%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP135-2.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 07:23:13 AM UTC 2026
% Result : Unsatisfiable 22.38s 8.36s
% Output : CNFRefutation 22.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of clauses : 59 ( 13 unt; 36 nHn; 59 RR)
% Number of literals : 196 ( 0 equ; 83 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 74 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(element_1,axiom,
'group$uelement'('e$u1') ).
cnf(element_2,axiom,
'group$uelement'('e$u2') ).
cnf(e_1_is_not_e_2,axiom,
~ equalish('e$u1','e$u2') ).
cnf(e_2_is_not_e_1,axiom,
~ equalish('e$u2','e$u1') ).
cnf(product_total_function1,axiom,
( product(X0,X1,'e$u2')
| product(X0,X1,'e$u1')
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ) ).
cnf(product_total_function2,axiom,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(product_right_cancellation,axiom,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ) ).
cnf(product_left_cancellation,axiom,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ) ).
cnf(qg3,negated_conjecture,
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c3,plain,
'group$uelement'('e$u1'),
inference(clausification,[status(esa)],[element_1]) ).
cnf(c4,plain,
'group$uelement'('e$u2'),
inference(clausification,[status(esa)],[element_2]) ).
cnf(c5,plain,
~ equalish('e$u1','e$u2'),
inference(clausification,[status(esa)],[e_1_is_not_e_2]) ).
cnf(c6,plain,
~ equalish('e$u2','e$u1'),
inference(clausification,[status(esa)],[e_2_is_not_e_1]) ).
cnf(c7,plain,
( product(X0,X1,'e$u2')
| product(X0,X1,'e$u1')
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ),
inference(clausification,[status(esa)],[product_total_function1]) ).
cnf(c8,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_total_function2]) ).
cnf(c9,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_right_cancellation]) ).
cnf(c10,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_left_cancellation]) ).
cnf(c11,plain,
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg3]) ).
cnf(d0,plain,
( ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X2)
| product(X1,X2,'e$u1')
| ~ product('e$u2',X1,X0)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c11,c7]) ).
cnf(d1,plain,
( ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'(X0)
| product('e$u2',X0,'e$u1')
| ~ 'group$uelement'(X0)
| ~ 'group$uelement'(X1)
| product('e$u2',X0,X1)
| product(X0,X1,'e$u1') ),
inference(resolution,[status(thm)],[d0,c7]) ).
cnf(d2,plain,
( ~ 'group$uelement'(X0)
| ~ 'group$uelement'(X1)
| product('e$u2',X0,'e$u1')
| product('e$u2',X0,X1)
| product(X0,X1,'e$u1') ),
inference(resolution,[status(thm)],[c4,d1]) ).
cnf(d3,plain,
( ~ 'group$uelement'(X0)
| ~ 'group$uelement'(X1)
| product('e$u1',X0,X1)
| product(X0,X1,'e$u1')
| ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'(X0)
| product('e$u2','e$u2','e$u1')
| product('e$u2','e$u2',X0) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( ~ 'group$uelement'(X0)
| ~ 'group$uelement'(X1)
| product('e$u2','e$u2','e$u1')
| product('e$u2','e$u2',X0)
| product('e$u1',X0,X1)
| product(X0,X1,'e$u1') ),
inference(resolution,[status(thm)],[c4,d3]) ).
cnf(d5,plain,
( ~ 'group$uelement'('e$u1')
| ~ 'group$uelement'('e$u1')
| product('e$u2','e$u2','e$u1')
| product('e$u2','e$u2','e$u1')
| product('e$u1','e$u1','e$u1') ),
inference(factoring,[status(thm)],[d4]) ).
cnf(d6,plain,
( product('e$u2','e$u2','e$u1')
| product('e$u1','e$u1','e$u1') ),
inference(resolution,[status(thm)],[c3,d5]) ).
cnf(d7,plain,
( equalish(X0,'e$u1')
| ~ product('e$u2','e$u2',X0)
| product('e$u1','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d6,c8]) ).
cnf(d8,plain,
( ~ product('e$u1','e$u2',X0)
| product(X0,'e$u2','e$u2')
| product('e$u1','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d6,c11]) ).
cnf(d9,plain,
( ~ 'group$uelement'(X0)
| ~ 'group$uelement'(X2)
| product(X0,X2,'e$u1')
| equalish(X2,X1)
| ~ product(X0,X1,'e$u2') ),
inference(resolution,[status(thm)],[c9,c7]) ).
cnf(d10,plain,
( ~ 'group$uelement'(X0)
| ~ 'group$uelement'(X2)
| product(X0,X2,'e$u1')
| equalish(X1,X2)
| ~ 'group$uelement'(X0)
| ~ 'group$uelement'(X1)
| product(X0,X1,'e$u1') ),
inference(resolution,[status(thm)],[d9,c7]) ).
cnf(d11,plain,
( ~ 'group$uelement'(X0)
| ~ 'group$uelement'('e$u1')
| ~ 'group$uelement'('e$u2')
| product(X0,'e$u1','e$u1')
| product(X0,'e$u2','e$u1') ),
inference(resolution,[status(thm)],[d10,c5]) ).
cnf(d12,plain,
( ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'(X0)
| product(X0,'e$u2','e$u1')
| product(X0,'e$u1','e$u1') ),
inference(resolution,[status(thm)],[c3,d11]) ).
cnf(d13,plain,
( ~ 'group$uelement'(X0)
| product(X0,'e$u2','e$u1')
| product(X0,'e$u1','e$u1') ),
inference(resolution,[status(thm)],[c4,d12]) ).
cnf(d14,plain,
( ~ 'group$uelement'('e$u1')
| product('e$u1','e$u1','e$u1')
| product('e$u1','e$u1','e$u1')
| product('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d8,d13]) ).
cnf(d15,plain,
( product('e$u1','e$u2','e$u2')
| product('e$u1','e$u1','e$u1') ),
inference(resolution,[status(thm)],[c3,d14]) ).
cnf(d16,plain,
( product('e$u1','e$u1','e$u1')
| product('e$u2','e$u2','e$u2')
| product('e$u1','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d15,d8]) ).
cnf(d17,plain,
( equalish('e$u2','e$u1')
| product('e$u1','e$u1','e$u1')
| product('e$u1','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d16,d7]) ).
cnf(d18,plain,
product('e$u1','e$u1','e$u1'),
inference(resolution,[status(thm)],[c6,d17]) ).
cnf(d19,plain,
( equalish('e$u1',X0)
| ~ product('e$u1',X0,'e$u1') ),
inference(resolution,[status(thm)],[d18,c9]) ).
cnf(d20,plain,
( ~ 'group$uelement'(X2)
| ~ 'group$uelement'(X1)
| product(X2,X1,'e$u1')
| equalish(X0,X2)
| ~ product(X0,X1,'e$u2') ),
inference(resolution,[status(thm)],[c10,c7]) ).
cnf(d21,plain,
( ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'('e$u2')
| product('e$u2','e$u2','e$u2')
| product('e$u2','e$u2','e$u1') ),
inference(factoring,[status(thm)],[d2]) ).
cnf(d22,plain,
( product('e$u2','e$u2','e$u2')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[c4,d21]) ).
cnf(d23,plain,
( equalish('e$u2',X0)
| ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'(X0)
| product(X0,'e$u2','e$u1')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d22,d20]) ).
cnf(d24,plain,
( equalish('e$u2',X0)
| ~ 'group$uelement'(X0)
| product('e$u2','e$u2','e$u1')
| product(X0,'e$u2','e$u1') ),
inference(resolution,[status(thm)],[c4,d23]) ).
cnf(d25,plain,
( equalish('e$u1','e$u2')
| equalish('e$u2','e$u1')
| ~ 'group$uelement'('e$u1')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d24,d19]) ).
cnf(d26,plain,
( equalish('e$u2','e$u1')
| equalish('e$u1','e$u2')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[c3,d25]) ).
cnf(d27,plain,
( equalish('e$u2','e$u1')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[c5,d26]) ).
cnf(d28,plain,
product('e$u2','e$u2','e$u1'),
inference(resolution,[status(thm)],[c6,d27]) ).
cnf(d29,plain,
( equalish('e$u2',X0)
| ~ product('e$u2',X0,'e$u1') ),
inference(resolution,[status(thm)],[d28,c9]) ).
cnf(d30,plain,
( ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X2)
| product('e$u1',X1,X2)
| product(X1,X2,'e$u1')
| equalish(X0,X1)
| ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'(X0)
| ~ 'group$uelement'(X1)
| product('e$u2',X0,'e$u1') ),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d31,plain,
( equalish(X2,X0)
| ~ 'group$uelement'(X2)
| ~ 'group$uelement'(X0)
| ~ 'group$uelement'(X1)
| product('e$u2',X2,'e$u1')
| product('e$u1',X0,X1)
| product(X0,X1,'e$u1') ),
inference(resolution,[status(thm)],[c4,d30]) ).
cnf(d32,plain,
( ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'(X0)
| ~ 'group$uelement'('e$u1')
| product('e$u2','e$u1','e$u1')
| product('e$u1','e$u2',X0)
| product('e$u2',X0,'e$u1') ),
inference(resolution,[status(thm)],[d31,c5]) ).
cnf(d33,plain,
( ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'(X0)
| product('e$u2','e$u1','e$u1')
| product('e$u2',X0,'e$u1')
| product('e$u1','e$u2',X0) ),
inference(resolution,[status(thm)],[c3,d32]) ).
cnf(d34,plain,
( ~ 'group$uelement'(X0)
| product('e$u2','e$u1','e$u1')
| product('e$u2',X0,'e$u1')
| product('e$u1','e$u2',X0) ),
inference(resolution,[status(thm)],[c4,d33]) ).
cnf(d35,plain,
( ~ 'group$uelement'('e$u1')
| product('e$u2','e$u1','e$u1')
| product('e$u1','e$u2','e$u1') ),
inference(factoring,[status(thm)],[d34]) ).
cnf(d36,plain,
( product('e$u2','e$u1','e$u1')
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[c3,d35]) ).
cnf(d37,plain,
( equalish('e$u2','e$u1')
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d36,d29]) ).
cnf(d38,plain,
product('e$u1','e$u2','e$u1'),
inference(resolution,[status(thm)],[c6,d37]) ).
cnf(d39,plain,
equalish('e$u1','e$u2'),
inference(resolution,[status(thm)],[d38,d19]) ).
cnf(d40,plain,
$false,
inference(resolution,[status(thm)],[c5,d39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP135-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/5.44 % Computer : n020.cluster.edu
% 0.19/5.44 % Model : x86_64 x86_64
% 0.19/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.44 % Memory : 8046.5625MB
% 0.19/5.44 % OS : Linux 6.8.0-71-generic
% 0.19/5.44 % CPULimit : 300
% 0.19/5.44 % WCLimit : 300
% 0.19/5.44 % DateTime : Fri Sep 25 14:31:39 UTC 2026
% 0.19/5.44 % CPUTime :
% 0.19/5.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.38/8.36 % SZS status Unsatisfiable for theBenchmark.p
% 22.38/8.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------