
cnf(d0,plain,
X0 = add('additive$uidentity',X0),
inference(superposition,[status(thm)],[c5,c1]) ).
cnf(d1,plain,
multiply(X0,add(inverse(X0),X1)) = add('additive$uidentity',multiply(X0,X1)),
inference(superposition,[status(thm)],[c8,c4]) ).
cnf(d2,plain,
multiply(X0,add(inverse(X0),X1)) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
multiply(X0,'multiplicative$uidentity') = multiply(X0,inverse(inverse(X0))),
inference(superposition,[status(thm)],[c7,d2]) ).
cnf(d4,plain,
X0 = multiply(X0,inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d3,c6]) ).
cnf(d5,plain,
multiply('multiplicative$uidentity',X0) = X0,
inference(superposition,[status(thm)],[c2,c6]) ).
cnf(d6,plain,
add(X0,multiply(inverse(X0),X1)) = multiply('multiplicative$uidentity',add(X0,X1)),
inference(superposition,[status(thm)],[c7,c3]) ).
cnf(d7,plain,
add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(demodulation,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
X0 = multiply(X0,'multiplicative$uidentity'),
inference(superposition,[status(thm)],[d5,c2]) ).
cnf(d9,plain,
add(X0,inverse(X0)) = add(X0,'multiplicative$uidentity'),
inference(superposition,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
'multiplicative$uidentity' = add(X0,'multiplicative$uidentity'),
inference(demodulation,[status(thm)],[d9,c7]) ).
cnf(d11,plain,
add('multiplicative$uidentity',X0) = 'multiplicative$uidentity',
inference(superposition,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
multiply(X0,add('multiplicative$uidentity',X1)) = add(X0,multiply(X0,X1)),
inference(superposition,[status(thm)],[c6,c4]) ).
cnf(d13,plain,
multiply(X1,'multiplicative$uidentity') = add(X1,multiply(X1,X0)),
inference(demodulation,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
X0 = add(X0,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d13,c6]) ).
cnf(d15,plain,
multiply('additive$uidentity',X0) = 'additive$uidentity',
inference(superposition,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
add(X0,multiply('additive$uidentity',X1)) = multiply(X0,add(X0,X1)),
inference(superposition,[status(thm)],[c5,c3]) ).
cnf(d17,plain,
add(X0,multiply('additive$uidentity',X1)) = multiply(X0,add(X1,X0)),
inference(superposition,[status(thm)],[c1,d16]) ).
cnf(d18,plain,
add(X1,'additive$uidentity') = multiply(X1,add(X0,X1)),
inference(demodulation,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
X0 = multiply(X0,add(X1,X0)),
inference(demodulation,[status(thm)],[d18,c5]) ).
cnf(d20,plain,
multiply('multiplicative$uidentity',add(X0,X1)) = add(X0,multiply('multiplicative$uidentity',X1)),
inference(superposition,[status(thm)],[d5,c4]) ).
cnf(d21,plain,
add(X0,X1) = add(X0,multiply('multiplicative$uidentity',X1)),
inference(demodulation,[status(thm)],[d20,d5]) ).
cnf(d22,plain,
add(X1,X0) = add(X1,X0),
inference(demodulation,[status(thm)],[d21,d5]) ).
cnf(d23,plain,
add(X0,'additive$uidentity') = add(X0,inverse(inverse(X0))),
inference(superposition,[status(thm)],[c8,d7]) ).
cnf(d24,plain,
X0 = add(X0,inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d23,c5]) ).
cnf(d25,plain,
add(X0,inverse(inverse(X0))) = X0,
inference(superposition,[status(thm)],[d24,d22]) ).
cnf(d26,plain,
inverse(inverse(X0)) = multiply(inverse(inverse(X0)),X0),
inference(superposition,[status(thm)],[d25,d19]) ).
cnf(d27,plain,
inverse(inverse(X0)) = multiply(X0,inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d26,c2]) ).
cnf(d28,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d27,d4]) ).
cnf(d29,plain,
$false,
inference(resolution,[status(thm)],[d28,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.44 % Computer : n003.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Sat Sep 26 22:37:17 UTC 2026
% 0.17/5.44 % CPUTime :
% 0.17/5.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.09/11.65 % SZS status Unsatisfiable for theBenchmark.p
% 28.09/11.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------