%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP012-2 : 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 : n001.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 07:22:05 AM UTC 2026
% Result : Unsatisfiable 10.10s 3.34s
% Output : CNFRefutation 10.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 38 ( 23 unt; 0 nHn; 27 RR)
% Number of literals : 66 ( 11 equ; 31 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_multiply_b_is_c,hypothesis,
product(a,b,c) ).
cnf(inverse_b_multiply_inverse_a_is_d,hypothesis,
product(inverse(b),inverse(a),d) ).
cnf(prove_c_inverse_equals_d,negated_conjecture,
inverse(c) != d ).
cnf(left_identity,axiom,
product(identity,X0,X0) ).
cnf(right_identity,axiom,
product(X0,identity,X0) ).
cnf(left_inverse,axiom,
product(inverse(X0),X0,identity) ).
cnf(right_inverse,axiom,
product(X0,inverse(X0),identity) ).
cnf(total_function1,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(total_function2,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(associativity1,axiom,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(associativity2,axiom,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
product(a,b,c),
inference(clausification,[status(esa)],[a_multiply_b_is_c]) ).
cnf(c1,plain,
product(inverse(b),inverse(a),d),
inference(clausification,[status(esa)],[inverse_b_multiply_inverse_a_is_d]) ).
cnf(c2,plain,
inverse(c) != d,
inference(clausification,[status(esa)],[prove_c_inverse_equals_d]) ).
cnf(c3,plain,
product(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c4,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c5,plain,
product(inverse(X0),X0,identity),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c6,plain,
product(X0,inverse(X0),identity),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c7,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[total_function1]) ).
cnf(c8,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[total_function2]) ).
cnf(c9,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity1]) ).
cnf(c10,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity2]) ).
cnf(d0,plain,
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[c8,c7]) ).
cnf(d1,plain,
multiply(identity,X0) = X0,
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( ~ product(X3,X0,identity)
| product(X3,X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c9,c3]) ).
cnf(d3,plain,
( ~ product(X0,a,identity)
| product(X0,c,b) ),
inference(resolution,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
product(inverse(a),c,b),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
( ~ product(inverse(X3),X2,X0)
| ~ product(X2,X1,X3)
| product(X0,X1,identity) ),
inference(resolution,[status(thm)],[c10,c5]) ).
cnf(d6,plain,
( product(d,X0,identity)
| ~ product(inverse(a),X0,b) ),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
product(d,c,identity),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
( ~ product(X0,identity,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c8,c4]) ).
cnf(d9,plain,
( ~ product(X3,X0,X4)
| product(X3,X2,multiply(X4,X1))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c9,c7]) ).
cnf(d10,plain,
( ~ product(X0,X2,X1)
| product(X0,identity,multiply(X1,inverse(X2))) ),
inference(resolution,[status(thm)],[d9,c6]) ).
cnf(d11,plain,
( X0 = multiply(X2,inverse(X1))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
d = multiply(identity,inverse(c)),
inference(resolution,[status(thm)],[d11,d7]) ).
cnf(d13,plain,
d = inverse(c),
inference(demodulation,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
d != d,
inference(demodulation,[status(thm)],[c2,d13]) ).
cnf(d15,plain,
$false,
inference(equality_resolution,[status(thm)],[d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n001.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 14:22:11 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.10/3.34 % SZS status Unsatisfiable for theBenchmark.p
% 10.10/3.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------