%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP129-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 07:23:10 AM UTC 2026
% Result : Unsatisfiable 33.56s 4.88s
% Output : CNFRefutation 33.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 24
% Syntax : Number of clauses : 172 ( 36 unt; 121 nHn; 172 RR)
% Number of literals : 632 ( 0 equ; 104 neg)
% Maximal clause size : 7 ( 3 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 : 106 ( 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(qg3_1,negated_conjecture,
( ~ product(X1,X2,X3)
| ~ product(X2,X0,X3)
| product(X0,X1,X2) ) ).
cnf(qg3_2,negated_conjecture,
( ~ product(X3,X0,X1)
| ~ product(X1,X3,X2)
| product(X0,X1,X2) ) ).
cnf(element_1,axiom,
'group$uelement'('e$u1') ).
cnf(element_2,axiom,
'group$uelement'('e$u2') ).
cnf(element_3,axiom,
'group$uelement'('e$u3') ).
cnf(element_4,axiom,
'group$uelement'('e$u4') ).
cnf(e_1_is_not_e_2,axiom,
~ equalish('e$u1','e$u2') ).
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_2_is_not_e_1,axiom,
~ equalish('e$u2','e$u1') ).
cnf(e_2_is_not_e_3,axiom,
~ equalish('e$u2','e$u3') ).
cnf(e_2_is_not_e_4,axiom,
~ equalish('e$u2','e$u4') ).
cnf(e_3_is_not_e_1,axiom,
~ equalish('e$u3','e$u1') ).
cnf(e_3_is_not_e_2,axiom,
~ equalish('e$u3','e$u2') ).
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_function1,axiom,
( product(X0,X1,'e$u4')
| product(X0,X1,'e$u3')
| 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(X2,X0,X3)
| ~ product(X1,X2,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(X3,X0,X2)
| product(X1,X3,X0)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg3_1]) ).
cnf(c3,plain,
( ~ product(X1,X3,X0)
| product(X3,X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg3_2]) ).
cnf(c4,plain,
'group$uelement'('e$u1'),
inference(clausification,[status(esa)],[element_1]) ).
cnf(c5,plain,
'group$uelement'('e$u2'),
inference(clausification,[status(esa)],[element_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(c8,plain,
~ equalish('e$u1','e$u2'),
inference(clausification,[status(esa)],[e_1_is_not_e_2]) ).
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(c11,plain,
~ equalish('e$u2','e$u1'),
inference(clausification,[status(esa)],[e_2_is_not_e_1]) ).
cnf(c12,plain,
~ equalish('e$u2','e$u3'),
inference(clausification,[status(esa)],[e_2_is_not_e_3]) ).
cnf(c13,plain,
~ equalish('e$u2','e$u4'),
inference(clausification,[status(esa)],[e_2_is_not_e_4]) ).
cnf(c14,plain,
~ equalish('e$u3','e$u1'),
inference(clausification,[status(esa)],[e_3_is_not_e_1]) ).
cnf(c15,plain,
~ equalish('e$u3','e$u2'),
inference(clausification,[status(esa)],[e_3_is_not_e_2]) ).
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(c20,plain,
( product(X1,X0,'e$u2')
| ~ 'group$uelement'(X1)
| product(X1,X0,'e$u3')
| product(X1,X0,'e$u1')
| product(X1,X0,'e$u4')
| ~ 'group$uelement'(X0) ),
inference(clausification,[status(esa)],[product_total_function1]) ).
cnf(c21,plain,
( equalish(X3,X2)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_total_function2]) ).
cnf(c22,plain,
( equalish(X3,X1)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_right_cancellation]) ).
cnf(c23,plain,
( equalish(X3,X0)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_left_cancellation]) ).
cnf(c24,plain,
( product(X1,X3,X2)
| ~ product(X3,X0,X1)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg3]) ).
cnf(d0,plain,
( product(X0,'e$u3','e$u3')
| product(X0,'e$u3','e$u4')
| product(X0,'e$u3','e$u1')
| product(X0,'e$u3','e$u2')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c20,c6]) ).
cnf(d1,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u4')
| product('e$u3','e$u3','e$u1')
| product('e$u3','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d0,c6]) ).
cnf(d2,plain,
( ~ product(X0,'e$u3','e$u2')
| product('e$u3',X0,'e$u3')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u4')
| product('e$u3','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u4')
| product('e$u3','e$u3','e$u1')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u4')
| product('e$u3','e$u3','e$u1')
| product('e$u3','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ product(X0,'e$u3','e$u1')
| product('e$u3',X0,'e$u3')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u4')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u4')
| product('e$u3','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ product(X0,'e$u3','e$u4')
| product('e$u3',X0,'e$u3')
| product('e$u3','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( equalish('e$u3',X0)
| ~ product(X0,'e$u3','e$u3') ),
inference(resolution,[status(thm)],[d7,c23]) ).
cnf(d9,plain,
( product(X0,'e$u4','e$u3')
| product(X0,'e$u4','e$u4')
| product(X0,'e$u4','e$u1')
| product(X0,'e$u4','e$u2')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c20,c7]) ).
cnf(d10,plain,
( product('e$u4','e$u4','e$u3')
| product('e$u4','e$u4','e$u4')
| product('e$u4','e$u4','e$u1')
| product('e$u4','e$u4','e$u2') ),
inference(resolution,[status(thm)],[d9,c7]) ).
cnf(d11,plain,
( ~ product(X0,'e$u4','e$u2')
| product('e$u4',X0,'e$u4')
| product('e$u4','e$u4','e$u3')
| product('e$u4','e$u4','e$u4')
| product('e$u4','e$u4','e$u1') ),
inference(resolution,[status(thm)],[d10,c2]) ).
cnf(d12,plain,
( product('e$u4','e$u4','e$u3')
| product('e$u4','e$u4','e$u4')
| product('e$u4','e$u4','e$u1')
| product('e$u4','e$u4','e$u3')
| product('e$u4','e$u4','e$u4')
| product('e$u4','e$u4','e$u1')
| product('e$u4','e$u4','e$u4') ),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( ~ product(X0,'e$u4','e$u1')
| product('e$u4',X0,'e$u4')
| product('e$u4','e$u4','e$u3')
| product('e$u4','e$u4','e$u4') ),
inference(resolution,[status(thm)],[d12,c2]) ).
cnf(d14,plain,
( product('e$u4','e$u4','e$u3')
| product('e$u4','e$u4','e$u4')
| product('e$u4','e$u4','e$u3')
| product('e$u4','e$u4','e$u4')
| product('e$u4','e$u4','e$u4') ),
inference(resolution,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
( equalish('e$u4',X0)
| ~ product(X0,'e$u4','e$u4')
| product('e$u4','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d14,c23]) ).
cnf(d16,plain,
( product('e$u3',X0,'e$u1')
| product('e$u4',X0,'e$u1')
| product('e$u1',X0,'e$u1')
| product('e$u2',X0,'e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c0,c4]) ).
cnf(d17,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u2','e$u1')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
( equalish(X0,'e$u1')
| ~ product('e$u2','e$u2',X0)
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d17,c21]) ).
cnf(d19,plain,
( ~ product(X0,'e$u2','e$u1')
| product('e$u2',X0,'e$u2')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d17,c2]) ).
cnf(d20,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u2','e$u1')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u2','e$u1')
| product('e$u2','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
( equalish('e$u2','e$u1')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u2','e$u1')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[c11,d21]) ).
cnf(d23,plain,
( ~ product('e$u1','e$u1',X0)
| product('e$u2','e$u1',X0)
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d22,c3]) ).
cnf(d24,plain,
( equalish('e$u2',X0)
| ~ product('e$u1',X0,'e$u1')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d22,c22]) ).
cnf(d25,plain,
( product(X0,'e$u1','e$u3')
| product(X0,'e$u1','e$u4')
| product(X0,'e$u1','e$u1')
| product(X0,'e$u1','e$u2')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c20,c4]) ).
cnf(d26,plain,
( product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u4')
| product('e$u1','e$u1','e$u1')
| product('e$u1','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d25,c4]) ).
cnf(d27,plain,
( ~ product(X0,'e$u1','e$u2')
| product('e$u1',X0,'e$u1')
| product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u4')
| product('e$u1','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d26,c2]) ).
cnf(d28,plain,
( product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u4')
| product('e$u1','e$u1','e$u1')
| product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u4')
| product('e$u1','e$u1','e$u1')
| product('e$u1','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
( equalish('e$u2','e$u1')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d28,d24]) ).
cnf(d30,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u4') ),
inference(resolution,[status(thm)],[c11,d29]) ).
cnf(d31,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u2','e$u1','e$u4')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d30,d23]) ).
cnf(d32,plain,
( equalish('e$u1',X0)
| ~ product(X0,'e$u1','e$u4')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d30,c23]) ).
cnf(d33,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u1','e$u3')
| equalish('e$u1','e$u2')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c8,d33]) ).
cnf(d35,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u2','e$u1','e$u3')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d34,d23]) ).
cnf(d36,plain,
( equalish('e$u1',X0)
| ~ product(X0,'e$u1','e$u3')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d34,c23]) ).
cnf(d37,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| equalish('e$u1','e$u2')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d36,d35]) ).
cnf(d38,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1') ),
inference(resolution,[status(thm)],[c8,d37]) ).
cnf(d39,plain,
( ~ product('e$u2','e$u1',X0)
| product('e$u1','e$u4',X0)
| product('e$u3','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d38,c24]) ).
cnf(d40,plain,
( ~ product(X0,'e$u4','e$u1')
| product('e$u2',X0,'e$u4')
| product('e$u3','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d38,c2]) ).
cnf(d41,plain,
( product(X0,'e$u3','e$u4')
| product(X0,'e$u4','e$u4')
| product(X0,'e$u1','e$u4')
| product(X0,'e$u2','e$u4')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d42,plain,
( product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u4')
| product('e$u2','e$u1','e$u4')
| product('e$u2','e$u2','e$u4') ),
inference(resolution,[status(thm)],[d41,c5]) ).
cnf(d43,plain,
( ~ product(X0,'e$u2','e$u4')
| product('e$u2',X0,'e$u2')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u4')
| product('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d42,c2]) ).
cnf(d44,plain,
( product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u4')
| product('e$u2','e$u1','e$u4')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u4')
| product('e$u2','e$u1','e$u4')
| product('e$u2','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d43,d42]) ).
cnf(d45,plain,
( equalish(X0,'e$u4')
| ~ product('e$u2','e$u2',X0)
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u4')
| product('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d42,c21]) ).
cnf(d46,plain,
( product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u4')
| product('e$u2','e$u1','e$u4')
| equalish('e$u2','e$u4')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u4')
| product('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d45,d44]) ).
cnf(d47,plain,
( product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u4')
| product('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[c13,d46]) ).
cnf(d48,plain,
( ~ product('e$u4','e$u2',X0)
| product('e$u1','e$u4',X0)
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u4') ),
inference(resolution,[status(thm)],[d47,c3]) ).
cnf(d49,plain,
( product('e$u1','e$u4','e$u1')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u4')
| product('e$u3','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d38,d48]) ).
cnf(d50,plain,
( equalish('e$u4','e$u2')
| product('e$u4','e$u4','e$u3')
| product('e$u3','e$u2','e$u1')
| product('e$u1','e$u4','e$u1')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d49,d15]) ).
cnf(d51,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u4','e$u3')
| product('e$u1','e$u4','e$u1')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[c18,d50]) ).
cnf(d52,plain,
( equalish(X0,'e$u4')
| ~ product('e$u2','e$u3',X0)
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u4','e$u3')
| product('e$u1','e$u4','e$u1') ),
inference(resolution,[status(thm)],[d51,c21]) ).
cnf(d53,plain,
( product(X0,'e$u3','e$u1')
| product(X0,'e$u4','e$u1')
| product(X0,'e$u1','e$u1')
| product(X0,'e$u2','e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c1,c4]) ).
cnf(d54,plain,
( product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1')
| product('e$u2','e$u1','e$u1')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d53,c5]) ).
cnf(d55,plain,
( equalish(X0,'e$u1')
| ~ product('e$u2','e$u2',X0)
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1')
| product('e$u2','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d54,c21]) ).
cnf(d56,plain,
( ~ product(X0,'e$u2','e$u1')
| product('e$u2',X0,'e$u2')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1')
| product('e$u2','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d54,c2]) ).
cnf(d57,plain,
( product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1')
| product('e$u2','e$u1','e$u1')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1')
| product('e$u2','e$u1','e$u1')
| product('e$u2','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d56,d54]) ).
cnf(d58,plain,
( equalish('e$u2','e$u1')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1')
| product('e$u2','e$u1','e$u1')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1')
| product('e$u2','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d57,d55]) ).
cnf(d59,plain,
( product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1')
| product('e$u2','e$u1','e$u1') ),
inference(resolution,[status(thm)],[c11,d58]) ).
cnf(d60,plain,
( product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1')
| product('e$u3','e$u2','e$u1')
| product('e$u1','e$u4','e$u1') ),
inference(resolution,[status(thm)],[d39,d59]) ).
cnf(d61,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u2','e$u2','e$u4')
| product('e$u3','e$u2','e$u1')
| product('e$u1','e$u4','e$u1')
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d60,d40]) ).
cnf(d62,plain,
( equalish('e$u2',X0)
| ~ product('e$u2',X0,'e$u4')
| product('e$u3','e$u2','e$u1')
| product('e$u1','e$u4','e$u1')
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d61,c22]) ).
cnf(d63,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u4','e$u3')
| product('e$u1','e$u4','e$u1')
| equalish('e$u2','e$u3')
| product('e$u3','e$u2','e$u1')
| product('e$u1','e$u4','e$u1')
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d62,d51]) ).
cnf(d64,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u4','e$u3')
| product('e$u1','e$u4','e$u1')
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[c12,d63]) ).
cnf(d65,plain,
( equalish('e$u1','e$u4')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u4','e$u3')
| product('e$u1','e$u4','e$u1')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u4','e$u3')
| product('e$u1','e$u4','e$u1') ),
inference(resolution,[status(thm)],[d64,d52]) ).
cnf(d66,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u4','e$u3')
| product('e$u1','e$u4','e$u1') ),
inference(resolution,[status(thm)],[c10,d65]) ).
cnf(d67,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u2','e$u1','e$u4')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d66,d40]) ).
cnf(d68,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u1','e$u4','e$u4')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d67,d39]) ).
cnf(d69,plain,
( equalish('e$u4','e$u1')
| product('e$u4','e$u4','e$u3')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d68,d15]) ).
cnf(d70,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u4','e$u3') ),
inference(resolution,[status(thm)],[c17,d69]) ).
cnf(d71,plain,
( equalish(X0,'e$u3')
| ~ product('e$u4','e$u4',X0)
| product('e$u3','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d70,c21]) ).
cnf(d72,plain,
( ~ product(X0,'e$u4','e$u3')
| product('e$u4',X0,'e$u4')
| product('e$u3','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d70,c2]) ).
cnf(d73,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u4','e$u4') ),
inference(resolution,[status(thm)],[d72,d70]) ).
cnf(d74,plain,
( equalish('e$u4','e$u3')
| product('e$u3','e$u2','e$u1')
| product('e$u3','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d73,d71]) ).
cnf(d75,plain,
product('e$u3','e$u2','e$u1'),
inference(resolution,[status(thm)],[c19,d74]) ).
cnf(d76,plain,
( ~ product('e$u2','e$u1',X0)
| product('e$u1','e$u3',X0) ),
inference(resolution,[status(thm)],[d75,c24]) ).
cnf(d77,plain,
( ~ product(X0,'e$u3','e$u1')
| product('e$u2',X0,'e$u3') ),
inference(resolution,[status(thm)],[d75,c2]) ).
cnf(d78,plain,
( product(X0,'e$u3','e$u3')
| product(X0,'e$u4','e$u3')
| product(X0,'e$u1','e$u3')
| product(X0,'e$u2','e$u3')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(d79,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d78,c5]) ).
cnf(d80,plain,
( equalish(X0,'e$u3')
| ~ product('e$u2','e$u2',X0)
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d79,c21]) ).
cnf(d81,plain,
( ~ product(X0,'e$u2','e$u3')
| product('e$u2',X0,'e$u2')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d79,c2]) ).
cnf(d82,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d81,d79]) ).
cnf(d83,plain,
( equalish('e$u2','e$u3')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d82,d80]) ).
cnf(d84,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c12,d83]) ).
cnf(d85,plain,
( equalish('e$u1',X0)
| ~ product('e$u2',X0,'e$u3')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d84,c22]) ).
cnf(d86,plain,
( equalish(X0,'e$u1')
| ~ product('e$u2','e$u1',X0)
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1') ),
inference(resolution,[status(thm)],[d59,c21]) ).
cnf(d87,plain,
( equalish('e$u4','e$u1')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u4') ),
inference(resolution,[status(thm)],[d47,d86]) ).
cnf(d88,plain,
( product('e$u2','e$u3','e$u4')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u4')
| product('e$u2','e$u4','e$u1') ),
inference(resolution,[status(thm)],[c17,d87]) ).
cnf(d89,plain,
( equalish(X0,'e$u1')
| ~ product('e$u2','e$u4',X0)
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u4') ),
inference(resolution,[status(thm)],[d88,c21]) ).
cnf(d90,plain,
( equalish(X0,'e$u3')
| ~ product('e$u2','e$u1',X0)
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d84,c21]) ).
cnf(d91,plain,
( equalish('e$u4','e$u3')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u4') ),
inference(resolution,[status(thm)],[d47,d90]) ).
cnf(d92,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u3')
| product('e$u2','e$u4','e$u4') ),
inference(resolution,[status(thm)],[c19,d91]) ).
cnf(d93,plain,
( equalish('e$u3','e$u1')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d84,d86]) ).
cnf(d94,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u3')
| product('e$u2','e$u4','e$u1') ),
inference(resolution,[status(thm)],[c14,d93]) ).
cnf(d95,plain,
( equalish(X0,'e$u1')
| ~ product('e$u2','e$u4',X0)
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d94,c21]) ).
cnf(d96,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u3')
| equalish('e$u4','e$u1')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d95,d92]) ).
cnf(d97,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[c17,d96]) ).
cnf(d98,plain,
( equalish('e$u3','e$u1')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u4')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d97,d89]) ).
cnf(d99,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u4') ),
inference(resolution,[status(thm)],[c14,d98]) ).
cnf(d100,plain,
( equalish(X0,'e$u3')
| ~ product('e$u2','e$u4',X0)
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d97,c21]) ).
cnf(d101,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u3','e$u1')
| equalish('e$u4','e$u3')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d100,d99]) ).
cnf(d102,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[c19,d101]) ).
cnf(d103,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d77,d102]) ).
cnf(d104,plain,
( equalish('e$u1','e$u2')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d103,d85]) ).
cnf(d105,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[c8,d104]) ).
cnf(d106,plain,
( equalish('e$u2',X0)
| ~ product('e$u2',X0,'e$u3')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d103,c22]) ).
cnf(d107,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4')
| equalish('e$u2','e$u4')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d106,d105]) ).
cnf(d108,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[c13,d107]) ).
cnf(d109,plain,
( equalish(X0,'e$u4')
| ~ product('e$u2','e$u3',X0)
| product('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d108,c21]) ).
cnf(d110,plain,
( product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1')
| product('e$u1','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d76,d59]) ).
cnf(d111,plain,
( ~ product('e$u3','e$u2',X0)
| product('e$u1','e$u3',X0)
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d84,c3]) ).
cnf(d112,plain,
( product('e$u1','e$u3','e$u1')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d75,d111]) ).
cnf(d113,plain,
( equalish(X0,'e$u3')
| ~ product('e$u2','e$u4',X0)
| product('e$u1','e$u3','e$u1')
| product('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d112,c21]) ).
cnf(d114,plain,
( product('e$u1','e$u3','e$u1')
| product('e$u2','e$u3','e$u1')
| equalish('e$u1','e$u3')
| product('e$u1','e$u3','e$u1')
| product('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d113,d110]) ).
cnf(d115,plain,
( product('e$u1','e$u3','e$u1')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[c9,d114]) ).
cnf(d116,plain,
( equalish('e$u1','e$u4')
| product('e$u2','e$u3','e$u3')
| product('e$u1','e$u3','e$u1')
| product('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d115,d109]) ).
cnf(d117,plain,
( product('e$u1','e$u3','e$u1')
| product('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[c10,d116]) ).
cnf(d118,plain,
( equalish('e$u3','e$u2')
| product('e$u1','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d117,d8]) ).
cnf(d119,plain,
product('e$u1','e$u3','e$u1'),
inference(resolution,[status(thm)],[c15,d118]) ).
cnf(d120,plain,
product('e$u2','e$u1','e$u3'),
inference(resolution,[status(thm)],[d119,d77]) ).
cnf(d121,plain,
product('e$u1','e$u3','e$u3'),
inference(resolution,[status(thm)],[d120,d76]) ).
cnf(d122,plain,
equalish('e$u3','e$u1'),
inference(resolution,[status(thm)],[d121,d8]) ).
cnf(d123,plain,
$false,
inference(resolution,[status(thm)],[c14,d122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP129-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:30:56 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.56/4.88 % SZS status Unsatisfiable for theBenchmark.p
% 33.56/4.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------