%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP130-3.003 : 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 : n018.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 07:23:11 AM UTC 2026
% Result : Unsatisfiable 42.51s 6.47s
% Output : CNFRefutation 42.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 27
% Syntax : Number of clauses : 166 ( 41 unt; 85 nHn; 166 RR)
% Number of literals : 501 ( 0 equ; 161 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 115 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(e_0_then_e_1,axiom,
next('e$u0','e$u1') ).
cnf(e_1_then_e_2,axiom,
next('e$u1','e$u2') ).
cnf(e_2_then_e_3,axiom,
next('e$u2','e$u3') ).
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_2_greater_e_1,axiom,
greater('e$u2','e$u1') ).
cnf(e_3_greater_e_1,axiom,
greater('e$u3','e$u1') ).
cnf(cycle2,axiom,
( cycle(X0,'e$u2')
| cycle(X0,'e$u1')
| cycle(X0,'e$u0')
| ~ 'group$uelement'(X0) ) ).
cnf(cycle3,axiom,
cycle('e$u3','e$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(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_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(product_total_function1,axiom,
( product(X0,X1,'e$u3')
| product(X0,X1,'e$u2')
| product(X0,X1,'e$u1')
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ) ).
cnf(product_total_function2,axiom,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(product_right_cancellation,axiom,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ) ).
cnf(product_left_cancellation,axiom,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ) ).
cnf(qg3,negated_conjecture,
( product(X3,X1,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
next('e$u0','e$u1'),
inference(clausification,[status(esa)],[e_0_then_e_1]) ).
cnf(c1,plain,
next('e$u1','e$u2'),
inference(clausification,[status(esa)],[e_1_then_e_2]) ).
cnf(c2,plain,
next('e$u2','e$u3'),
inference(clausification,[status(esa)],[e_2_then_e_3]) ).
cnf(c3,plain,
greater('e$u1','e$u0'),
inference(clausification,[status(esa)],[e_1_greater_e_0]) ).
cnf(c4,plain,
greater('e$u2','e$u0'),
inference(clausification,[status(esa)],[e_2_greater_e_0]) ).
cnf(c6,plain,
greater('e$u2','e$u1'),
inference(clausification,[status(esa)],[e_2_greater_e_1]) ).
cnf(c7,plain,
greater('e$u3','e$u1'),
inference(clausification,[status(esa)],[e_3_greater_e_1]) ).
cnf(c10,plain,
( cycle(X0,'e$u2')
| cycle(X0,'e$u0')
| ~ 'group$uelement'(X0)
| cycle(X0,'e$u1') ),
inference(clausification,[status(esa)],[cycle2]) ).
cnf(c11,plain,
cycle('e$u3','e$u0'),
inference(clausification,[status(esa)],[cycle3]) ).
cnf(c12,plain,
( ~ next(X1,X3)
| ~ next(X4,X0)
| ~ cycle(X4,X2)
| ~ greater(X2,'e$u0')
| equalish(X2,X3)
| ~ cycle(X0,X1) ),
inference(clausification,[status(esa)],[cycle4]) ).
cnf(c13,plain,
( ~ greater(X2,X3)
| ~ next(X2,X4)
| ~ cycle(X4,X1)
| ~ cycle(X3,X0)
| ~ cycle(X2,'e$u0')
| ~ greater(X0,X1) ),
inference(clausification,[status(esa)],[cycle5]) ).
cnf(c14,plain,
( ~ greater(X1,X0)
| ~ cycle(X0,'e$u0')
| ~ product(X0,'e$u1',X1) ),
inference(clausification,[status(esa)],[cycle6]) ).
cnf(c15,plain,
( ~ greater(X2,'e$u0')
| ~ product(X0,'e$u1',X3)
| equalish(X3,X1)
| ~ cycle(X0,X2)
| ~ next(X0,X1) ),
inference(clausification,[status(esa)],[cycle7]) ).
cnf(c16,plain,
'group$uelement'('e$u1'),
inference(clausification,[status(esa)],[element_1]) ).
cnf(c17,plain,
'group$uelement'('e$u2'),
inference(clausification,[status(esa)],[element_2]) ).
cnf(c18,plain,
'group$uelement'('e$u3'),
inference(clausification,[status(esa)],[element_3]) ).
cnf(c19,plain,
~ equalish('e$u1','e$u2'),
inference(clausification,[status(esa)],[e_1_is_not_e_2]) ).
cnf(c20,plain,
~ equalish('e$u1','e$u3'),
inference(clausification,[status(esa)],[e_1_is_not_e_3]) ).
cnf(c21,plain,
~ equalish('e$u2','e$u1'),
inference(clausification,[status(esa)],[e_2_is_not_e_1]) ).
cnf(c22,plain,
~ equalish('e$u2','e$u3'),
inference(clausification,[status(esa)],[e_2_is_not_e_3]) ).
cnf(c23,plain,
~ equalish('e$u3','e$u1'),
inference(clausification,[status(esa)],[e_3_is_not_e_1]) ).
cnf(c24,plain,
~ equalish('e$u3','e$u2'),
inference(clausification,[status(esa)],[e_3_is_not_e_2]) ).
cnf(c25,plain,
( product(X0,X1,'e$u3')
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0)
| product(X0,X1,'e$u1')
| product(X0,X1,'e$u2') ),
inference(clausification,[status(esa)],[product_total_function1]) ).
cnf(c26,plain,
( equalish(X3,X2)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_total_function2]) ).
cnf(c27,plain,
( equalish(X3,X1)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_right_cancellation]) ).
cnf(c28,plain,
( equalish(X3,X0)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_left_cancellation]) ).
cnf(c29,plain,
( product(X2,X3,X0)
| ~ product(X0,X3,X1)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg3]) ).
cnf(d0,plain,
( product('e$u2',X0,'e$u3')
| product('e$u2',X0,'e$u2')
| product('e$u2',X0,'e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c25,c17]) ).
cnf(d1,plain,
( product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2')
| product('e$u2','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d0,c16]) ).
cnf(d2,plain,
( ~ product('e$u2','e$u1',X1)
| equalish(X1,'e$u3')
| ~ cycle('e$u2',X0)
| ~ greater(X0,'e$u0') ),
inference(resolution,[status(thm)],[c15,c2]) ).
cnf(d3,plain,
( ~ product('e$u2','e$u1',X0)
| equalish(X0,'e$u3')
| ~ cycle('e$u2','e$u1') ),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
( cycle('e$u2','e$u2')
| cycle('e$u2','e$u1')
| cycle('e$u2','e$u0') ),
inference(resolution,[status(thm)],[c10,c17]) ).
cnf(d5,plain,
( equalish(X2,'e$u1')
| ~ cycle(X0,X2)
| ~ cycle(X1,'e$u0')
| ~ greater(X2,'e$u0')
| ~ next(X0,X1) ),
inference(resolution,[status(thm)],[c12,c0]) ).
cnf(d6,plain,
( equalish(X0,'e$u1')
| ~ cycle('e$u2',X0)
| ~ cycle('e$u3','e$u0')
| ~ greater(X0,'e$u0') ),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
( equalish(X0,'e$u1')
| ~ cycle('e$u2',X0)
| ~ greater(X0,'e$u0') ),
inference(resolution,[status(thm)],[c11,d6]) ).
cnf(d8,plain,
( equalish('e$u2','e$u1')
| ~ cycle('e$u2','e$u2') ),
inference(resolution,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
~ cycle('e$u2','e$u2'),
inference(resolution,[status(thm)],[c21,d8]) ).
cnf(d10,plain,
( cycle('e$u2','e$u1')
| cycle('e$u2','e$u0') ),
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
( equalish(X0,'e$u1')
| ~ cycle('e$u1',X0)
| ~ cycle('e$u2','e$u0')
| ~ greater(X0,'e$u0') ),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d12,plain,
( equalish('e$u2','e$u1')
| ~ cycle('e$u2','e$u0')
| ~ cycle('e$u1','e$u2') ),
inference(resolution,[status(thm)],[d11,c4]) ).
cnf(d13,plain,
( ~ cycle('e$u2','e$u0')
| ~ cycle('e$u1','e$u2') ),
inference(resolution,[status(thm)],[c21,d12]) ).
cnf(d14,plain,
( ~ cycle('e$u2','e$u0')
| ~ cycle(X2,X0)
| ~ cycle('e$u3',X1)
| ~ greater('e$u2',X2)
| ~ greater(X0,X1) ),
inference(resolution,[status(thm)],[c13,c2]) ).
cnf(d15,plain,
( ~ cycle('e$u3','e$u0')
| ~ cycle('e$u2','e$u0')
| ~ cycle(X0,'e$u1')
| ~ greater('e$u2',X0) ),
inference(resolution,[status(thm)],[d14,c3]) ).
cnf(d16,plain,
( ~ cycle('e$u2','e$u0')
| ~ cycle(X0,'e$u1')
| ~ greater('e$u2',X0) ),
inference(resolution,[status(thm)],[c11,d15]) ).
cnf(d17,plain,
( ~ cycle('e$u2','e$u0')
| ~ cycle('e$u1','e$u1') ),
inference(resolution,[status(thm)],[d16,c6]) ).
cnf(d18,plain,
( ~ product('e$u1','e$u1','e$u2')
| ~ cycle('e$u1','e$u0') ),
inference(resolution,[status(thm)],[c14,c6]) ).
cnf(d19,plain,
( cycle('e$u1','e$u2')
| cycle('e$u1','e$u1')
| cycle('e$u1','e$u0') ),
inference(resolution,[status(thm)],[c10,c16]) ).
cnf(d20,plain,
( ~ product('e$u1','e$u1','e$u2')
| cycle('e$u1','e$u2')
| cycle('e$u1','e$u1') ),
inference(resolution,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
( ~ product('e$u2',X0,'e$u1')
| product('e$u1',X0,'e$u2')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d1,c29]) ).
cnf(d22,plain,
( product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2')
| product('e$u1','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d21,d1]) ).
cnf(d23,plain,
( cycle('e$u1','e$u2')
| cycle('e$u1','e$u1')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d22,d20]) ).
cnf(d24,plain,
( ~ cycle('e$u2','e$u0')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2')
| cycle('e$u1','e$u2') ),
inference(resolution,[status(thm)],[d23,d17]) ).
cnf(d25,plain,
( cycle('e$u2','e$u1')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2')
| cycle('e$u1','e$u2') ),
inference(resolution,[status(thm)],[d24,d10]) ).
cnf(d26,plain,
( ~ cycle('e$u2','e$u0')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2')
| cycle('e$u2','e$u1') ),
inference(resolution,[status(thm)],[d25,d13]) ).
cnf(d27,plain,
( cycle('e$u2','e$u1')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2')
| cycle('e$u2','e$u1') ),
inference(resolution,[status(thm)],[d26,d10]) ).
cnf(d28,plain,
( ~ product('e$u2','e$u1',X0)
| equalish(X0,'e$u3')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d27,d3]) ).
cnf(d29,plain,
( product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2')
| equalish('e$u1','e$u3') ),
inference(resolution,[status(thm)],[d28,d1]) ).
cnf(d30,plain,
( product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c20,d29]) ).
cnf(d31,plain,
( ~ product('e$u2',X0,'e$u2')
| equalish(X0,'e$u1')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d30,c27]) ).
cnf(d32,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2')
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d0,c18]) ).
cnf(d33,plain,
( ~ product('e$u2',X0,'e$u3')
| product('e$u1',X0,'e$u2')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d32,c29]) ).
cnf(d34,plain,
( ~ product('e$u2',X0,'e$u1')
| product('e$u2',X0,'e$u2')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d30,c29]) ).
cnf(d35,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d34,d32]) ).
cnf(d36,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2')
| product('e$u1','e$u1','e$u2')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d35,d33]) ).
cnf(d37,plain,
( product('e$u1',X0,'e$u3')
| product('e$u1',X0,'e$u2')
| product('e$u1',X0,'e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c25,c16]) ).
cnf(d38,plain,
( product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2')
| product('e$u1','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d37,c18]) ).
cnf(d39,plain,
( ~ product(X0,'e$u3','e$u1')
| equalish(X0,'e$u2')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d32,c28]) ).
cnf(d40,plain,
( product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2')
| equalish('e$u1','e$u2') ),
inference(resolution,[status(thm)],[d39,d38]) ).
cnf(d41,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2')
| product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[c19,d40]) ).
cnf(d42,plain,
( ~ product('e$u1',X0,'e$u2')
| equalish(X0,'e$u3')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2')
| product('e$u1','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d41,c27]) ).
cnf(d43,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2')
| product('e$u1','e$u3','e$u3')
| equalish('e$u1','e$u3') ),
inference(resolution,[status(thm)],[d42,d36]) ).
cnf(d44,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2')
| product('e$u1','e$u3','e$u3') ),
inference(resolution,[status(thm)],[c20,d43]) ).
cnf(d45,plain,
( ~ product('e$u1',X0,'e$u3')
| equalish(X0,'e$u3')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d44,c27]) ).
cnf(d46,plain,
( ~ product('e$u1',X0,'e$u2')
| equalish(X0,'e$u1')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d36,c27]) ).
cnf(d47,plain,
( product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d37,c17]) ).
cnf(d48,plain,
( ~ product('e$u1',X0,'e$u1')
| equalish(X0,'e$u2')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d47,c27]) ).
cnf(d49,plain,
( ~ product('e$u1',X0,'e$u2')
| product('e$u1',X0,'e$u1')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d47,c29]) ).
cnf(d50,plain,
( product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u2')
| product('e$u1','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d37,c16]) ).
cnf(d51,plain,
( product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u2')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| equalish('e$u1','e$u2') ),
inference(resolution,[status(thm)],[d48,d50]) ).
cnf(d52,plain,
( product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c19,d51]) ).
cnf(d53,plain,
( product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| product('e$u1','e$u1','e$u1')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d52,d49]) ).
cnf(d54,plain,
( product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| equalish('e$u1','e$u2')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d53,d48]) ).
cnf(d55,plain,
( product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c19,d54]) ).
cnf(d56,plain,
( ~ product('e$u1','e$u1',X1)
| equalish(X1,'e$u2')
| ~ cycle('e$u1',X0)
| ~ greater(X0,'e$u0') ),
inference(resolution,[status(thm)],[c15,c1]) ).
cnf(d57,plain,
( ~ product('e$u1','e$u1',X0)
| equalish(X0,'e$u2')
| ~ cycle('e$u1','e$u2') ),
inference(resolution,[status(thm)],[d56,c4]) ).
cnf(d58,plain,
( equalish(X2,'e$u2')
| ~ cycle(X0,X2)
| ~ cycle(X1,'e$u1')
| ~ greater(X2,'e$u0')
| ~ next(X0,X1) ),
inference(resolution,[status(thm)],[c12,c1]) ).
cnf(d59,plain,
( equalish(X0,'e$u2')
| ~ cycle('e$u1',X0)
| ~ cycle('e$u2','e$u1')
| ~ greater(X0,'e$u0') ),
inference(resolution,[status(thm)],[d58,c1]) ).
cnf(d60,plain,
( equalish('e$u1','e$u2')
| ~ cycle('e$u2','e$u1')
| ~ cycle('e$u1','e$u1') ),
inference(resolution,[status(thm)],[d59,c3]) ).
cnf(d61,plain,
( ~ cycle('e$u2','e$u1')
| ~ cycle('e$u1','e$u1') ),
inference(resolution,[status(thm)],[c19,d60]) ).
cnf(d62,plain,
( ~ product('e$u1','e$u1','e$u3')
| ~ cycle('e$u1','e$u0') ),
inference(resolution,[status(thm)],[c14,c7]) ).
cnf(d63,plain,
( cycle('e$u1','e$u2')
| cycle('e$u1','e$u1')
| ~ product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d62,d19]) ).
cnf(d64,plain,
( cycle('e$u1','e$u2')
| cycle('e$u1','e$u1')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d55,d63]) ).
cnf(d65,plain,
( ~ cycle('e$u2','e$u1')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| cycle('e$u1','e$u2') ),
inference(resolution,[status(thm)],[d64,d61]) ).
cnf(d66,plain,
( ~ cycle('e$u2','e$u0')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| cycle('e$u1','e$u2') ),
inference(resolution,[status(thm)],[d64,d17]) ).
cnf(d67,plain,
( cycle('e$u2','e$u1')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| cycle('e$u1','e$u2') ),
inference(resolution,[status(thm)],[d66,d10]) ).
cnf(d68,plain,
( ~ cycle('e$u2','e$u0')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| cycle('e$u2','e$u1') ),
inference(resolution,[status(thm)],[d67,d13]) ).
cnf(d69,plain,
( cycle('e$u2','e$u1')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| cycle('e$u2','e$u1') ),
inference(resolution,[status(thm)],[d68,d10]) ).
cnf(d70,plain,
( product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| cycle('e$u1','e$u2')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d69,d65]) ).
cnf(d71,plain,
( ~ product('e$u1','e$u1',X0)
| equalish(X0,'e$u2')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d70,d57]) ).
cnf(d72,plain,
( product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| equalish('e$u3','e$u2') ),
inference(resolution,[status(thm)],[d71,d55]) ).
cnf(d73,plain,
( product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[c24,d72]) ).
cnf(d74,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2')
| equalish('e$u2','e$u1')
| product('e$u1','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d73,d46]) ).
cnf(d75,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2')
| product('e$u1','e$u2','e$u3') ),
inference(resolution,[status(thm)],[c21,d74]) ).
cnf(d76,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2')
| equalish('e$u2','e$u3')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d75,d45]) ).
cnf(d77,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2') ),
inference(resolution,[status(thm)],[c22,d76]) ).
cnf(d78,plain,
( product('e$u2','e$u1','e$u3')
| equalish('e$u3','e$u1')
| product('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d77,d31]) ).
cnf(d79,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c23,d78]) ).
cnf(d80,plain,
( ~ product('e$u2','e$u1',X0)
| equalish(X0,'e$u3')
| product('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d79,c26]) ).
cnf(d81,plain,
( ~ product('e$u2',X0,'e$u3')
| product('e$u2',X0,'e$u2')
| product('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d77,c29]) ).
cnf(d82,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d81,d79]) ).
cnf(d83,plain,
( product('e$u2','e$u3','e$u3')
| equalish('e$u2','e$u3')
| product('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d82,d80]) ).
cnf(d84,plain,
product('e$u2','e$u3','e$u3'),
inference(resolution,[status(thm)],[c22,d83]) ).
cnf(d85,plain,
( ~ product('e$u2',X0,'e$u3')
| equalish(X0,'e$u3') ),
inference(resolution,[status(thm)],[d84,c27]) ).
cnf(d86,plain,
( ~ product(X0,'e$u1','e$u2')
| equalish(X0,'e$u2')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d30,c28]) ).
cnf(d87,plain,
( product('e$u3',X0,'e$u3')
| product('e$u3',X0,'e$u2')
| product('e$u3',X0,'e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c25,c18]) ).
cnf(d88,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u3','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d87,c16]) ).
cnf(d89,plain,
( ~ product('e$u3',X0,'e$u1')
| product('e$u1',X0,'e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d88,c29]) ).
cnf(d90,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d89,d88]) ).
cnf(d91,plain,
( cycle('e$u1','e$u2')
| cycle('e$u1','e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d90,d63]) ).
cnf(d92,plain,
( ~ cycle('e$u2','e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| cycle('e$u1','e$u2') ),
inference(resolution,[status(thm)],[d91,d61]) ).
cnf(d93,plain,
( ~ cycle('e$u2','e$u0')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| cycle('e$u1','e$u2') ),
inference(resolution,[status(thm)],[d91,d17]) ).
cnf(d94,plain,
( cycle('e$u2','e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| cycle('e$u1','e$u2') ),
inference(resolution,[status(thm)],[d93,d10]) ).
cnf(d95,plain,
( ~ cycle('e$u2','e$u0')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| cycle('e$u2','e$u1') ),
inference(resolution,[status(thm)],[d94,d13]) ).
cnf(d96,plain,
( cycle('e$u2','e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| cycle('e$u2','e$u1') ),
inference(resolution,[status(thm)],[d95,d10]) ).
cnf(d97,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| cycle('e$u1','e$u2')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d96,d92]) ).
cnf(d98,plain,
( ~ product('e$u1','e$u1',X0)
| equalish(X0,'e$u2')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d97,d57]) ).
cnf(d99,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| equalish('e$u3','e$u2') ),
inference(resolution,[status(thm)],[d98,d90]) ).
cnf(d100,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c24,d99]) ).
cnf(d101,plain,
( product('e$u2','e$u1','e$u3')
| equalish('e$u3','e$u2')
| product('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d100,d86]) ).
cnf(d102,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c24,d101]) ).
cnf(d103,plain,
( ~ product('e$u2',X0,'e$u3')
| equalish(X0,'e$u1')
| product('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d102,c27]) ).
cnf(d104,plain,
( product('e$u3','e$u1','e$u3')
| equalish('e$u3','e$u1') ),
inference(resolution,[status(thm)],[d84,d103]) ).
cnf(d105,plain,
product('e$u3','e$u1','e$u3'),
inference(resolution,[status(thm)],[c23,d104]) ).
cnf(d106,plain,
( ~ product('e$u2',X0,'e$u3')
| product('e$u3',X0,'e$u2') ),
inference(resolution,[status(thm)],[d84,c29]) ).
cnf(d107,plain,
product('e$u3','e$u3','e$u2'),
inference(resolution,[status(thm)],[d106,d84]) ).
cnf(d108,plain,
( ~ product('e$u3',X0,'e$u3')
| product('e$u2',X0,'e$u3') ),
inference(resolution,[status(thm)],[d107,c29]) ).
cnf(d109,plain,
product('e$u2','e$u1','e$u3'),
inference(resolution,[status(thm)],[d108,d105]) ).
cnf(d110,plain,
equalish('e$u1','e$u3'),
inference(resolution,[status(thm)],[d109,d85]) ).
cnf(d111,plain,
$false,
inference(resolution,[status(thm)],[c20,d110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP130-3.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.66 % Computer : n018.cluster.edu
% 0.19/0.66 % Model : x86_64 x86_64
% 0.19/0.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.66 % Memory : 8046.5625MB
% 0.19/0.66 % OS : Linux 6.8.0-71-generic
% 0.19/0.66 % CPULimit : 300
% 0.19/0.66 % WCLimit : 300
% 0.19/0.66 % DateTime : Fri Sep 25 14:31:37 UTC 2026
% 0.19/0.67 % CPUTime :
% 0.19/0.67 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.51/6.47 % SZS status Unsatisfiable for theBenchmark.p
% 42.51/6.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------