%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP126-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:22:28 AM UTC 2026
% Result : Unsatisfiable 16.93s 4.17s
% Output : CNFRefutation 16.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 18
% Syntax : Number of clauses : 105 ( 27 unt; 55 nHn; 103 RR)
% Number of literals : 275 ( 0 equ; 79 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 86 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(row_surjectivity,axiom,
( product('e$u4',X0,X1)
| product('e$u3',X0,X1)
| product('e$u2',X0,X1)
| product('e$u1',X0,X1)
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ) ).
cnf(column_surjectivity,axiom,
( product(X0,'e$u4',X1)
| product(X0,'e$u3',X1)
| product(X0,'e$u2',X1)
| product(X0,'e$u1',X1)
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ) ).
cnf(qg4_1,negated_conjecture,
( ~ product(X1,X0,X3)
| ~ product(X2,X3,X1)
| product(X0,X1,X2) ) ).
cnf(qg4_2,negated_conjecture,
( ~ product(X1,X0,X3)
| ~ product(X3,X2,X0)
| product(X0,X1,X2) ) ).
cnf(element_3,axiom,
'group$uelement'('e$u3') ).
cnf(element_4,axiom,
'group$uelement'('e$u4') ).
cnf(e_1_is_not_e_3,axiom,
~ equalish('e$u1','e$u3') ).
cnf(e_1_is_not_e_4,axiom,
~ equalish('e$u1','e$u4') ).
cnf(e_3_is_not_e_1,axiom,
~ equalish('e$u3','e$u1') ).
cnf(e_3_is_not_e_4,axiom,
~ equalish('e$u3','e$u4') ).
cnf(e_4_is_not_e_1,axiom,
~ equalish('e$u4','e$u1') ).
cnf(e_4_is_not_e_2,axiom,
~ equalish('e$u4','e$u2') ).
cnf(e_4_is_not_e_3,axiom,
~ equalish('e$u4','e$u3') ).
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(product_idempotence,axiom,
product(X0,X0,X0) ).
cnf(qg4,negated_conjecture,
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
( product('e$u4',X0,X1)
| ~ 'group$uelement'(X1)
| product('e$u2',X0,X1)
| product('e$u1',X0,X1)
| product('e$u3',X0,X1)
| ~ 'group$uelement'(X0) ),
inference(clausification,[status(esa)],[row_surjectivity]) ).
cnf(c1,plain,
( ~ 'group$uelement'(X1)
| product(X1,'e$u1',X0)
| product(X1,'e$u2',X0)
| product(X1,'e$u3',X0)
| product(X1,'e$u4',X0)
| ~ 'group$uelement'(X0) ),
inference(clausification,[status(esa)],[column_surjectivity]) ).
cnf(c2,plain,
( ~ product(X1,X0,X3)
| ~ product(X2,X3,X1)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg4_1]) ).
cnf(c3,plain,
( ~ product(X1,X0,X3)
| ~ product(X3,X2,X0)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg4_2]) ).
cnf(c6,plain,
'group$uelement'('e$u3'),
inference(clausification,[status(esa)],[element_3]) ).
cnf(c7,plain,
'group$uelement'('e$u4'),
inference(clausification,[status(esa)],[element_4]) ).
cnf(c9,plain,
~ equalish('e$u1','e$u3'),
inference(clausification,[status(esa)],[e_1_is_not_e_3]) ).
cnf(c10,plain,
~ equalish('e$u1','e$u4'),
inference(clausification,[status(esa)],[e_1_is_not_e_4]) ).
cnf(c14,plain,
~ equalish('e$u3','e$u1'),
inference(clausification,[status(esa)],[e_3_is_not_e_1]) ).
cnf(c16,plain,
~ equalish('e$u3','e$u4'),
inference(clausification,[status(esa)],[e_3_is_not_e_4]) ).
cnf(c17,plain,
~ equalish('e$u4','e$u1'),
inference(clausification,[status(esa)],[e_4_is_not_e_1]) ).
cnf(c18,plain,
~ equalish('e$u4','e$u2'),
inference(clausification,[status(esa)],[e_4_is_not_e_2]) ).
cnf(c19,plain,
~ equalish('e$u4','e$u3'),
inference(clausification,[status(esa)],[e_4_is_not_e_3]) ).
cnf(c21,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_total_function2]) ).
cnf(c22,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_right_cancellation]) ).
cnf(c23,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_left_cancellation]) ).
cnf(c24,plain,
product(X0,X0,X0),
inference(clausification,[status(esa)],[product_idempotence]) ).
cnf(c25,plain,
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg4]) ).
cnf(d0,plain,
( equalish(X0,X1)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[c23,c24]) ).
cnf(d1,plain,
( equalish(X1,X0)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[c22,c24]) ).
cnf(d2,plain,
( equalish(X0,X1)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[c21,c24]) ).
cnf(d3,plain,
( product('e$u4',X0,'e$u3')
| product('e$u1',X0,'e$u3')
| product('e$u2',X0,'e$u3')
| ~ 'group$uelement'(X0)
| ~ 'group$uelement'('e$u3')
| equalish(X0,'e$u3') ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d4,plain,
( equalish(X0,'e$u3')
| product('e$u4',X0,'e$u3')
| product('e$u1',X0,'e$u3')
| product('e$u2',X0,'e$u3')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c6,d3]) ).
cnf(d5,plain,
( equalish('e$u4','e$u3')
| equalish('e$u4','e$u3')
| product('e$u1','e$u4','e$u3')
| product('e$u2','e$u4','e$u3')
| ~ 'group$uelement'('e$u4') ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( equalish('e$u4','e$u3')
| product('e$u1','e$u4','e$u3')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[c7,d5]) ).
cnf(d7,plain,
( product('e$u1','e$u4','e$u3')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[c19,d6]) ).
cnf(d8,plain,
( ~ product('e$u3',X0,'e$u4')
| product(X0,'e$u3','e$u1')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
( product('e$u3','e$u4',X0)
| product('e$u3','e$u1',X0)
| product('e$u3','e$u2',X0)
| ~ 'group$uelement'('e$u3')
| ~ 'group$uelement'(X0)
| equalish('e$u3',X0) ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d10,plain,
( equalish('e$u3',X0)
| product('e$u3','e$u4',X0)
| product('e$u3','e$u1',X0)
| product('e$u3','e$u2',X0)
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c6,d9]) ).
cnf(d11,plain,
( equalish('e$u3','e$u4')
| equalish('e$u3','e$u4')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u2','e$u4')
| ~ 'group$uelement'('e$u4') ),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
( equalish('e$u3','e$u4')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u2','e$u4') ),
inference(resolution,[status(thm)],[c7,d11]) ).
cnf(d13,plain,
( product('e$u3','e$u1','e$u4')
| product('e$u3','e$u2','e$u4') ),
inference(resolution,[status(thm)],[c16,d12]) ).
cnf(d14,plain,
( product('e$u3','e$u2','e$u4')
| product('e$u2','e$u4','e$u3')
| product('e$u1','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d8,d13]) ).
cnf(d15,plain,
( product('e$u2','e$u4','e$u3')
| product('e$u2','e$u3','e$u1')
| product('e$u1','e$u3','e$u1')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d14,d8]) ).
cnf(d16,plain,
( equalish('e$u3','e$u1')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
( product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[c14,d16]) ).
cnf(d18,plain,
( equalish('e$u1',X0)
| ~ product('e$u2','e$u3',X0)
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d17,c21]) ).
cnf(d19,plain,
( product('e$u4','e$u1',X0)
| ~ product('e$u3',X0,'e$u4')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d7,c3]) ).
cnf(d20,plain,
( product('e$u3','e$u2','e$u4')
| product('e$u4','e$u1','e$u1')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d19,d13]) ).
cnf(d21,plain,
( product('e$u4','e$u1','e$u2')
| product('e$u2','e$u4','e$u3')
| product('e$u4','e$u1','e$u1')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
( equalish('e$u4','e$u1')
| product('e$u4','e$u1','e$u2')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
( product('e$u4','e$u1','e$u2')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[c17,d22]) ).
cnf(d24,plain,
( equalish(X0,'e$u4')
| ~ product(X0,'e$u1','e$u2')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d23,c23]) ).
cnf(d25,plain,
( product('e$u4','e$u3',X0)
| product('e$u1','e$u3',X0)
| product('e$u2','e$u3',X0)
| ~ 'group$uelement'('e$u3')
| ~ 'group$uelement'(X0)
| equalish('e$u3',X0) ),
inference(resolution,[status(thm)],[d2,c0]) ).
cnf(d26,plain,
( equalish('e$u3',X0)
| product('e$u4','e$u3',X0)
| product('e$u1','e$u3',X0)
| product('e$u2','e$u3',X0)
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c6,d25]) ).
cnf(d27,plain,
( equalish('e$u3','e$u4')
| equalish('e$u3','e$u4')
| product('e$u1','e$u3','e$u4')
| product('e$u2','e$u3','e$u4')
| ~ 'group$uelement'('e$u4') ),
inference(resolution,[status(thm)],[d26,d1]) ).
cnf(d28,plain,
( equalish('e$u3','e$u4')
| product('e$u1','e$u3','e$u4')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[c7,d27]) ).
cnf(d29,plain,
( product('e$u1','e$u3','e$u4')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[c16,d28]) ).
cnf(d30,plain,
( product('e$u3','e$u1',X0)
| ~ product('e$u4',X0,'e$u3')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d29,c3]) ).
cnf(d31,plain,
( product(X0,'e$u4','e$u3')
| product(X0,'e$u1','e$u3')
| product(X0,'e$u2','e$u3')
| ~ 'group$uelement'(X0)
| ~ 'group$uelement'('e$u3')
| equalish(X0,'e$u3') ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d32,plain,
( equalish(X0,'e$u3')
| product(X0,'e$u4','e$u3')
| product(X0,'e$u1','e$u3')
| product(X0,'e$u2','e$u3')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c6,d31]) ).
cnf(d33,plain,
( equalish('e$u4','e$u3')
| equalish('e$u4','e$u3')
| product('e$u4','e$u1','e$u3')
| product('e$u4','e$u2','e$u3')
| ~ 'group$uelement'('e$u4') ),
inference(resolution,[status(thm)],[d32,d2]) ).
cnf(d34,plain,
( equalish('e$u4','e$u3')
| product('e$u4','e$u1','e$u3')
| product('e$u4','e$u2','e$u3') ),
inference(resolution,[status(thm)],[c7,d33]) ).
cnf(d35,plain,
( product('e$u4','e$u1','e$u3')
| product('e$u4','e$u2','e$u3') ),
inference(resolution,[status(thm)],[c19,d34]) ).
cnf(d36,plain,
( product('e$u3','e$u1','e$u1')
| product('e$u2','e$u3','e$u4')
| product('e$u4','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d35,d30]) ).
cnf(d37,plain,
( equalish('e$u3','e$u1')
| product('e$u4','e$u2','e$u3')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d36,d0]) ).
cnf(d38,plain,
( product('e$u4','e$u2','e$u3')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[c14,d37]) ).
cnf(d39,plain,
( product('e$u3','e$u1','e$u2')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d38,d30]) ).
cnf(d40,plain,
( equalish('e$u3','e$u4')
| product('e$u2','e$u4','e$u3')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d39,d24]) ).
cnf(d41,plain,
( product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[c16,d40]) ).
cnf(d42,plain,
( equalish('e$u1','e$u4')
| product('e$u2','e$u4','e$u3')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d41,d18]) ).
cnf(d43,plain,
product('e$u2','e$u4','e$u3'),
inference(resolution,[status(thm)],[c10,d42]) ).
cnf(d44,plain,
( product('e$u4','e$u2',X0)
| ~ product('e$u3',X0,'e$u4') ),
inference(resolution,[status(thm)],[d43,c3]) ).
cnf(d45,plain,
( ~ product('e$u3',X0,'e$u4')
| product(X0,'e$u3','e$u2') ),
inference(resolution,[status(thm)],[d43,c2]) ).
cnf(d46,plain,
( product('e$u3','e$u2','e$u4')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d45,d13]) ).
cnf(d47,plain,
( product('e$u4','e$u2','e$u2')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d46,d44]) ).
cnf(d48,plain,
( equalish('e$u4','e$u2')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d47,d0]) ).
cnf(d49,plain,
product('e$u1','e$u3','e$u2'),
inference(resolution,[status(thm)],[c18,d48]) ).
cnf(d50,plain,
( equalish(X0,'e$u3')
| ~ product('e$u1',X0,'e$u2') ),
inference(resolution,[status(thm)],[d49,c22]) ).
cnf(d51,plain,
( equalish(X0,'e$u2')
| ~ product(X0,'e$u4','e$u3') ),
inference(resolution,[status(thm)],[d43,c23]) ).
cnf(d52,plain,
( product('e$u3','e$u2','e$u4')
| product('e$u4','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d44,d13]) ).
cnf(d53,plain,
( equalish(X0,'e$u1')
| ~ product(X0,'e$u3','e$u4')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d29,c23]) ).
cnf(d54,plain,
( ~ product('e$u4','e$u2',X0)
| product('e$u3',X0,'e$u4') ),
inference(resolution,[status(thm)],[d43,c25]) ).
cnf(d55,plain,
( product('e$u2','e$u3','e$u4')
| product('e$u3','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d54,d38]) ).
cnf(d56,plain,
( equalish('e$u3','e$u1')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d55,d53]) ).
cnf(d57,plain,
product('e$u2','e$u3','e$u4'),
inference(resolution,[status(thm)],[c14,d56]) ).
cnf(d58,plain,
( ~ product('e$u3','e$u2',X0)
| product('e$u4',X0,'e$u3') ),
inference(resolution,[status(thm)],[d57,c25]) ).
cnf(d59,plain,
( product('e$u4','e$u2','e$u1')
| product('e$u4','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d58,d52]) ).
cnf(d60,plain,
( equalish('e$u4','e$u2')
| product('e$u4','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d59,d51]) ).
cnf(d61,plain,
product('e$u4','e$u2','e$u1'),
inference(resolution,[status(thm)],[c18,d60]) ).
cnf(d62,plain,
( equalish('e$u1',X0)
| ~ product('e$u4','e$u2',X0) ),
inference(resolution,[status(thm)],[d61,c21]) ).
cnf(d63,plain,
( ~ product('e$u4',X0,'e$u3')
| product(X0,'e$u4','e$u2') ),
inference(resolution,[status(thm)],[d57,c2]) ).
cnf(d64,plain,
( product('e$u4','e$u2','e$u3')
| product('e$u1','e$u4','e$u2') ),
inference(resolution,[status(thm)],[d63,d35]) ).
cnf(d65,plain,
( equalish('e$u1','e$u3')
| product('e$u1','e$u4','e$u2') ),
inference(resolution,[status(thm)],[d64,d62]) ).
cnf(d66,plain,
product('e$u1','e$u4','e$u2'),
inference(resolution,[status(thm)],[c9,d65]) ).
cnf(d67,plain,
equalish('e$u4','e$u3'),
inference(resolution,[status(thm)],[d66,d50]) ).
cnf(d68,plain,
$false,
inference(resolution,[status(thm)],[c19,d67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP126-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n015.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 14:29:57 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.93/4.17 % SZS status Unsatisfiable for theBenchmark.p
% 16.93/4.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------