%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP127-4.004 : 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 : 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 07:22:28 AM UTC 2026
% Result : Unsatisfiable 11.73s 2.75s
% Output : CNFRefutation 11.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 22
% Syntax : Number of clauses : 128 ( 34 unt; 73 nHn; 126 RR)
% Number of literals : 334 ( 0 equ; 78 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 : 89 ( 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(X2,X0,X3)
| ~ product(X3,X0,X1)
| product(X0,X1,X2) ) ).
cnf(qg3_2,negated_conjecture,
( ~ product(X1,X3,X0)
| ~ product(X2,X1,X3)
| product(X0,X1,X2) ) ).
cnf(element_1,axiom,
'group$uelement'('e$u1') ).
cnf(element_2,axiom,
'group$uelement'('e$u2') ).
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_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_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(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(product_idempotence,axiom,
product(X0,X0,X0) ).
cnf(qg3,negated_conjecture,
( product(X3,X0,X1)
| ~ product(X2,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(X3,X1,X0)
| product(X1,X2,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg3_1]) ).
cnf(c3,plain,
( ~ product(X1,X2,X3)
| product(X3,X1,X0)
| ~ 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(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(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(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(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(X0,X0,X0),
inference(clausification,[status(esa)],[product_idempotence]) ).
cnf(c25,plain,
( product(X2,X1,X3)
| ~ product(X1,X3,X0)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg3]) ).
cnf(d0,plain,
( equalish(X1,X0)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[c21,c24]) ).
cnf(d1,plain,
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[c23,c24]) ).
cnf(d2,plain,
( product(X0,'e$u3','e$u2')
| product(X0,'e$u4','e$u2')
| product(X0,'e$u1','e$u2')
| product(X0,'e$u2','e$u2')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c1,c5]) ).
cnf(d3,plain,
( product('e$u1','e$u3','e$u2')
| product('e$u1','e$u4','e$u2')
| product('e$u1','e$u1','e$u2')
| product('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
( equalish('e$u2','e$u1')
| product('e$u1','e$u3','e$u2')
| product('e$u1','e$u4','e$u2')
| product('e$u1','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( product('e$u1','e$u3','e$u2')
| product('e$u1','e$u4','e$u2')
| product('e$u1','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c11,d4]) ).
cnf(d6,plain,
( equalish('e$u2','e$u1')
| product('e$u1','e$u3','e$u2')
| product('e$u1','e$u4','e$u2') ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
( product('e$u1','e$u3','e$u2')
| product('e$u1','e$u4','e$u2') ),
inference(resolution,[status(thm)],[c11,d6]) ).
cnf(d8,plain,
( equalish(X0,'e$u2')
| ~ product('e$u1','e$u4',X0)
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d7,c21]) ).
cnf(d9,plain,
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[c22,c24]) ).
cnf(d10,plain,
( product('e$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(d11,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)],[d10,c5]) ).
cnf(d12,plain,
( equalish('e$u1','e$u2')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1')
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[c8,d12]) ).
cnf(d14,plain,
( equalish('e$u1','e$u2')
| product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u4','e$u2','e$u1') ),
inference(resolution,[status(thm)],[c8,d14]) ).
cnf(d16,plain,
( ~ product('e$u4','e$u2',X0)
| product(X0,'e$u4','e$u1')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d7,c3]) ).
cnf(d17,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u1','e$u3','e$u2')
| product('e$u1','e$u4','e$u1') ),
inference(resolution,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
( equalish('e$u1','e$u2')
| product('e$u1','e$u3','e$u2')
| product('e$u3','e$u2','e$u1')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d17,d8]) ).
cnf(d19,plain,
( product('e$u3','e$u2','e$u1')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[c8,d18]) ).
cnf(d20,plain,
( equalish('e$u1',X0)
| ~ product(X0,'e$u3','e$u2')
| product('e$u3','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d19,c23]) ).
cnf(d21,plain,
( product('e$u4','e$u3','e$u2')
| product('e$u4','e$u4','e$u2')
| product('e$u4','e$u1','e$u2')
| product('e$u4','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d2,c7]) ).
cnf(d22,plain,
( equalish('e$u2','e$u4')
| product('e$u4','e$u3','e$u2')
| product('e$u4','e$u4','e$u2')
| product('e$u4','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d21,d1]) ).
cnf(d23,plain,
( product('e$u4','e$u3','e$u2')
| product('e$u4','e$u4','e$u2')
| product('e$u4','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c13,d22]) ).
cnf(d24,plain,
( product(X0,'e$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(d25,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)],[d24,c5]) ).
cnf(d26,plain,
( equalish('e$u1','e$u2')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1')
| product('e$u2','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d25,d0]) ).
cnf(d27,plain,
( product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1')
| product('e$u2','e$u1','e$u1') ),
inference(resolution,[status(thm)],[c8,d26]) ).
cnf(d28,plain,
( equalish('e$u1','e$u2')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1') ),
inference(resolution,[status(thm)],[d27,d1]) ).
cnf(d29,plain,
( product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u1') ),
inference(resolution,[status(thm)],[c8,d28]) ).
cnf(d30,plain,
( equalish(X0,'e$u1')
| ~ product('e$u2','e$u4',X0)
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d29,c21]) ).
cnf(d31,plain,
( product('e$u3',X0,'e$u2')
| product('e$u4',X0,'e$u2')
| product('e$u1',X0,'e$u2')
| product('e$u2',X0,'e$u2')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(d32,plain,
( product('e$u3','e$u1','e$u2')
| product('e$u4','e$u1','e$u2')
| product('e$u1','e$u1','e$u2')
| product('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d31,c4]) ).
cnf(d33,plain,
( equalish('e$u2','e$u1')
| product('e$u3','e$u1','e$u2')
| product('e$u4','e$u1','e$u2')
| product('e$u1','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d32,d9]) ).
cnf(d34,plain,
( product('e$u3','e$u1','e$u2')
| product('e$u4','e$u1','e$u2')
| product('e$u1','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c11,d33]) ).
cnf(d35,plain,
( equalish('e$u2','e$u1')
| product('e$u3','e$u1','e$u2')
| product('e$u4','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d34,d0]) ).
cnf(d36,plain,
( product('e$u3','e$u1','e$u2')
| product('e$u4','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c11,d35]) ).
cnf(d37,plain,
( ~ product('e$u4','e$u1',X0)
| product(X0,'e$u4','e$u2')
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d29,c3]) ).
cnf(d38,plain,
( product('e$u3','e$u1','e$u2')
| product('e$u2','e$u3','e$u1')
| product('e$u2','e$u4','e$u2') ),
inference(resolution,[status(thm)],[d37,d36]) ).
cnf(d39,plain,
( equalish('e$u2','e$u1')
| product('e$u2','e$u3','e$u1')
| product('e$u3','e$u1','e$u2')
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d38,d30]) ).
cnf(d40,plain,
( product('e$u3','e$u1','e$u2')
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[c11,d39]) ).
cnf(d41,plain,
( ~ product('e$u1','e$u3',X0)
| product('e$u3',X0,'e$u2')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d40,c2]) ).
cnf(d42,plain,
( product('e$u3','e$u1','e$u2')
| product('e$u3','e$u2','e$u2')
| product('e$u3','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d19,d41]) ).
cnf(d43,plain,
( equalish('e$u2','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u3','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d42,d1]) ).
cnf(d44,plain,
( product('e$u3','e$u1','e$u2')
| product('e$u3','e$u2','e$u1') ),
inference(resolution,[status(thm)],[c12,d43]) ).
cnf(d45,plain,
( equalish(X0,'e$u1')
| ~ product('e$u3','e$u2',X0)
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d44,c21]) ).
cnf(d46,plain,
( ~ product('e$u2','e$u1',X0)
| product(X0,'e$u2','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d44,c3]) ).
cnf(d47,plain,
( ~ product('e$u1',X0,'e$u4')
| product('e$u2','e$u1',X0)
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d36,c25]) ).
cnf(d48,plain,
( ~ product('e$u2','e$u1',X0)
| product('e$u1',X0,'e$u4')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d36,c2]) ).
cnf(d49,plain,
( product(X0,'e$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(d50,plain,
( product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u4')
| product('e$u2','e$u1','e$u1')
| product('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d49,c5]) ).
cnf(d51,plain,
( equalish('e$u2','e$u1')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u4')
| product('e$u2','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d50,d9]) ).
cnf(d52,plain,
( product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u4')
| product('e$u2','e$u1','e$u1') ),
inference(resolution,[status(thm)],[c11,d51]) ).
cnf(d53,plain,
( equalish('e$u1','e$u2')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d52,d1]) ).
cnf(d54,plain,
( product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[c8,d53]) ).
cnf(d55,plain,
( product('e$u3','e$u1','e$u2')
| product('e$u1','e$u4','e$u4')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d54,d48]) ).
cnf(d56,plain,
( product('e$u3','e$u1','e$u2')
| product('e$u1','e$u3','e$u4')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u4','e$u4') ),
inference(resolution,[status(thm)],[d55,d48]) ).
cnf(d57,plain,
( equalish('e$u4','e$u1')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d56,d1]) ).
cnf(d58,plain,
( product('e$u3','e$u1','e$u2')
| product('e$u1','e$u3','e$u4') ),
inference(resolution,[status(thm)],[c17,d57]) ).
cnf(d59,plain,
( product('e$u3','e$u1','e$u2')
| product('e$u2','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d58,d47]) ).
cnf(d60,plain,
( product('e$u3','e$u1','e$u2')
| product('e$u3','e$u2','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d59,d46]) ).
cnf(d61,plain,
( equalish('e$u3','e$u1')
| product('e$u3','e$u1','e$u2')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d60,d45]) ).
cnf(d62,plain,
product('e$u3','e$u1','e$u2'),
inference(resolution,[status(thm)],[c14,d61]) ).
cnf(d63,plain,
( equalish('e$u3',X0)
| ~ product(X0,'e$u1','e$u2') ),
inference(resolution,[status(thm)],[d62,c23]) ).
cnf(d64,plain,
( product('e$u4','e$u3','e$u2')
| product('e$u4','e$u4','e$u2')
| equalish('e$u3','e$u4') ),
inference(resolution,[status(thm)],[d63,d23]) ).
cnf(d65,plain,
( product('e$u4','e$u3','e$u2')
| product('e$u4','e$u4','e$u2') ),
inference(resolution,[status(thm)],[c16,d64]) ).
cnf(d66,plain,
( equalish('e$u2','e$u4')
| product('e$u4','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d65,d0]) ).
cnf(d67,plain,
product('e$u4','e$u3','e$u2'),
inference(resolution,[status(thm)],[c13,d66]) ).
cnf(d68,plain,
( equalish('e$u1','e$u4')
| product('e$u3','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d67,d20]) ).
cnf(d69,plain,
product('e$u3','e$u2','e$u1'),
inference(resolution,[status(thm)],[c10,d68]) ).
cnf(d70,plain,
( ~ product('e$u3','e$u2',X0)
| product(X0,'e$u3','e$u4') ),
inference(resolution,[status(thm)],[d67,c3]) ).
cnf(d71,plain,
product('e$u1','e$u3','e$u4'),
inference(resolution,[status(thm)],[d70,d69]) ).
cnf(d72,plain,
( equalish(X0,'e$u4')
| ~ product('e$u1','e$u3',X0) ),
inference(resolution,[status(thm)],[d71,c21]) ).
cnf(d73,plain,
( equalish('e$u3',X0)
| ~ product(X0,'e$u2','e$u1') ),
inference(resolution,[status(thm)],[d69,c23]) ).
cnf(d74,plain,
( ~ product('e$u2','e$u1',X0)
| product('e$u1',X0,'e$u3') ),
inference(resolution,[status(thm)],[d62,c2]) ).
cnf(d75,plain,
( product('e$u2','e$u1','e$u3')
| product('e$u1','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d74,d54]) ).
cnf(d76,plain,
( ~ product('e$u2',X0,'e$u3')
| product('e$u1','e$u2',X0) ),
inference(resolution,[status(thm)],[d69,c25]) ).
cnf(d77,plain,
( product('e$u1','e$u4','e$u3')
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d76,d75]) ).
cnf(d78,plain,
( equalish('e$u3','e$u1')
| product('e$u1','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d77,d73]) ).
cnf(d79,plain,
product('e$u1','e$u4','e$u3'),
inference(resolution,[status(thm)],[c14,d78]) ).
cnf(d80,plain,
( equalish('e$u3','e$u2')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d79,d8]) ).
cnf(d81,plain,
product('e$u1','e$u3','e$u2'),
inference(resolution,[status(thm)],[c15,d80]) ).
cnf(d82,plain,
equalish('e$u2','e$u4'),
inference(resolution,[status(thm)],[d81,d72]) ).
cnf(d83,plain,
$false,
inference(resolution,[status(thm)],[c13,d82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP127-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.73 % Computer : n012.cluster.edu
% 0.04/0.73 % Model : x86_64 x86_64
% 0.04/0.73 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.73 % Memory : 8046.5625MB
% 0.04/0.73 % OS : Linux 6.8.0-71-generic
% 0.04/0.73 % CPULimit : 300
% 0.04/0.73 % WCLimit : 300
% 0.04/0.73 % DateTime : Fri Sep 25 14:26:57 UTC 2026
% 0.04/0.73 % CPUTime :
% 0.04/0.73 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.73/2.75 % SZS status Unsatisfiable for theBenchmark.p
% 11.73/2.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------