%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO034-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 06:54:43 AM UTC 2026
% Result : Unsatisfiable 115.46s 44.68s
% Output : CNFRefutation 115.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 10 RR)
% Number of literals : 45 ( 44 equ; 9 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 : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 90 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_single_axiom,negated_conjecture,
multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) != b ).
cnf(associativity,axiom,
multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4)) ).
cnf(ternary_multiply_1,axiom,
multiply(X0,X1,X1) = X1 ).
cnf(ternary_multiply_2,axiom,
multiply(X0,X0,X1) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0,X1) = X1 ).
cnf(right_inverse,axiom,
multiply(X0,X1,inverse(X1)) = X0 ).
cnf(c0,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) != b,
inference(clausification,[status(esa)],[prove_single_axiom]) ).
cnf(c1,plain,
multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(c2,plain,
multiply(X0,X1,X1) = X1,
inference(clausification,[status(esa)],[ternary_multiply_1]) ).
cnf(c3,plain,
multiply(X0,X0,X1) = X0,
inference(clausification,[status(esa)],[ternary_multiply_2]) ).
cnf(c4,plain,
multiply(inverse(X0),X0,X1) = X1,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c5,plain,
multiply(X0,X1,inverse(X1)) = X0,
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(d0,plain,
multiply(X0,X2,multiply(X0,X1,X3)) = multiply(X0,X1,multiply(inverse(X1),X2,X3)),
inference(superposition,[status(thm)],[c5,c1]) ).
cnf(d1,plain,
multiply(X0,X1,multiply(inverse(X1),X0,X2)) = X0,
inference(superposition,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
multiply(X1,X2,multiply(X0,X1,X3)) = multiply(X0,X1,multiply(X1,X2,X3)),
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d3,plain,
multiply(inverse(X1),X0,multiply(X0,X1,X2)) = X0,
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
multiply(inverse(X1),X0,X1) = X0,
inference(superposition,[status(thm)],[c2,d3]) ).
cnf(d5,plain,
multiply(X0,X2,X1) = multiply(X0,X1,multiply(inverse(X1),X2,X1)),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d6,plain,
multiply(X2,X1,X0) = multiply(X2,X0,X1),
inference(demodulation,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
X0 = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d4,c5]) ).
cnf(d8,plain,
multiply(X0,X1,inverse(X0)) = X1,
inference(superposition,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
multiply(X0,X1,multiply(X2,multiply(X0,X1,X3),X3)) = multiply(X0,X1,X3),
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d10,plain,
multiply(X0,X1,multiply(X0,X1,X2)) = multiply(X0,X1,X2),
inference(superposition,[status(thm)],[c3,d9]) ).
cnf(d11,plain,
multiply(X0,X1,X0) = multiply(X0,X1,inverse(X1)),
inference(superposition,[status(thm)],[c5,d10]) ).
cnf(d12,plain,
multiply(X0,X1,X0) = X0,
inference(demodulation,[status(thm)],[d11,c5]) ).
cnf(d13,plain,
multiply(X0,X1,X2) = multiply(X0,X1,multiply(X2,X3,X2)),
inference(superposition,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
multiply(X2,X3,X0) = multiply(X2,X3,X0),
inference(demodulation,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
X0 = multiply(X0,X1,inverse(X1)),
inference(superposition,[status(thm)],[c5,d14]) ).
cnf(d16,plain,
multiply(X1,X2,X0) = multiply(X0,X1,multiply(X1,X2,inverse(X1))),
inference(superposition,[status(thm)],[d15,d2]) ).
cnf(d17,plain,
multiply(X0,X1,X2) = multiply(X2,X0,X1),
inference(demodulation,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
X1 = multiply(inverse(X0),X0,X1),
inference(superposition,[status(thm)],[c4,d14]) ).
cnf(d19,plain,
X1 = multiply(X0,inverse(X0),X1),
inference(superposition,[status(thm)],[d7,d18]) ).
cnf(d20,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != b,
inference(demodulation,[status(thm)],[c0,c1]) ).
cnf(d21,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != b,
inference(demodulation,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))) != b,
inference(demodulation,[status(thm)],[d21,d6]) ).
cnf(d23,plain,
multiply(b,multiply(c,d,multiply(g,f,e)),inverse(multiply(c,d,multiply(e,f,g)))) != b,
inference(demodulation,[status(thm)],[d22,d17]) ).
cnf(d24,plain,
multiply(b,multiply(c,d,multiply(e,g,f)),inverse(multiply(c,d,multiply(e,f,g)))) != b,
inference(demodulation,[status(thm)],[d23,d17]) ).
cnf(d25,plain,
multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g)))) != b,
inference(demodulation,[status(thm)],[d24,d6]) ).
cnf(d26,plain,
b != b,
inference(demodulation,[status(thm)],[d25,c5]) ).
cnf(d27,plain,
multiply(X0,X1,X2) = multiply(X0,X1,multiply(X0,X1,X2)),
inference(superposition,[status(thm)],[d10,d14]) ).
cnf(d28,plain,
X0 = multiply(X0,X0,X2),
inference(superposition,[status(thm)],[c3,d9]) ).
cnf(d29,plain,
multiply(X0,X0,X1) = multiply(X0,X0,X0),
inference(superposition,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
X0 = multiply(X0,X0,X0),
inference(demodulation,[status(thm)],[d29,c3]) ).
cnf(d31,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d30,c2]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[d31,d26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO034-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n015.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 22:41:14 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 115.46/44.68 % SZS status Unsatisfiable for theBenchmark.p
% 115.46/44.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------