%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP126-3.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 07:22:27 AM UTC 2026
% Result : Unsatisfiable 25.41s 7.05s
% Output : CNFRefutation 25.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 34
% Syntax : Number of clauses : 167 ( 57 unt; 70 nHn; 165 RR)
% Number of literals : 444 ( 0 equ; 151 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 107 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(e_0_then_e_1,axiom,
next('e$u0','e$u1') ).
cnf(e_2_then_e_3,axiom,
next('e$u2','e$u3') ).
cnf(e_3_then_e_4,axiom,
next('e$u3','e$u4') ).
cnf(e_1_greater_e_0,axiom,
greater('e$u1','e$u0') ).
cnf(e_2_greater_e_0,axiom,
greater('e$u2','e$u0') ).
cnf(e_3_greater_e_0,axiom,
greater('e$u3','e$u0') ).
cnf(e_3_greater_e_2,axiom,
greater('e$u3','e$u2') ).
cnf(e_4_greater_e_2,axiom,
greater('e$u4','e$u2') ).
cnf(cycle2,axiom,
( cycle(X0,'e$u3')
| cycle(X0,'e$u2')
| cycle(X0,'e$u1')
| cycle(X0,'e$u0')
| ~ 'group$uelement'(X0) ) ).
cnf(cycle3,axiom,
cycle('e$u4','e$u0') ).
cnf(cycle4,axiom,
( equalish(X1,X4)
| ~ next(X3,X4)
| ~ greater(X1,'e$u0')
| ~ next(X0,X2)
| ~ cycle(X2,X3)
| ~ cycle(X0,X1) ) ).
cnf(cycle5,axiom,
( ~ greater(X1,X4)
| ~ greater(X2,X0)
| ~ next(X2,X3)
| ~ cycle(X3,X4)
| ~ cycle(X2,'e$u0')
| ~ cycle(X0,X1) ) ).
cnf(cycle6,axiom,
( ~ greater(X1,X0)
| ~ product(X0,'e$u1',X1)
| ~ cycle(X0,'e$u0') ) ).
cnf(cycle7,axiom,
( equalish(X2,X3)
| ~ next(X0,X3)
| ~ greater(X1,'e$u0')
| ~ product(X0,'e$u1',X2)
| ~ cycle(X0,X1) ) ).
cnf(element_1,axiom,
'group$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$u3') ).
cnf(e_2_is_not_e_1,axiom,
~ equalish('e$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$uelement'(X0) ) ).
cnf(product_total_function2,axiom,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(product_right_cancellation,axiom,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ) ).
cnf(product_left_cancellation,axiom,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ) ).
cnf(product_idempotence,axiom,
product(X0,X0,X0) ).
cnf(qg4,negated_conjecture,
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
next('e$u0','e$u1'),
inference(clausification,[status(esa)],[e_0_then_e_1]) ).
cnf(c2,plain,
next('e$u2','e$u3'),
inference(clausification,[status(esa)],[e_2_then_e_3]) ).
cnf(c3,plain,
next('e$u3','e$u4'),
inference(clausification,[status(esa)],[e_3_then_e_4]) ).
cnf(c4,plain,
greater('e$u1','e$u0'),
inference(clausification,[status(esa)],[e_1_greater_e_0]) ).
cnf(c5,plain,
greater('e$u2','e$u0'),
inference(clausification,[status(esa)],[e_2_greater_e_0]) ).
cnf(c6,plain,
greater('e$u3','e$u0'),
inference(clausification,[status(esa)],[e_3_greater_e_0]) ).
cnf(c11,plain,
greater('e$u3','e$u2'),
inference(clausification,[status(esa)],[e_3_greater_e_2]) ).
cnf(c12,plain,
greater('e$u4','e$u2'),
inference(clausification,[status(esa)],[e_4_greater_e_2]) ).
cnf(c15,plain,
( ~ 'group$uelement'(X0)
| cycle(X0,'e$u2')
| cycle(X0,'e$u0')
| cycle(X0,'e$u3')
| cycle(X0,'e$u1') ),
inference(clausification,[status(esa)],[cycle2]) ).
cnf(c16,plain,
cycle('e$u4','e$u0'),
inference(clausification,[status(esa)],[cycle3]) ).
cnf(c17,plain,
( ~ next(X1,X3)
| ~ next(X4,X0)
| ~ cycle(X4,X2)
| ~ greater(X2,'e$u0')
| equalish(X2,X3)
| ~ cycle(X0,X1) ),
inference(clausification,[status(esa)],[cycle4]) ).
cnf(c18,plain,
( ~ greater(X2,X3)
| ~ next(X2,X4)
| ~ cycle(X4,X1)
| ~ cycle(X3,X0)
| ~ cycle(X2,'e$u0')
| ~ greater(X0,X1) ),
inference(clausification,[status(esa)],[cycle5]) ).
cnf(c19,plain,
( ~ greater(X1,X0)
| ~ cycle(X0,'e$u0')
| ~ product(X0,'e$u1',X1) ),
inference(clausification,[status(esa)],[cycle6]) ).
cnf(c20,plain,
( ~ greater(X2,'e$u0')
| ~ product(X0,'e$u1',X3)
| equalish(X3,X1)
| ~ cycle(X0,X2)
| ~ next(X0,X1) ),
inference(clausification,[status(esa)],[cycle7]) ).
cnf(c21,plain,
'group$uelement'('e$u1'),
inference(clausification,[status(esa)],[element_1]) ).
cnf(c22,plain,
'group$uelement'('e$u2'),
inference(clausification,[status(esa)],[element_2]) ).
cnf(c23,plain,
'group$uelement'('e$u3'),
inference(clausification,[status(esa)],[element_3]) ).
cnf(c24,plain,
'group$uelement'('e$u4'),
inference(clausification,[status(esa)],[element_4]) ).
cnf(c25,plain,
~ equalish('e$u1','e$u2'),
inference(clausification,[status(esa)],[e_1_is_not_e_2]) ).
cnf(c26,plain,
~ equalish('e$u1','e$u3'),
inference(clausification,[status(esa)],[e_1_is_not_e_3]) ).
cnf(c28,plain,
~ equalish('e$u2','e$u1'),
inference(clausification,[status(esa)],[e_2_is_not_e_1]) ).
cnf(c29,plain,
~ equalish('e$u2','e$u3'),
inference(clausification,[status(esa)],[e_2_is_not_e_3]) ).
cnf(c30,plain,
~ equalish('e$u2','e$u4'),
inference(clausification,[status(esa)],[e_2_is_not_e_4]) ).
cnf(c31,plain,
~ equalish('e$u3','e$u1'),
inference(clausification,[status(esa)],[e_3_is_not_e_1]) ).
cnf(c32,plain,
~ equalish('e$u3','e$u2'),
inference(clausification,[status(esa)],[e_3_is_not_e_2]) ).
cnf(c34,plain,
~ equalish('e$u4','e$u1'),
inference(clausification,[status(esa)],[e_4_is_not_e_1]) ).
cnf(c35,plain,
~ equalish('e$u4','e$u2'),
inference(clausification,[status(esa)],[e_4_is_not_e_2]) ).
cnf(c36,plain,
~ equalish('e$u4','e$u3'),
inference(clausification,[status(esa)],[e_4_is_not_e_3]) ).
cnf(c37,plain,
( product(X0,X1,'e$u3')
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0)
| product(X0,X1,'e$u4')
| product(X0,X1,'e$u1')
| product(X0,X1,'e$u2') ),
inference(clausification,[status(esa)],[product_total_function1]) ).
cnf(c38,plain,
( equalish(X3,X2)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_total_function2]) ).
cnf(c39,plain,
( equalish(X3,X1)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_right_cancellation]) ).
cnf(c40,plain,
( equalish(X3,X0)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_left_cancellation]) ).
cnf(c41,plain,
product(X0,X0,X0),
inference(clausification,[status(esa)],[product_idempotence]) ).
cnf(c42,plain,
( product(X3,X2,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg4]) ).
cnf(d0,plain,
( ~ product(X1,X0,X1)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c39,c41]) ).
cnf(d1,plain,
( ~ product(X0,X1,X1)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c40,c41]) ).
cnf(d2,plain,
( product('e$u3',X0,'e$u4')
| product('e$u3',X0,'e$u3')
| product('e$u3',X0,'e$u2')
| product('e$u3',X0,'e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c37,c23]) ).
cnf(d3,plain,
( product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u3','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d2,c21]) ).
cnf(d4,plain,
( equalish('e$u3','e$u1')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c31,d4]) ).
cnf(d6,plain,
( ~ product('e$u3','e$u1',X1)
| equalish(X1,'e$u4')
| ~ cycle('e$u3',X0)
| ~ greater(X0,'e$u0') ),
inference(resolution,[status(thm)],[c20,c3]) ).
cnf(d7,plain,
( ~ product('e$u3','e$u1',X0)
| equalish(X0,'e$u4')
| ~ cycle('e$u3','e$u1') ),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
( cycle('e$u3','e$u3')
| cycle('e$u3','e$u2')
| cycle('e$u3','e$u1')
| cycle('e$u3','e$u0') ),
inference(resolution,[status(thm)],[c15,c23]) ).
cnf(d9,plain,
( equalish(X2,'e$u1')
| ~ cycle(X0,X2)
| ~ cycle(X1,'e$u0')
| ~ greater(X2,'e$u0')
| ~ next(X0,X1) ),
inference(resolution,[status(thm)],[c17,c0]) ).
cnf(d10,plain,
( equalish(X0,'e$u1')
| ~ cycle('e$u3',X0)
| ~ cycle('e$u4','e$u0')
| ~ greater(X0,'e$u0') ),
inference(resolution,[status(thm)],[d9,c3]) ).
cnf(d11,plain,
( equalish(X0,'e$u1')
| ~ cycle('e$u3',X0)
| ~ greater(X0,'e$u0') ),
inference(resolution,[status(thm)],[c16,d10]) ).
cnf(d12,plain,
( equalish('e$u2','e$u1')
| ~ cycle('e$u3','e$u2') ),
inference(resolution,[status(thm)],[d11,c5]) ).
cnf(d13,plain,
~ cycle('e$u3','e$u2'),
inference(resolution,[status(thm)],[c28,d12]) ).
cnf(d14,plain,
( cycle('e$u3','e$u3')
| cycle('e$u3','e$u1')
| cycle('e$u3','e$u0') ),
inference(resolution,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
( equalish('e$u3','e$u1')
| ~ cycle('e$u3','e$u3') ),
inference(resolution,[status(thm)],[d11,c6]) ).
cnf(d16,plain,
~ cycle('e$u3','e$u3'),
inference(resolution,[status(thm)],[c31,d15]) ).
cnf(d17,plain,
( cycle('e$u3','e$u1')
| cycle('e$u3','e$u0') ),
inference(resolution,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
( equalish(X0,'e$u1')
| ~ cycle('e$u2',X0)
| ~ cycle('e$u3','e$u0')
| ~ greater(X0,'e$u0') ),
inference(resolution,[status(thm)],[d9,c2]) ).
cnf(d19,plain,
( equalish('e$u3','e$u1')
| ~ cycle('e$u3','e$u0')
| ~ cycle('e$u2','e$u3') ),
inference(resolution,[status(thm)],[d18,c6]) ).
cnf(d20,plain,
( ~ cycle('e$u3','e$u0')
| ~ cycle('e$u2','e$u3') ),
inference(resolution,[status(thm)],[c31,d19]) ).
cnf(d21,plain,
( equalish('e$u2','e$u1')
| ~ cycle('e$u3','e$u0')
| ~ cycle('e$u2','e$u2') ),
inference(resolution,[status(thm)],[d18,c5]) ).
cnf(d22,plain,
( ~ cycle('e$u3','e$u0')
| ~ cycle('e$u2','e$u2') ),
inference(resolution,[status(thm)],[c28,d21]) ).
cnf(d23,plain,
( ~ cycle('e$u3','e$u0')
| ~ cycle(X2,X0)
| ~ cycle('e$u4',X1)
| ~ greater('e$u3',X2)
| ~ greater(X0,X1) ),
inference(resolution,[status(thm)],[c18,c3]) ).
cnf(d24,plain,
( ~ cycle('e$u4','e$u0')
| ~ cycle('e$u3','e$u0')
| ~ cycle(X0,'e$u1')
| ~ greater('e$u3',X0) ),
inference(resolution,[status(thm)],[d23,c4]) ).
cnf(d25,plain,
( ~ cycle('e$u3','e$u0')
| ~ cycle(X0,'e$u1')
| ~ greater('e$u3',X0) ),
inference(resolution,[status(thm)],[c16,d24]) ).
cnf(d26,plain,
( ~ cycle('e$u3','e$u0')
| ~ cycle('e$u2','e$u1') ),
inference(resolution,[status(thm)],[d25,c11]) ).
cnf(d27,plain,
( ~ product('e$u2','e$u1','e$u4')
| ~ cycle('e$u2','e$u0') ),
inference(resolution,[status(thm)],[c19,c12]) ).
cnf(d28,plain,
( cycle('e$u2','e$u3')
| cycle('e$u2','e$u2')
| cycle('e$u2','e$u1')
| cycle('e$u2','e$u0') ),
inference(resolution,[status(thm)],[c15,c22]) ).
cnf(d29,plain,
( ~ product('e$u2','e$u1','e$u4')
| cycle('e$u2','e$u3')
| cycle('e$u2','e$u2')
| cycle('e$u2','e$u1') ),
inference(resolution,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
( ~ product('e$u2','e$u1','e$u3')
| ~ cycle('e$u2','e$u0') ),
inference(resolution,[status(thm)],[c19,c11]) ).
cnf(d31,plain,
( cycle('e$u2','e$u3')
| cycle('e$u2','e$u2')
| cycle('e$u2','e$u1')
| ~ product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d30,d28]) ).
cnf(d32,plain,
( product('e$u2',X0,'e$u4')
| product('e$u2',X0,'e$u3')
| product('e$u2',X0,'e$u2')
| product('e$u2',X0,'e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c37,c22]) ).
cnf(d33,plain,
( product('e$u2','e$u1','e$u4')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2')
| product('e$u2','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d32,c21]) ).
cnf(d34,plain,
( equalish('e$u2','e$u1')
| product('e$u2','e$u1','e$u4')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d33,d1]) ).
cnf(d35,plain,
( product('e$u2','e$u1','e$u4')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c28,d34]) ).
cnf(d36,plain,
( equalish('e$u1','e$u2')
| product('e$u2','e$u1','e$u4')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d35,d0]) ).
cnf(d37,plain,
( product('e$u2','e$u1','e$u4')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c25,d36]) ).
cnf(d38,plain,
( cycle('e$u2','e$u3')
| cycle('e$u2','e$u2')
| cycle('e$u2','e$u1')
| product('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d37,d31]) ).
cnf(d39,plain,
( ~ cycle('e$u3','e$u0')
| product('e$u2','e$u1','e$u4')
| cycle('e$u2','e$u3')
| cycle('e$u2','e$u2') ),
inference(resolution,[status(thm)],[d38,d26]) ).
cnf(d40,plain,
( cycle('e$u3','e$u1')
| product('e$u2','e$u1','e$u4')
| cycle('e$u2','e$u3')
| cycle('e$u2','e$u2') ),
inference(resolution,[status(thm)],[d39,d17]) ).
cnf(d41,plain,
( ~ cycle('e$u3','e$u0')
| product('e$u2','e$u1','e$u4')
| cycle('e$u3','e$u1')
| cycle('e$u2','e$u3') ),
inference(resolution,[status(thm)],[d40,d22]) ).
cnf(d42,plain,
( cycle('e$u3','e$u1')
| product('e$u2','e$u1','e$u4')
| cycle('e$u3','e$u1')
| cycle('e$u2','e$u3') ),
inference(resolution,[status(thm)],[d41,d17]) ).
cnf(d43,plain,
( ~ cycle('e$u3','e$u0')
| product('e$u2','e$u1','e$u4')
| cycle('e$u3','e$u1') ),
inference(resolution,[status(thm)],[d42,d20]) ).
cnf(d44,plain,
( cycle('e$u3','e$u1')
| product('e$u2','e$u1','e$u4')
| cycle('e$u3','e$u1') ),
inference(resolution,[status(thm)],[d43,d17]) ).
cnf(d45,plain,
( ~ product('e$u3','e$u1',X0)
| equalish(X0,'e$u4')
| product('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d44,d7]) ).
cnf(d46,plain,
( product('e$u2','e$u1','e$u4')
| equalish('e$u2','e$u4')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d5,d45]) ).
cnf(d47,plain,
( product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| product('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[c30,d46]) ).
cnf(d48,plain,
( cycle('e$u2','e$u3')
| cycle('e$u2','e$u2')
| cycle('e$u2','e$u1')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d47,d29]) ).
cnf(d49,plain,
( ~ cycle('e$u3','e$u0')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| cycle('e$u2','e$u3')
| cycle('e$u2','e$u2') ),
inference(resolution,[status(thm)],[d48,d26]) ).
cnf(d50,plain,
( cycle('e$u3','e$u1')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| cycle('e$u2','e$u3')
| cycle('e$u2','e$u2') ),
inference(resolution,[status(thm)],[d49,d17]) ).
cnf(d51,plain,
( ~ cycle('e$u3','e$u0')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| cycle('e$u3','e$u1')
| cycle('e$u2','e$u3') ),
inference(resolution,[status(thm)],[d50,d22]) ).
cnf(d52,plain,
( cycle('e$u3','e$u1')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| cycle('e$u3','e$u1')
| cycle('e$u2','e$u3') ),
inference(resolution,[status(thm)],[d51,d17]) ).
cnf(d53,plain,
( ~ cycle('e$u3','e$u0')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| cycle('e$u3','e$u1') ),
inference(resolution,[status(thm)],[d52,d20]) ).
cnf(d54,plain,
( cycle('e$u3','e$u1')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| cycle('e$u3','e$u1') ),
inference(resolution,[status(thm)],[d53,d17]) ).
cnf(d55,plain,
( ~ product('e$u3','e$u1',X0)
| equalish(X0,'e$u4')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d54,d7]) ).
cnf(d56,plain,
( product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| equalish('e$u2','e$u4') ),
inference(resolution,[status(thm)],[d55,d5]) ).
cnf(d57,plain,
( product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c30,d56]) ).
cnf(d58,plain,
( equalish('e$u1','e$u3')
| product('e$u3','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d57,d0]) ).
cnf(d59,plain,
product('e$u3','e$u1','e$u4'),
inference(resolution,[status(thm)],[c26,d58]) ).
cnf(d60,plain,
( ~ product(X0,'e$u1','e$u4')
| equalish(X0,'e$u3') ),
inference(resolution,[status(thm)],[d59,c40]) ).
cnf(d61,plain,
( ~ product(X1,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c38,c41]) ).
cnf(d62,plain,
( product('e$u1',X0,'e$u4')
| product('e$u1',X0,'e$u3')
| product('e$u1',X0,'e$u2')
| product('e$u1',X0,'e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c37,c21]) ).
cnf(d63,plain,
( product('e$u1','e$u2','e$u4')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d62,c22]) ).
cnf(d64,plain,
( equalish('e$u2','e$u1')
| product('e$u1','e$u2','e$u4')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d63,d0]) ).
cnf(d65,plain,
( product('e$u1','e$u2','e$u4')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[c28,d64]) ).
cnf(d66,plain,
( equalish('e$u1','e$u2')
| product('e$u1','e$u2','e$u4')
| product('e$u1','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d65,d1]) ).
cnf(d67,plain,
( product('e$u1','e$u2','e$u4')
| product('e$u1','e$u2','e$u3') ),
inference(resolution,[status(thm)],[c25,d66]) ).
cnf(d68,plain,
( ~ product('e$u2','e$u1',X0)
| product(X0,'e$u3','e$u1')
| product('e$u1','e$u2','e$u4') ),
inference(resolution,[status(thm)],[d67,c42]) ).
cnf(d69,plain,
( product('e$u2','e$u1','e$u4')
| product('e$u1','e$u2','e$u4')
| product('e$u3','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d68,d37]) ).
cnf(d70,plain,
( ~ product('e$u2','e$u1',X0)
| product(X0,'e$u4','e$u1')
| product('e$u3','e$u3','e$u1')
| product('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d69,c42]) ).
cnf(d71,plain,
( product('e$u2','e$u1','e$u4')
| product('e$u3','e$u3','e$u1')
| product('e$u2','e$u1','e$u4')
| product('e$u3','e$u4','e$u1') ),
inference(resolution,[status(thm)],[d70,d37]) ).
cnf(d72,plain,
( ~ product(X0,'e$u1','e$u4')
| equalish(X0,'e$u2')
| product('e$u3','e$u4','e$u1')
| product('e$u3','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d71,c40]) ).
cnf(d73,plain,
( product('e$u3','e$u4','e$u1')
| product('e$u3','e$u3','e$u1')
| equalish('e$u3','e$u2') ),
inference(resolution,[status(thm)],[d59,d72]) ).
cnf(d74,plain,
( product('e$u3','e$u4','e$u1')
| product('e$u3','e$u3','e$u1') ),
inference(resolution,[status(thm)],[c32,d73]) ).
cnf(d75,plain,
( equalish('e$u1','e$u3')
| product('e$u3','e$u4','e$u1') ),
inference(resolution,[status(thm)],[d74,d61]) ).
cnf(d76,plain,
product('e$u3','e$u4','e$u1'),
inference(resolution,[status(thm)],[c26,d75]) ).
cnf(d77,plain,
( ~ product('e$u4','e$u3',X0)
| product(X0,'e$u1','e$u3') ),
inference(resolution,[status(thm)],[d76,c42]) ).
cnf(d78,plain,
( ~ product('e$u1','e$u2',X0)
| product(X0,'e$u3','e$u2')
| product('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d37,c42]) ).
cnf(d79,plain,
( product('e$u2','e$u1','e$u4')
| product('e$u3','e$u3','e$u2')
| product('e$u1','e$u2','e$u4') ),
inference(resolution,[status(thm)],[d67,d78]) ).
cnf(d80,plain,
( product('e$u2','e$u1','e$u4')
| product('e$u4','e$u3','e$u2')
| product('e$u3','e$u3','e$u2')
| product('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d79,d78]) ).
cnf(d81,plain,
( ~ product(X0,'e$u1','e$u4')
| equalish(X0,'e$u2')
| product('e$u4','e$u3','e$u2')
| product('e$u3','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d80,c40]) ).
cnf(d82,plain,
( product('e$u4','e$u3','e$u2')
| product('e$u3','e$u3','e$u2')
| equalish('e$u3','e$u2') ),
inference(resolution,[status(thm)],[d59,d81]) ).
cnf(d83,plain,
( product('e$u4','e$u3','e$u2')
| product('e$u3','e$u3','e$u2') ),
inference(resolution,[status(thm)],[c32,d82]) ).
cnf(d84,plain,
( equalish('e$u2','e$u3')
| product('e$u4','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d83,d61]) ).
cnf(d85,plain,
product('e$u4','e$u3','e$u2'),
inference(resolution,[status(thm)],[c29,d84]) ).
cnf(d86,plain,
product('e$u2','e$u1','e$u3'),
inference(resolution,[status(thm)],[d85,d77]) ).
cnf(d87,plain,
( ~ product(X0,'e$u1','e$u3')
| equalish(X0,'e$u2') ),
inference(resolution,[status(thm)],[d86,c40]) ).
cnf(d88,plain,
( product('e$u4',X0,'e$u4')
| product('e$u4',X0,'e$u3')
| product('e$u4',X0,'e$u2')
| product('e$u4',X0,'e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c37,c24]) ).
cnf(d89,plain,
( product('e$u4','e$u1','e$u4')
| product('e$u4','e$u1','e$u3')
| product('e$u4','e$u1','e$u2')
| product('e$u4','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d88,c21]) ).
cnf(d90,plain,
( equalish('e$u4','e$u1')
| product('e$u4','e$u1','e$u4')
| product('e$u4','e$u1','e$u3')
| product('e$u4','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d89,d1]) ).
cnf(d91,plain,
( product('e$u4','e$u1','e$u4')
| product('e$u4','e$u1','e$u3')
| product('e$u4','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c34,d90]) ).
cnf(d92,plain,
( ~ product('e$u4',X0,'e$u2')
| equalish(X0,'e$u1')
| product('e$u4','e$u1','e$u4')
| product('e$u4','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d91,c39]) ).
cnf(d93,plain,
( product('e$u4','e$u1','e$u4')
| product('e$u4','e$u1','e$u3')
| equalish('e$u3','e$u1') ),
inference(resolution,[status(thm)],[d85,d92]) ).
cnf(d94,plain,
( product('e$u4','e$u1','e$u4')
| product('e$u4','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c31,d93]) ).
cnf(d95,plain,
( equalish('e$u4','e$u2')
| product('e$u4','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d94,d87]) ).
cnf(d96,plain,
product('e$u4','e$u1','e$u4'),
inference(resolution,[status(thm)],[c35,d95]) ).
cnf(d97,plain,
equalish('e$u4','e$u3'),
inference(resolution,[status(thm)],[d96,d60]) ).
cnf(d98,plain,
$false,
inference(resolution,[status(thm)],[c36,d97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP126-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n011.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 14:26:43 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.41/7.05 % SZS status Unsatisfiable for theBenchmark.p
% 25.41/7.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------