%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP132-1.002 : 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 : n004.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 07:23:12 AM UTC 2026
% Result : Unsatisfiable 16.19s 3.32s
% Output : CNFRefutation 16.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of clauses : 59 ( 13 unt; 36 nHn; 59 RR)
% Number of literals : 229 ( 0 equ; 109 neg)
% Maximal clause size : 11 ( 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 : 90 ( 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_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(qg2_1,negated_conjecture,
( equalish(X0,X3)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
'group$uelement'('e$u1'),
inference(clausification,[status(esa)],[element_1]) ).
cnf(c1,plain,
'group$uelement'('e$u2'),
inference(clausification,[status(esa)],[element_2]) ).
cnf(c2,plain,
~ equalish('e$u1','e$u2'),
inference(clausification,[status(esa)],[e_1_is_not_e_2]) ).
cnf(c3,plain,
~ equalish('e$u2','e$u1'),
inference(clausification,[status(esa)],[e_2_is_not_e_1]) ).
cnf(c4,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(c6,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_right_cancellation]) ).
cnf(c7,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_left_cancellation]) ).
cnf(c8,plain,
( ~ product(X3,X4,X5)
| ~ product(X1,X2,X5)
| ~ product(X0,X3,X4)
| equalish(X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg2_1]) ).
cnf(d0,plain,
( product(X2,X0,'e$u1')
| ~ 'group$uelement'(X2)
| ~ 'group$uelement'(X0)
| ~ product(X2,X1,'e$u2')
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(d1,plain,
( product(X0,X2,'e$u1')
| ~ 'group$uelement'(X0)
| ~ 'group$uelement'(X2)
| product(X0,X1,'e$u1')
| equalish(X1,X2)
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( product(X0,'e$u1','e$u1')
| product(X0,'e$u2','e$u1')
| ~ 'group$uelement'(X0)
| ~ 'group$uelement'('e$u1')
| ~ 'group$uelement'('e$u2') ),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
( product(X0,'e$u2','e$u1')
| product(X0,'e$u1','e$u1')
| ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c0,d2]) ).
cnf(d4,plain,
( product(X0,'e$u2','e$u1')
| product(X0,'e$u1','e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c1,d3]) ).
cnf(d5,plain,
( ~ product(X1,'e$u2','e$u1')
| equalish(X1,X0)
| product(X0,'e$u1','e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
( product(X1,X2,'e$u1')
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X2)
| ~ product(X0,X2,'e$u2')
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(d7,plain,
( product(X2,X0,'e$u1')
| ~ 'group$uelement'(X2)
| ~ 'group$uelement'(X0)
| product(X1,X0,'e$u1')
| equalish(X2,X1)
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
( product('e$u2',X0,'e$u1')
| product('e$u1',X0,'e$u1')
| ~ 'group$uelement'(X0)
| ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'('e$u1') ),
inference(resolution,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
( product('e$u2',X0,'e$u1')
| product('e$u1',X0,'e$u1')
| ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c0,d8]) ).
cnf(d10,plain,
( product('e$u2',X0,'e$u1')
| product('e$u1',X0,'e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c1,d9]) ).
cnf(d11,plain,
( product(X0,'e$u1','e$u1')
| equalish('e$u2',X0)
| ~ 'group$uelement'(X0)
| product('e$u1','e$u2','e$u1')
| ~ 'group$uelement'('e$u2') ),
inference(resolution,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
( product('e$u1','e$u2','e$u1')
| product(X0,'e$u1','e$u1')
| equalish('e$u2',X0)
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c1,d11]) ).
cnf(d13,plain,
( ~ product(X1,'e$u1','e$u1')
| equalish(X1,X0)
| product('e$u1','e$u2','e$u1')
| equalish('e$u2',X0)
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[d12,c7]) ).
cnf(d14,plain,
( product(X0,X4,'e$u1')
| ~ 'group$uelement'(X0)
| ~ 'group$uelement'(X4)
| ~ product(X1,X3,'e$u2')
| ~ product(X2,X0,X4)
| ~ product(X2,X1,X3)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c8,c4]) ).
cnf(d15,plain,
( product(X2,X4,'e$u1')
| ~ 'group$uelement'(X2)
| ~ 'group$uelement'(X4)
| product(X1,X0,'e$u1')
| ~ product(X3,X1,X0)
| ~ product(X3,X2,X4)
| equalish(X1,X2)
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[d14,c4]) ).
cnf(d16,plain,
( product(X3,X2,'e$u1')
| ~ 'group$uelement'(X3)
| ~ 'group$uelement'(X2)
| product(X2,'e$u2','e$u1')
| product(X1,X0,'e$u1')
| ~ product(X3,X1,X0)
| equalish(X2,X1)
| ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'(X2)
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[d15,c4]) ).
cnf(d17,plain,
( product(X2,X3,'e$u1')
| product(X1,'e$u2','e$u1')
| ~ product(X0,X2,X3)
| product(X0,X1,'e$u1')
| equalish(X1,X2)
| ~ 'group$uelement'(X3)
| ~ 'group$uelement'(X2)
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c1,d16]) ).
cnf(d18,plain,
( product('e$u1',X0,'e$u1')
| ~ 'group$uelement'(X0)
| product('e$u2',X1,'e$u1')
| product(X1,'e$u2','e$u1')
| product(X0,'e$u1','e$u1')
| equalish(X1,X0)
| ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0)
| ~ 'group$uelement'('e$u1') ),
inference(resolution,[status(thm)],[d17,d10]) ).
cnf(d19,plain,
( product('e$u2',X0,'e$u1')
| product('e$u1',X1,'e$u1')
| product(X1,'e$u1','e$u1')
| product(X0,'e$u2','e$u1')
| equalish(X0,X1)
| ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c0,d18]) ).
cnf(d20,plain,
( product('e$u2',X1,'e$u1')
| product('e$u1',X0,'e$u1')
| product(X1,'e$u2','e$u1')
| product(X0,'e$u1','e$u1')
| equalish(X1,X0)
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c1,d19]) ).
cnf(d21,plain,
( product('e$u2','e$u1','e$u1')
| product('e$u1','e$u2','e$u1')
| product('e$u2','e$u1','e$u1')
| product('e$u1','e$u2','e$u1')
| ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'('e$u1') ),
inference(resolution,[status(thm)],[d20,c2]) ).
cnf(d22,plain,
( product('e$u2','e$u1','e$u1')
| product('e$u1','e$u2','e$u1')
| ~ 'group$uelement'('e$u2') ),
inference(resolution,[status(thm)],[c0,d21]) ).
cnf(d23,plain,
( product('e$u2','e$u1','e$u1')
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[c1,d22]) ).
cnf(d24,plain,
( product('e$u1','e$u2','e$u1')
| equalish('e$u2',X0)
| equalish('e$u2',X0)
| ~ 'group$uelement'(X0)
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d23,d13]) ).
cnf(d25,plain,
( product('e$u1','e$u2','e$u1')
| ~ 'group$uelement'('e$u1') ),
inference(resolution,[status(thm)],[d24,c3]) ).
cnf(d26,plain,
product('e$u1','e$u2','e$u1'),
inference(resolution,[status(thm)],[c0,d25]) ).
cnf(d27,plain,
( ~ product('e$u1',X0,'e$u1')
| equalish('e$u2',X0) ),
inference(resolution,[status(thm)],[d26,c6]) ).
cnf(d28,plain,
( ~ product('e$u2',X1,'e$u1')
| equalish(X0,X1)
| product('e$u1',X0,'e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[d10,c6]) ).
cnf(d29,plain,
( product('e$u2','e$u1','e$u1')
| ~ 'group$uelement'('e$u2')
| product('e$u1',X0,'e$u1')
| equalish(X0,'e$u2')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[d28,d4]) ).
cnf(d30,plain,
( product('e$u2','e$u1','e$u1')
| product('e$u1',X0,'e$u1')
| equalish(X0,'e$u2')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c1,d29]) ).
cnf(d31,plain,
( ~ product('e$u1',X1,'e$u1')
| equalish(X0,X1)
| product('e$u2','e$u1','e$u1')
| equalish(X0,'e$u2')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[d30,c6]) ).
cnf(d32,plain,
( product('e$u2','e$u1','e$u1')
| equalish(X0,'e$u2')
| equalish(X0,'e$u2')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[d26,d31]) ).
cnf(d33,plain,
( product('e$u2','e$u1','e$u1')
| ~ 'group$uelement'('e$u1') ),
inference(resolution,[status(thm)],[d32,c2]) ).
cnf(d34,plain,
product('e$u2','e$u1','e$u1'),
inference(resolution,[status(thm)],[c0,d33]) ).
cnf(d35,plain,
( ~ product('e$u2',X0,'e$u1')
| equalish('e$u1',X0) ),
inference(resolution,[status(thm)],[d34,c6]) ).
cnf(d36,plain,
( product('e$u2','e$u2','e$u1')
| product('e$u1','e$u1','e$u1')
| product('e$u1','e$u1','e$u1')
| product('e$u2','e$u2','e$u1')
| ~ 'group$uelement'('e$u1')
| ~ 'group$uelement'('e$u2') ),
inference(resolution,[status(thm)],[d20,c3]) ).
cnf(d37,plain,
( product('e$u2','e$u2','e$u1')
| product('e$u1','e$u1','e$u1')
| ~ 'group$uelement'('e$u2') ),
inference(resolution,[status(thm)],[c0,d36]) ).
cnf(d38,plain,
( product('e$u2','e$u2','e$u1')
| product('e$u1','e$u1','e$u1') ),
inference(resolution,[status(thm)],[c1,d37]) ).
cnf(d39,plain,
( equalish('e$u1','e$u2')
| product('e$u1','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
product('e$u1','e$u1','e$u1'),
inference(resolution,[status(thm)],[c2,d39]) ).
cnf(d41,plain,
equalish('e$u2','e$u1'),
inference(resolution,[status(thm)],[d40,d27]) ).
cnf(d42,plain,
$false,
inference(resolution,[status(thm)],[c3,d41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP132-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.57 % Computer : n004.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Fri Sep 25 14:29:22 UTC 2026
% 0.11/0.57 % CPUTime :
% 0.11/0.57 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.19/3.32 % SZS status Unsatisfiable for theBenchmark.p
% 16.19/3.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------