%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP039-6 : 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 : n026.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 07:22:11 AM UTC 2026
% Result : Unsatisfiable 22.15s 4.73s
% Output : CNFRefutation 22.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of clauses : 75 ( 26 unt; 8 nHn; 61 RR)
% Number of literals : 162 ( 0 equ; 79 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subgroup_member_substitution,axiom,
( 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0)
| ~ equalish(X0,X1) ) ).
cnf(product_substitution3,axiom,
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ) ).
cnf(closure_of_inverse,axiom,
( 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(X0) ) ).
cnf(closure_of_product,axiom,
( 'subgroup$umember'(X2)
| ~ product(X0,X1,X2)
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ) ).
cnf(left_identity,axiom,
product(identity,X0,X0) ).
cnf(right_identity,axiom,
product(X0,identity,X0) ).
cnf(left_inverse,axiom,
product(inverse(X0),X0,identity) ).
cnf(right_inverse,axiom,
product(X0,inverse(X0),identity) ).
cnf(associativity1,axiom,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(associativity2,axiom,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(well_defined,axiom,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(product_right_cancellation,axiom,
( equalish(X3,X1)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ) ).
cnf(an_element_in_O2,axiom,
( 'subgroup$umember'(X0)
| 'subgroup$umember'(X1)
| 'subgroup$umember'('element$uin$uO2'(X0,X1)) ) ).
cnf(property_of_O2,axiom,
( 'subgroup$umember'(X0)
| 'subgroup$umember'(X1)
| product(X0,'element$uin$uO2'(X0,X1),X1) ) ).
cnf(b_is_in_subgroup,negated_conjecture,
'subgroup$umember'(b) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
product(b,inverse(a),c) ).
cnf(a_times_c_is_d,negated_conjecture,
product(a,c,d) ).
cnf(prove_d_is_in_subgroup,negated_conjecture,
~ 'subgroup$umember'(d) ).
cnf(c0,plain,
( 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[subgroup_member_substitution]) ).
cnf(c1,plain,
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[product_substitution3]) ).
cnf(c4,plain,
( 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[closure_of_inverse]) ).
cnf(c5,plain,
( 'subgroup$umember'(X2)
| ~ product(X0,X1,X2)
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[closure_of_product]) ).
cnf(c6,plain,
product(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c7,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c8,plain,
product(inverse(X0),X0,identity),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c9,plain,
product(X0,inverse(X0),identity),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c10,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity1]) ).
cnf(c11,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity2]) ).
cnf(c12,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[well_defined]) ).
cnf(c14,plain,
( equalish(X3,X1)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_right_cancellation]) ).
cnf(c16,plain,
( 'subgroup$umember'(X0)
| 'subgroup$umember'(X1)
| 'subgroup$umember'('element$uin$uO2'(X0,X1)) ),
inference(clausification,[status(esa)],[an_element_in_O2]) ).
cnf(c17,plain,
( 'subgroup$umember'(X0)
| 'subgroup$umember'(X1)
| product(X0,'element$uin$uO2'(X0,X1),X1) ),
inference(clausification,[status(esa)],[property_of_O2]) ).
cnf(c18,plain,
'subgroup$umember'(b),
inference(clausification,[status(esa)],[b_is_in_subgroup]) ).
cnf(c19,plain,
product(b,inverse(a),c),
inference(clausification,[status(esa)],[b_times_a_inverse_is_c]) ).
cnf(c20,plain,
product(a,c,d),
inference(clausification,[status(esa)],[a_times_c_is_d]) ).
cnf(c21,plain,
~ 'subgroup$umember'(d),
inference(clausification,[status(esa)],[prove_d_is_in_subgroup]) ).
cnf(d0,plain,
( ~ product(X3,inverse(X1),X0)
| ~ product(X3,identity,X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c11,c8]) ).
cnf(d1,plain,
( product(c,a,X0)
| ~ product(b,identity,X0) ),
inference(resolution,[status(thm)],[d0,c19]) ).
cnf(d2,plain,
product(c,a,b),
inference(resolution,[status(thm)],[d1,c7]) ).
cnf(d3,plain,
( product(inverse(X2),X3,X1)
| ~ product(X2,X0,X3)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[c10,c8]) ).
cnf(d4,plain,
( product(inverse(X0),X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d3,c6]) ).
cnf(d5,plain,
( ~ 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(X2)
| 'subgroup$umember'(X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
( ~ 'subgroup$umember'(inverse(c))
| 'subgroup$umember'(a)
| ~ 'subgroup$umember'(b) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( 'subgroup$umember'(a)
| ~ 'subgroup$umember'(inverse(c)) ),
inference(resolution,[status(thm)],[c18,d6]) ).
cnf(d8,plain,
( ~ product(inverse(X0),X1,identity)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c14,c8]) ).
cnf(d9,plain,
equalish(X0,inverse(inverse(X0))),
inference(resolution,[status(thm)],[d8,c9]) ).
cnf(d10,plain,
( product(b,inverse(a),X0)
| ~ equalish(c,X0) ),
inference(resolution,[status(thm)],[c19,c1]) ).
cnf(d11,plain,
( ~ 'subgroup$umember'(b)
| ~ 'subgroup$umember'(inverse(a))
| 'subgroup$umember'(X0)
| ~ equalish(c,X0) ),
inference(resolution,[status(thm)],[d10,c5]) ).
cnf(d12,plain,
( ~ 'subgroup$umember'(inverse(a))
| 'subgroup$umember'(X0)
| ~ equalish(c,X0) ),
inference(resolution,[status(thm)],[c18,d11]) ).
cnf(d13,plain,
( ~ 'subgroup$umember'(a)
| 'subgroup$umember'(X0)
| ~ equalish(c,X0) ),
inference(resolution,[status(thm)],[d12,c4]) ).
cnf(d14,plain,
( ~ 'subgroup$umember'(a)
| 'subgroup$umember'(inverse(inverse(c))) ),
inference(resolution,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
( product(a,X2,X1)
| ~ product(c,X0,X2)
| ~ product(d,X0,X1) ),
inference(resolution,[status(thm)],[c10,c20]) ).
cnf(d16,plain,
( ~ product(c,identity,X0)
| product(a,X0,d) ),
inference(resolution,[status(thm)],[d15,c7]) ).
cnf(d17,plain,
( product(X2,X3,X1)
| ~ product(inverse(X2),X0,X3)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[c10,c9]) ).
cnf(d18,plain,
( ~ product(identity,inverse(inverse(X0)),X1)
| product(X0,identity,X1) ),
inference(resolution,[status(thm)],[d17,c9]) ).
cnf(d19,plain,
product(X0,identity,inverse(inverse(X0))),
inference(resolution,[status(thm)],[d18,c6]) ).
cnf(d20,plain,
product(a,inverse(inverse(c)),d),
inference(resolution,[status(thm)],[d19,d16]) ).
cnf(d21,plain,
( ~ 'subgroup$umember'(a)
| ~ 'subgroup$umember'(inverse(inverse(c)))
| 'subgroup$umember'(d) ),
inference(resolution,[status(thm)],[d20,c5]) ).
cnf(d22,plain,
( ~ 'subgroup$umember'(a)
| ~ 'subgroup$umember'(inverse(inverse(c))) ),
inference(resolution,[status(thm)],[c21,d21]) ).
cnf(d23,plain,
( ~ 'subgroup$umember'(a)
| ~ 'subgroup$umember'(a) ),
inference(resolution,[status(thm)],[d22,d14]) ).
cnf(d24,plain,
~ 'subgroup$umember'(inverse(c)),
inference(resolution,[status(thm)],[d23,d7]) ).
cnf(d25,plain,
~ 'subgroup$umember'(c),
inference(resolution,[status(thm)],[d24,c4]) ).
cnf(d26,plain,
( product(X0,identity,X1)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d27,plain,
( ~ product(X1,identity,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c12,c7]) ).
cnf(d28,plain,
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
( ~ product(a,X0,d)
| equalish(c,X0) ),
inference(resolution,[status(thm)],[c14,c20]) ).
cnf(d30,plain,
( 'subgroup$umember'(d)
| 'subgroup$umember'(a)
| equalish(c,'element$uin$uO2'(a,d)) ),
inference(resolution,[status(thm)],[d29,c17]) ).
cnf(d31,plain,
( 'subgroup$umember'(a)
| equalish(c,'element$uin$uO2'(a,d)) ),
inference(resolution,[status(thm)],[c21,d30]) ).
cnf(d32,plain,
equalish(c,'element$uin$uO2'(a,d)),
inference(resolution,[status(thm)],[d23,d31]) ).
cnf(d33,plain,
equalish('element$uin$uO2'(a,d),c),
inference(resolution,[status(thm)],[d32,d28]) ).
cnf(d34,plain,
( ~ 'subgroup$umember'('element$uin$uO2'(a,d))
| 'subgroup$umember'(c) ),
inference(resolution,[status(thm)],[d33,c0]) ).
cnf(d35,plain,
( 'subgroup$umember'(a)
| 'subgroup$umember'(d)
| 'subgroup$umember'(c) ),
inference(resolution,[status(thm)],[d34,c16]) ).
cnf(d36,plain,
( 'subgroup$umember'(c)
| 'subgroup$umember'(a) ),
inference(resolution,[status(thm)],[c21,d35]) ).
cnf(d37,plain,
'subgroup$umember'(c),
inference(resolution,[status(thm)],[d23,d36]) ).
cnf(d38,plain,
$false,
inference(resolution,[status(thm)],[d37,d25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:21:54 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.15/4.73 % SZS status Unsatisfiable for theBenchmark.p
% 22.15/4.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------