%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP133-1.003 : 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 : n020.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 07:23:12 AM UTC 2026
% Result : Unsatisfiable 21.70s 6.17s
% Output : CNFRefutation 21.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 14
% Syntax : Number of clauses : 169 ( 22 unt; 137 nHn; 169 RR)
% Number of literals : 630 ( 0 equ; 80 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 84 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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$uelement'(X0) ) ).
cnf(product_total_function2,axiom,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(product_right_cancellation,axiom,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ) ).
cnf(product_left_cancellation,axiom,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ) ).
cnf(qg3,negated_conjecture,
( product(X2,X3,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
'group$uelement'('e$u1'),
inference(clausification,[status(esa)],[element_1]) ).
cnf(c1,plain,
'group$uelement'('e$u2'),
inference(clausification,[status(esa)],[element_2]) ).
cnf(c2,plain,
'group$uelement'('e$u3'),
inference(clausification,[status(esa)],[element_3]) ).
cnf(c3,plain,
~ equalish('e$u1','e$u2'),
inference(clausification,[status(esa)],[e_1_is_not_e_2]) ).
cnf(c4,plain,
~ equalish('e$u1','e$u3'),
inference(clausification,[status(esa)],[e_1_is_not_e_3]) ).
cnf(c5,plain,
~ equalish('e$u2','e$u1'),
inference(clausification,[status(esa)],[e_2_is_not_e_1]) ).
cnf(c6,plain,
~ equalish('e$u2','e$u3'),
inference(clausification,[status(esa)],[e_2_is_not_e_3]) ).
cnf(c7,plain,
~ equalish('e$u3','e$u1'),
inference(clausification,[status(esa)],[e_3_is_not_e_1]) ).
cnf(c8,plain,
~ equalish('e$u3','e$u2'),
inference(clausification,[status(esa)],[e_3_is_not_e_2]) ).
cnf(c9,plain,
( product(X0,X1,'e$u3')
| ~ 'group$uelement'(X1)
| product(X0,X1,'e$u1')
| product(X0,X1,'e$u2')
| ~ 'group$uelement'(X0) ),
inference(clausification,[status(esa)],[product_total_function1]) ).
cnf(c10,plain,
( equalish(X3,X2)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_total_function2]) ).
cnf(c11,plain,
( equalish(X3,X1)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_right_cancellation]) ).
cnf(c12,plain,
( equalish(X3,X0)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_left_cancellation]) ).
cnf(c13,plain,
( product(X3,X2,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg3]) ).
cnf(d0,plain,
( product(X0,'e$u1','e$u3')
| product(X0,'e$u1','e$u2')
| product(X0,'e$u1','e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d1,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u3','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
( product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u2')
| product('e$u1','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d3,plain,
( ~ product(X0,'e$u1','e$u1')
| equalish('e$u1',X0)
| product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d2,c12]) ).
cnf(d4,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u2')
| equalish('e$u1','e$u3') ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c4,d4]) ).
cnf(d6,plain,
( ~ product('e$u1',X0,'e$u2')
| equalish(X0,'e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d5,c11]) ).
cnf(d7,plain,
( product(X0,'e$u3','e$u3')
| product(X0,'e$u3','e$u2')
| product(X0,'e$u3','e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c9,c2]) ).
cnf(d8,plain,
( product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2')
| product('e$u1','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
( ~ product('e$u1',X0,'e$u1')
| equalish(X0,'e$u3')
| product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d8,c11]) ).
cnf(d10,plain,
( ~ product('e$u1','e$u3',X0)
| product(X0,'e$u1','e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d1,c13]) ).
cnf(d11,plain,
( product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2')
| equalish('e$u1','e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[c4,d12]) ).
cnf(d14,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u1','e$u3')
| equalish('e$u3','e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d13,d6]) ).
cnf(d15,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u3','e$u3')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c7,d14]) ).
cnf(d16,plain,
( ~ product('e$u1','e$u1',X0)
| equalish(X0,'e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d15,c10]) ).
cnf(d17,plain,
( ~ product(X0,'e$u1','e$u1')
| equalish('e$u3',X0)
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d1,c12]) ).
cnf(d18,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u2','e$u1','e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d13,d10]) ).
cnf(d19,plain,
( ~ product('e$u1','e$u1',X0)
| product(X0,'e$u2','e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d5,c13]) ).
cnf(d20,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u1','e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u1','e$u3')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d19,d5]) ).
cnf(d21,plain,
( ~ product('e$u1',X0,'e$u3')
| equalish(X0,'e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d20,c11]) ).
cnf(d22,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u2','e$u1','e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u2','e$u2','e$u1')
| equalish('e$u3','e$u1') ),
inference(resolution,[status(thm)],[d21,d18]) ).
cnf(d23,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u2','e$u2','e$u1')
| product('e$u2','e$u1','e$u1') ),
inference(resolution,[status(thm)],[c7,d22]) ).
cnf(d24,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| equalish('e$u3','e$u2')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d23,d17]) ).
cnf(d25,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[c8,d24]) ).
cnf(d26,plain,
( ~ product('e$u2','e$u2',X0)
| product(X0,'e$u1','e$u2')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d25,c13]) ).
cnf(d27,plain,
( product('e$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$u1','e$u2') ),
inference(resolution,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u3','e$u3')
| equalish('e$u2','e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d27,d16]) ).
cnf(d29,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u3','e$u3') ),
inference(resolution,[status(thm)],[c6,d28]) ).
cnf(d30,plain,
( ~ product('e$u1',X0,'e$u3')
| equalish(X0,'e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d29,c11]) ).
cnf(d31,plain,
( ~ product('e$u1',X0,'e$u2')
| equalish(X0,'e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d27,c11]) ).
cnf(d32,plain,
( product(X0,'e$u2','e$u3')
| product(X0,'e$u2','e$u2')
| product(X0,'e$u2','e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d33,plain,
( product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d32,c0]) ).
cnf(d34,plain,
( ~ product('e$u2','e$u1',X0)
| product(X0,'e$u1','e$u2')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d33,c13]) ).
cnf(d35,plain,
( product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2')
| product('e$u2','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d36,plain,
( product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| equalish('e$u3','e$u2') ),
inference(resolution,[status(thm)],[d17,d35]) ).
cnf(d37,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c8,d36]) ).
cnf(d38,plain,
( ~ product(X0,'e$u1','e$u2')
| equalish('e$u1',X0)
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d5,c12]) ).
cnf(d39,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u2','e$u1','e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u1','e$u3')
| equalish('e$u1','e$u2') ),
inference(resolution,[status(thm)],[d38,d37]) ).
cnf(d40,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u2','e$u1','e$u3')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c3,d39]) ).
cnf(d41,plain,
( ~ product('e$u1','e$u1',X0)
| equalish(X0,'e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d40,c10]) ).
cnf(d42,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u2','e$u1','e$u3')
| equalish('e$u2','e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d27,d41]) ).
cnf(d43,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c6,d42]) ).
cnf(d44,plain,
( product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| product('e$u3','e$u1','e$u2')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d43,d34]) ).
cnf(d45,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| equalish('e$u2','e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d44,d31]) ).
cnf(d46,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| product('e$u1','e$u2','e$u3') ),
inference(resolution,[status(thm)],[c5,d45]) ).
cnf(d47,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| equalish('e$u2','e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d46,d30]) ).
cnf(d48,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c6,d47]) ).
cnf(d49,plain,
( ~ product('e$u1','e$u3',X0)
| product(X0,'e$u2','e$u1')
| product('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d48,c13]) ).
cnf(d50,plain,
( product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2')
| product('e$u3','e$u1','e$u3')
| product('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d49,d8]) ).
cnf(d51,plain,
( product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2')
| equalish('e$u2','e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d50,d9]) ).
cnf(d52,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[c6,d51]) ).
cnf(d53,plain,
( ~ product('e$u3','e$u1',X0)
| product(X0,'e$u2','e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u1','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d52,c13]) ).
cnf(d54,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u1','e$u3','e$u3')
| product('e$u2','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d53,d48]) ).
cnf(d55,plain,
( ~ product(X0,'e$u3','e$u3')
| equalish('e$u1',X0)
| product('e$u3','e$u1','e$u3')
| product('e$u2','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d54,c12]) ).
cnf(d56,plain,
( product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d32,c1]) ).
cnf(d57,plain,
( ~ product('e$u2','e$u2',X0)
| product(X0,'e$u1','e$u2')
| product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d56,c13]) ).
cnf(d58,plain,
( product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| product('e$u1','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d57,d56]) ).
cnf(d59,plain,
( ~ product(X0,'e$u1','e$u2')
| equalish('e$u1',X0)
| product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d58,c12]) ).
cnf(d60,plain,
( product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| equalish('e$u1','e$u3')
| product('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d48,d59]) ).
cnf(d61,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2') ),
inference(resolution,[status(thm)],[c4,d60]) ).
cnf(d62,plain,
( ~ product('e$u2','e$u2',X0)
| equalish(X0,'e$u2')
| product('e$u3','e$u1','e$u3')
| product('e$u2','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d61,c10]) ).
cnf(d63,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u2','e$u2','e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u1','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d52,d49]) ).
cnf(d64,plain,
( ~ product('e$u3','e$u1',X0)
| product(X0,'e$u3','e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d63,c13]) ).
cnf(d65,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u2','e$u2','e$u1')
| product('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d64,d48]) ).
cnf(d66,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u2','e$u2','e$u3')
| equalish('e$u1','e$u2')
| product('e$u3','e$u1','e$u3')
| product('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d65,d62]) ).
cnf(d67,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u2','e$u3') ),
inference(resolution,[status(thm)],[c3,d66]) ).
cnf(d68,plain,
( ~ product('e$u2','e$u2',X0)
| equalish(X0,'e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d65,c10]) ).
cnf(d69,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u2','e$u3','e$u3')
| product('e$u3','e$u1','e$u3')
| product('e$u2','e$u3','e$u3')
| equalish('e$u3','e$u1') ),
inference(resolution,[status(thm)],[d68,d67]) ).
cnf(d70,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[c7,d69]) ).
cnf(d71,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u2','e$u2','e$u3')
| equalish('e$u1','e$u2')
| product('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d70,d55]) ).
cnf(d72,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u2','e$u2','e$u3') ),
inference(resolution,[status(thm)],[c3,d71]) ).
cnf(d73,plain,
( ~ product('e$u2',X0,'e$u3')
| equalish(X0,'e$u3')
| product('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d70,c11]) ).
cnf(d74,plain,
( product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u3')
| equalish('e$u2','e$u3') ),
inference(resolution,[status(thm)],[d73,d72]) ).
cnf(d75,plain,
product('e$u3','e$u1','e$u3'),
inference(resolution,[status(thm)],[c6,d74]) ).
cnf(d76,plain,
( ~ product('e$u3',X0,'e$u3')
| equalish(X0,'e$u1') ),
inference(resolution,[status(thm)],[d75,c11]) ).
cnf(d77,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2')
| product('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d78,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u3','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d7,c2]) ).
cnf(d79,plain,
( ~ product(X0,'e$u3','e$u1')
| equalish('e$u3',X0)
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d78,c12]) ).
cnf(d80,plain,
( product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| equalish('e$u3','e$u2') ),
inference(resolution,[status(thm)],[d79,d77]) ).
cnf(d81,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u3','e$u2') ),
inference(resolution,[status(thm)],[c8,d80]) ).
cnf(d82,plain,
( ~ product('e$u2',X0,'e$u1')
| equalish(X0,'e$u1')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d35,c11]) ).
cnf(d83,plain,
( product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2')
| equalish('e$u2','e$u1') ),
inference(resolution,[status(thm)],[d82,d56]) ).
cnf(d84,plain,
( product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c5,d83]) ).
cnf(d85,plain,
( product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| equalish('e$u1','e$u2')
| product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d84,d59]) ).
cnf(d86,plain,
( product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c3,d85]) ).
cnf(d87,plain,
( ~ product('e$u1',X0,'e$u2')
| equalish(X0,'e$u1')
| product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d58,c11]) ).
cnf(d88,plain,
( ~ product(X0,'e$u2','e$u1')
| equalish('e$u1',X0)
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d33,c12]) ).
cnf(d89,plain,
( product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2')
| equalish('e$u1','e$u2') ),
inference(resolution,[status(thm)],[d88,d56]) ).
cnf(d90,plain,
( product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[c3,d89]) ).
cnf(d91,plain,
( product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| equalish('e$u2','e$u1')
| product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| product('e$u1','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d90,d87]) ).
cnf(d92,plain,
( product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| product('e$u1','e$u2','e$u3') ),
inference(resolution,[status(thm)],[c5,d91]) ).
cnf(d93,plain,
( ~ product('e$u2','e$u1',X0)
| product(X0,'e$u3','e$u2')
| product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d92,c13]) ).
cnf(d94,plain,
( product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| product('e$u2','e$u2','e$u3')
| product('e$u2','e$u2','e$u2')
| product('e$u3','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d93,d86]) ).
cnf(d95,plain,
( ~ product('e$u2',X0,'e$u2')
| equalish(X0,'e$u2')
| product('e$u3','e$u3','e$u2')
| product('e$u2','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d94,c11]) ).
cnf(d96,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u2','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u2','e$u2','e$u3')
| equalish('e$u3','e$u2') ),
inference(resolution,[status(thm)],[d95,d81]) ).
cnf(d97,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u2','e$u3','e$u3')
| product('e$u2','e$u2','e$u3') ),
inference(resolution,[status(thm)],[c8,d96]) ).
cnf(d98,plain,
( ~ product('e$u3','e$u3',X0)
| product(X0,'e$u1','e$u3')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d78,c13]) ).
cnf(d99,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d98,d78]) ).
cnf(d100,plain,
( ~ product(X0,'e$u1','e$u3')
| equalish('e$u1',X0)
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d99,c12]) ).
cnf(d101,plain,
( product('e$u3','e$u2','e$u3')
| product('e$u3','e$u2','e$u2')
| product('e$u3','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d32,c2]) ).
cnf(d102,plain,
( ~ product('e$u3',X0,'e$u1')
| equalish(X0,'e$u3')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d78,c11]) ).
cnf(d103,plain,
( product('e$u3','e$u2','e$u3')
| product('e$u3','e$u2','e$u2')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| equalish('e$u2','e$u3') ),
inference(resolution,[status(thm)],[d102,d101]) ).
cnf(d104,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u3','e$u2','e$u3')
| product('e$u3','e$u2','e$u2') ),
inference(resolution,[status(thm)],[c6,d103]) ).
cnf(d105,plain,
( ~ product('e$u3',X0,'e$u1')
| equalish(X0,'e$u1')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d1,c11]) ).
cnf(d106,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2')
| equalish('e$u3','e$u1') ),
inference(resolution,[status(thm)],[d105,d78]) ).
cnf(d107,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c7,d106]) ).
cnf(d108,plain,
( ~ product('e$u3',X0,'e$u2')
| equalish(X0,'e$u1')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d107,c11]) ).
cnf(d109,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u3','e$u2','e$u3')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u3','e$u1','e$u3')
| equalish('e$u2','e$u1') ),
inference(resolution,[status(thm)],[d108,d104]) ).
cnf(d110,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u3','e$u2','e$u3')
| product('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c5,d109]) ).
cnf(d111,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| equalish('e$u1','e$u3')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u3','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d110,d100]) ).
cnf(d112,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u3','e$u2','e$u3') ),
inference(resolution,[status(thm)],[c4,d111]) ).
cnf(d113,plain,
( ~ product(X0,'e$u2','e$u3')
| equalish('e$u3',X0)
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d112,c12]) ).
cnf(d114,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u2','e$u3','e$u3')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| equalish('e$u3','e$u2') ),
inference(resolution,[status(thm)],[d113,d97]) ).
cnf(d115,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[c8,d114]) ).
cnf(d116,plain,
( ~ product('e$u2','e$u3',X0)
| product(X0,'e$u3','e$u2')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d112,c13]) ).
cnf(d117,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u2')
| product('e$u3','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d116,d115]) ).
cnf(d118,plain,
( ~ product('e$u3','e$u3',X0)
| equalish(X0,'e$u2')
| product('e$u3','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d117,c10]) ).
cnf(d119,plain,
( ~ product('e$u3','e$u3',X0)
| product(X0,'e$u2','e$u3')
| product('e$u3','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d117,c13]) ).
cnf(d120,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u3')
| product('e$u2','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d119,d117]) ).
cnf(d121,plain,
( ~ product('e$u2','e$u2',X0)
| equalish(X0,'e$u3')
| product('e$u3','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d120,c10]) ).
cnf(d122,plain,
( ~ product('e$u1','e$u3',X0)
| product(X0,'e$u3','e$u1') ),
inference(resolution,[status(thm)],[d75,c13]) ).
cnf(d123,plain,
( ~ product(X0,'e$u3','e$u2')
| equalish('e$u3',X0)
| product('e$u3','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d117,c12]) ).
cnf(d124,plain,
( ~ product('e$u1',X0,'e$u1')
| equalish(X0,'e$u1')
| product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d2,c11]) ).
cnf(d125,plain,
( product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2')
| product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u2')
| equalish('e$u3','e$u1') ),
inference(resolution,[status(thm)],[d124,d8]) ).
cnf(d126,plain,
( product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2')
| product('e$u1','e$u1','e$u3')
| product('e$u1','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c7,d125]) ).
cnf(d127,plain,
( ~ product('e$u1','e$u1',X0)
| product(X0,'e$u2','e$u1')
| product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2')
| product('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d126,c13]) ).
cnf(d128,plain,
( product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2')
| product('e$u1','e$u1','e$u3')
| product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2')
| product('e$u1','e$u1','e$u3')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d127,d126]) ).
cnf(d129,plain,
( ~ product(X0,'e$u1','e$u3')
| equalish('e$u1',X0)
| product('e$u2','e$u2','e$u1')
| product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d128,c12]) ).
cnf(d130,plain,
( product('e$u2','e$u2','e$u1')
| product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2')
| equalish('e$u1','e$u3') ),
inference(resolution,[status(thm)],[d75,d129]) ).
cnf(d131,plain,
( product('e$u2','e$u2','e$u1')
| product('e$u1','e$u3','e$u3')
| product('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[c4,d130]) ).
cnf(d132,plain,
( product('e$u3','e$u3','e$u3')
| equalish('e$u3','e$u1')
| product('e$u2','e$u2','e$u1')
| product('e$u1','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d131,d123]) ).
cnf(d133,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u2','e$u2','e$u1')
| product('e$u1','e$u3','e$u3') ),
inference(resolution,[status(thm)],[c7,d132]) ).
cnf(d134,plain,
( product('e$u3','e$u3','e$u1')
| product('e$u3','e$u3','e$u3')
| product('e$u2','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d133,d122]) ).
cnf(d135,plain,
( product('e$u3','e$u3','e$u3')
| equalish('e$u1','e$u3')
| product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d134,d121]) ).
cnf(d136,plain,
( product('e$u3','e$u3','e$u3')
| product('e$u3','e$u3','e$u1') ),
inference(resolution,[status(thm)],[c4,d135]) ).
cnf(d137,plain,
( product('e$u3','e$u3','e$u3')
| equalish('e$u1','e$u2')
| product('e$u3','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d136,d118]) ).
cnf(d138,plain,
product('e$u3','e$u3','e$u3'),
inference(resolution,[status(thm)],[c3,d137]) ).
cnf(d139,plain,
equalish('e$u3','e$u1'),
inference(resolution,[status(thm)],[d138,d76]) ).
cnf(d140,plain,
$false,
inference(resolution,[status(thm)],[c7,d139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP133-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n020.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 14:30:48 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.70/6.17 % SZS status Unsatisfiable for theBenchmark.p
% 21.70/6.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------