%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP206-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 07:23:25 AM UTC 2026
% Result : Unsatisfiable 44.02s 6.72s
% Output : CNFRefutation 44.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 5 RR)
% Number of literals : 25 ( 24 equ; 4 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(right_identity,axiom,
multiply(X0,identity) = X0 ).
cnf(multiply_left_division,axiom,
multiply(X0,'left$udivision'(X0,X1)) = X1 ).
cnf(left_division_multiply,axiom,
'left$udivision'(X0,multiply(X0,X1)) = X1 ).
cnf(moufang4,axiom,
multiply(X0,multiply(multiply(X1,X2),X0)) = multiply(multiply(X0,X1),multiply(X2,X0)) ).
cnf(prove_moufang1,negated_conjecture,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)) ).
cnf(c0,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c1,plain,
multiply(X0,identity) = X0,
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c2,plain,
multiply(X0,'left$udivision'(X0,X1)) = X1,
inference(clausification,[status(esa)],[multiply_left_division]) ).
cnf(c3,plain,
'left$udivision'(X0,multiply(X0,X1)) = X1,
inference(clausification,[status(esa)],[left_division_multiply]) ).
cnf(c8,plain,
multiply(X0,multiply(multiply(X1,X2),X0)) = multiply(multiply(X0,X1),multiply(X2,X0)),
inference(clausification,[status(esa)],[moufang4]) ).
cnf(c9,plain,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
inference(clausification,[status(esa)],[prove_moufang1]) ).
cnf(d0,plain,
multiply(X0,multiply(multiply(X1,identity),X0)) = multiply(multiply(X0,X1),X0),
inference(superposition,[status(thm)],[c0,c8]) ).
cnf(d1,plain,
multiply(X1,multiply(X0,X1)) = multiply(multiply(X1,X0),X1),
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
multiply(multiply(a,multiply(b,c)),a) != multiply(a,multiply(multiply(b,c),a)),
inference(demodulation,[status(thm)],[c9,c8]) ).
cnf(d3,plain,
multiply(a,multiply(multiply(b,c),a)) != multiply(a,multiply(multiply(b,c),a)),
inference(demodulation,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
'left$udivision'(multiply(X0,X1),multiply(X0,multiply(multiply(X1,X2),X0))) = multiply(X2,X0),
inference(superposition,[status(thm)],[c8,c3]) ).
cnf(d5,plain,
'left$udivision'(multiply(X1,X0),multiply(X1,multiply(X0,X1))) = multiply(identity,X1),
inference(superposition,[status(thm)],[c1,d4]) ).
cnf(d6,plain,
'left$udivision'(multiply(X0,X1),multiply(X0,multiply(X1,X0))) = X0,
inference(demodulation,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
'left$udivision'(identity,X0) = X0,
inference(superposition,[status(thm)],[c0,c2]) ).
cnf(d8,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c3,d7]) ).
cnf(d9,plain,
'left$udivision'(multiply(X0,identity),multiply(X0,X0)) = X0,
inference(superposition,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
'left$udivision'(X0,multiply(X0,X0)) = X0,
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP206-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.34 % Computer : n014.cluster.edu
% 0.06/0.34 % Model : x86_64 x86_64
% 0.06/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.34 % Memory : 8046.5625MB
% 0.06/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/0.34 % CPULimit : 300
% 0.06/0.34 % WCLimit : 300
% 0.06/0.34 % DateTime : Fri Sep 25 14:37:48 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.06/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.02/6.72 % SZS status Unsatisfiable for theBenchmark.p
% 44.02/6.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------