%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP040-4 : 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 : 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 07:22:11 AM UTC 2026
% Result : Unsatisfiable 13.83s 2.11s
% Output : CNFRefutation 13.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 54 ( 26 unt; 8 nHn; 41 RR)
% Number of literals : 107 ( 8 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_inverse,axiom,
( 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(X0) ) ).
cnf(product_right_cancellation,axiom,
( 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$uO2'(X0,X1),X1) ) ).
cnf(a_in_subgroup,hypothesis,
~ 'subgroup$umember'(a) ).
cnf(b_is_in_subgroup,hypothesis,
'subgroup$umember'(b) ).
cnf(d_in_subgroup,hypothesis,
~ 'subgroup$umember'(d) ).
cnf(b_times_a_inverse_is_c,hypothesis,
product(b,inverse(a),c) ).
cnf(a_times_c_is_d,hypothesis,
product(a,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(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$umember'(X0) ) ).
cnf(c1,plain,
( 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[closure_of_inverse]) ).
cnf(c2,plain,
( X3 = X1
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_right_cancellation]) ).
cnf(c4,plain,
( 'subgroup$umember'(X0)
| 'subgroup$umember'(X1)
| 'subgroup$umember'('element$uin$uO2'(X0,X1)) ),
inference(clausification,[status(esa)],[an_element_in_O2]) ).
cnf(c5,plain,
( 'subgroup$umember'(X0)
| 'subgroup$umember'(X1)
| product(X0,'element$uin$uO2'(X0,X1),X1) ),
inference(clausification,[status(esa)],[property_of_O2]) ).
cnf(c6,plain,
~ 'subgroup$umember'(a),
inference(clausification,[status(esa)],[a_in_subgroup]) ).
cnf(c7,plain,
'subgroup$umember'(b),
inference(clausification,[status(esa)],[b_is_in_subgroup]) ).
cnf(c8,plain,
~ 'subgroup$umember'(d),
inference(clausification,[status(esa)],[d_in_subgroup]) ).
cnf(c9,plain,
product(b,inverse(a),c),
inference(clausification,[status(esa)],[b_times_a_inverse_is_c]) ).
cnf(c10,plain,
product(a,c,d),
inference(clausification,[status(esa)],[a_times_c_is_d]) ).
cnf(c12,plain,
product(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c13,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c14,plain,
product(inverse(X0),X0,identity),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c15,plain,
product(X0,inverse(X0),identity),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c18,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity1]) ).
cnf(c19,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity2]) ).
cnf(c20,plain,
( 'subgroup$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,
( ~ product(inverse(X0),X1,identity)
| X0 = X1 ),
inference(resolution,[status(thm)],[c2,c14]) ).
cnf(d1,plain,
X0 = inverse(inverse(X0)),
inference(resolution,[status(thm)],[d0,c15]) ).
cnf(d2,plain,
( ~ 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(X1)
| 'subgroup$umember'(X2)
| ~ product(X1,X0,X2) ),
inference(superposition,[status(thm)],[d1,c20]) ).
cnf(d3,plain,
( ~ product(X3,X0,identity)
| product(X3,X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c18,c12]) ).
cnf(d4,plain,
( ~ product(b,X2,X1)
| ~ product(inverse(a),X0,X2)
| product(c,X0,X1) ),
inference(resolution,[status(thm)],[c19,c9]) ).
cnf(d5,plain,
( product(c,a,X0)
| ~ product(b,identity,X0) ),
inference(resolution,[status(thm)],[d4,c14]) ).
cnf(d6,plain,
product(c,a,b),
inference(resolution,[status(thm)],[d5,c13]) ).
cnf(d7,plain,
( ~ product(X0,c,identity)
| product(X0,b,a) ),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
product(inverse(c),b,a),
inference(resolution,[status(thm)],[d7,c14]) ).
cnf(d9,plain,
( ~ 'subgroup$umember'(inverse(b))
| ~ 'subgroup$umember'(inverse(c))
| 'subgroup$umember'(a) ),
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
( ~ 'subgroup$umember'(inverse(c))
| ~ 'subgroup$umember'(inverse(b)) ),
inference(resolution,[status(thm)],[c6,d9]) ).
cnf(d11,plain,
( ~ 'subgroup$umember'(c)
| ~ 'subgroup$umember'(inverse(b)) ),
inference(resolution,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
( ~ product(a,X0,d)
| c = X0 ),
inference(resolution,[status(thm)],[c2,c10]) ).
cnf(d13,plain,
( c = 'element$uin$uO2'(a,d)
| 'subgroup$umember'(d)
| 'subgroup$umember'(a) ),
inference(resolution,[status(thm)],[c5,d12]) ).
cnf(d14,plain,
( 'subgroup$umember'(d)
| c = 'element$uin$uO2'(a,d) ),
inference(resolution,[status(thm)],[c6,d13]) ).
cnf(d15,plain,
c = 'element$uin$uO2'(a,d),
inference(resolution,[status(thm)],[c8,d14]) ).
cnf(d16,plain,
( 'subgroup$umember'(d)
| 'subgroup$umember'(a)
| 'subgroup$umember'(c) ),
inference(superposition,[status(thm)],[d15,c4]) ).
cnf(d17,plain,
( 'subgroup$umember'(c)
| 'subgroup$umember'(d) ),
inference(resolution,[status(thm)],[c6,d16]) ).
cnf(d18,plain,
'subgroup$umember'(c),
inference(resolution,[status(thm)],[c8,d17]) ).
cnf(d19,plain,
~ 'subgroup$umember'(inverse(b)),
inference(resolution,[status(thm)],[d18,d11]) ).
cnf(d20,plain,
~ 'subgroup$umember'(b),
inference(resolution,[status(thm)],[d19,c1]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[c7,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP040-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Fri Sep 25 14:19:05 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.83/2.11 % SZS status Unsatisfiable for theBenchmark.p
% 13.83/2.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------