%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP035-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 07:22:10 AM UTC 2026
% Result : Unsatisfiable 28.20s 9.44s
% Output : CNFRefutation 28.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 45 ( 23 unt; 0 nHn; 36 RR)
% Number of literals : 88 ( 7 equ; 47 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_in_subgroup,hypothesis,
'subgroup$umember'(a) ).
cnf(b_is_in_subgroup,hypothesis,
'subgroup$umember'(b) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c) ).
cnf(prove_c_is_in_subgroup,negated_conjecture,
~ 'subgroup$umember'(c) ).
cnf(left_identity,axiom,
product(identity,X0,X0) ).
cnf(right_identity,axiom,
product(X0,identity,X0) ).
cnf(right_inverse,axiom,
product(X0,inverse(X0),identity) ).
cnf(total_function1,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(total_function2,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(associativity1,axiom,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(associativity2,axiom,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(closure_of_product_and_inverse,axiom,
( 'subgroup$umember'(X2)
| ~ product(X0,inverse(X1),X2)
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ) ).
cnf(c0,plain,
'subgroup$umember'(a),
inference(clausification,[status(esa)],[a_is_in_subgroup]) ).
cnf(c1,plain,
'subgroup$umember'(b),
inference(clausification,[status(esa)],[b_is_in_subgroup]) ).
cnf(c2,plain,
product(a,b,c),
inference(clausification,[status(esa)],[a_times_b_is_c]) ).
cnf(c3,plain,
~ 'subgroup$umember'(c),
inference(clausification,[status(esa)],[prove_c_is_in_subgroup]) ).
cnf(c4,plain,
product(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c5,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c7,plain,
product(X0,inverse(X0),identity),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c8,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[total_function1]) ).
cnf(c9,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[total_function2]) ).
cnf(c10,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity1]) ).
cnf(c11,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity2]) ).
cnf(c12,plain,
( 'subgroup$umember'(X2)
| ~ product(X0,inverse(X1),X2)
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[closure_of_product_and_inverse]) ).
cnf(d0,plain,
( ~ 'subgroup$umember'(identity)
| ~ 'subgroup$umember'(X0)
| 'subgroup$umember'(inverse(X0)) ),
inference(resolution,[status(thm)],[c12,c4]) ).
cnf(d1,plain,
( ~ 'subgroup$umember'(X0)
| ~ 'subgroup$umember'(X0)
| 'subgroup$umember'(identity) ),
inference(resolution,[status(thm)],[c12,c7]) ).
cnf(d2,plain,
'subgroup$umember'(identity),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
( 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(X0) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( ~ 'subgroup$umember'(X0)
| ~ 'subgroup$umember'(X1)
| 'subgroup$umember'(multiply(X0,inverse(X1))) ),
inference(resolution,[status(thm)],[c12,c8]) ).
cnf(d5,plain,
( ~ product(X0,identity,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c9,c5]) ).
cnf(d6,plain,
( ~ product(X3,X0,X4)
| product(X3,X2,multiply(X4,X1))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c8]) ).
cnf(d7,plain,
( ~ product(X0,X2,X1)
| product(X0,identity,multiply(X1,inverse(X2))) ),
inference(resolution,[status(thm)],[d6,c7]) ).
cnf(d8,plain,
( X0 = multiply(X2,inverse(X1))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
X0 = multiply(multiply(X0,X1),inverse(X1)),
inference(resolution,[status(thm)],[d8,c8]) ).
cnf(d10,plain,
( ~ 'subgroup$umember'(multiply(X0,X1))
| ~ 'subgroup$umember'(X1)
| 'subgroup$umember'(X0) ),
inference(superposition,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[c9,c8]) ).
cnf(d12,plain,
( ~ product(X2,X3,X0)
| ~ product(X3,X1,identity)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c11,c5]) ).
cnf(d13,plain,
( product(c,X0,a)
| ~ product(b,X0,identity) ),
inference(resolution,[status(thm)],[d12,c2]) ).
cnf(d14,plain,
product(c,inverse(b),a),
inference(resolution,[status(thm)],[d13,c7]) ).
cnf(d15,plain,
multiply(c,inverse(b)) = a,
inference(resolution,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
( 'subgroup$umember'(c)
| ~ 'subgroup$umember'(inverse(b))
| ~ 'subgroup$umember'(a) ),
inference(superposition,[status(thm)],[d15,d10]) ).
cnf(d17,plain,
( ~ 'subgroup$umember'(inverse(b))
| 'subgroup$umember'(c) ),
inference(resolution,[status(thm)],[c0,d16]) ).
cnf(d18,plain,
~ 'subgroup$umember'(inverse(b)),
inference(resolution,[status(thm)],[c3,d17]) ).
cnf(d19,plain,
~ 'subgroup$umember'(b),
inference(resolution,[status(thm)],[d18,d3]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[c1,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP035-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.61 % Computer : n013.cluster.edu
% 0.14/5.61 % Model : x86_64 x86_64
% 0.14/5.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.61 % Memory : 8046.5625MB
% 0.14/5.61 % OS : Linux 6.8.0-71-generic
% 0.14/5.61 % CPULimit : 300
% 0.14/5.61 % WCLimit : 300
% 0.14/5.61 % DateTime : Fri Sep 25 14:18:27 UTC 2026
% 0.14/5.61 % CPUTime :
% 0.14/5.62 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.20/9.44 % SZS status Unsatisfiable for theBenchmark.p
% 28.20/9.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------