%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP001-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 07:22:02 AM UTC 2026
% Result : Unsatisfiable 11.80s 11.81s
% Output : CNFRefutation 11.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 10 RR)
% Number of literals : 24 ( 23 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
multiply(X0,identity) = X0 ).
cnf(squareness,hypothesis,
multiply(X0,X0) = identity ).
cnf(a_times_b_is_c,hypothesis,
multiply(a,b) = c ).
cnf(prove_b_times_a_is_c,negated_conjecture,
multiply(b,a) != c ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c0,plain,
multiply(X0,identity) = X0,
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c2,plain,
multiply(X0,X0) = identity,
inference(clausification,[status(esa)],[squareness]) ).
cnf(c3,plain,
multiply(a,b) = c,
inference(clausification,[status(esa)],[a_times_b_is_c]) ).
cnf(c4,plain,
multiply(b,a) != c,
inference(clausification,[status(esa)],[prove_b_times_a_is_c]) ).
cnf(c5,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c7,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(d0,plain,
multiply(X0,multiply(X1,identity)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c7,c0]) ).
cnf(d1,plain,
multiply(X1,X0) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
multiply(identity,X1) = multiply(X0,multiply(X0,X1)),
inference(superposition,[status(thm)],[c2,c7]) ).
cnf(d3,plain,
X0 = multiply(X1,multiply(X1,X0)),
inference(demodulation,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
multiply(X0,multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
multiply(X0,multiply(X1,multiply(X0,X1))) = identity,
inference(superposition,[status(thm)],[c7,c2]) ).
cnf(d6,plain,
multiply(a,multiply(b,c)) = identity,
inference(superposition,[status(thm)],[c3,d5]) ).
cnf(d7,plain,
identity = multiply(a,multiply(b,c)),
inference(superposition,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
multiply(b,c) = multiply(a,identity),
inference(superposition,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
multiply(b,c) = a,
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
multiply(b,a) = c,
inference(superposition,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[c4,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/10.33 % Computer : n012.cluster.edu
% 0.07/10.33 % Model : x86_64 x86_64
% 0.07/10.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/10.33 % Memory : 8046.5625MB
% 0.07/10.33 % OS : Linux 6.8.0-71-generic
% 0.07/10.33 % CPULimit : 300
% 0.07/10.33 % WCLimit : 300
% 0.07/10.33 % DateTime : Fri Sep 25 14:15:07 UTC 2026
% 0.07/10.33 % CPUTime :
% 0.07/10.33 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.80/11.81 % SZS status Unsatisfiable for theBenchmark.p
% 11.80/11.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------