%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP124-8.004 : 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 : n004.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 07:22:25 AM UTC 2026
% Result : Unsatisfiable 49.35s 7.12s
% Output : CNFRefutation 49.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 24
% Syntax : Number of clauses : 158 ( 40 unt; 104 nHn; 154 RR)
% Number of literals : 513 ( 0 equ; 71 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 74 ( 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(element_4,axiom,
'group$uelement'('e$u4') ).
cnf(e_1_is_not_e_2,axiom,
~ equalish('e$u1','e$u2') ).
cnf(e_1_is_not_e_3,axiom,
~ equalish('e$u1','e$u3') ).
cnf(e_1_is_not_e_4,axiom,
~ equalish('e$u1','e$u4') ).
cnf(e_2_is_not_e_1,axiom,
~ equalish('e$u2','e$u1') ).
cnf(e_2_is_not_e_3,axiom,
~ equalish('e$u2','e$u3') ).
cnf(e_2_is_not_e_4,axiom,
~ equalish('e$u2','e$u4') ).
cnf(e_3_is_not_e_1,axiom,
~ equalish('e$u3','e$u1') ).
cnf(e_3_is_not_e_2,axiom,
~ equalish('e$u3','e$u2') ).
cnf(e_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(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(product1_total_function1,axiom,
( product1(X0,X1,'e$u4')
| product1(X0,X1,'e$u3')
| product1(X0,X1,'e$u2')
| product1(X0,X1,'e$u1')
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ) ).
cnf(product1_right_cancellation,axiom,
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ) ).
cnf(product1_left_cancellation,axiom,
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ) ).
cnf(product1_idempotence,axiom,
product1(X0,X0,X0) ).
cnf(product2_total_function2,axiom,
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ) ).
cnf(product2_right_cancellation,axiom,
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ) ).
cnf(product2_idempotence,axiom,
product2(X0,X0,X0) ).
cnf(qg2a,negated_conjecture,
( product2(X3,X1,X0)
| ~ product1(X2,X0,X3)
| ~ product1(X0,X1,X2) ) ).
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(c27,plain,
~ equalish('e$u1','e$u4'),
inference(clausification,[status(esa)],[e_1_is_not_e_4]) ).
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(c33,plain,
~ equalish('e$u3','e$u4'),
inference(clausification,[status(esa)],[e_3_is_not_e_4]) ).
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,
( ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0)
| product1(X0,X1,'e$u3')
| product1(X0,X1,'e$u2')
| product1(X0,X1,'e$u4')
| product1(X0,X1,'e$u1') ),
inference(clausification,[status(esa)],[product1_total_function1]) ).
cnf(c39,plain,
( equalish(X3,X1)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(clausification,[status(esa)],[product1_right_cancellation]) ).
cnf(c40,plain,
( equalish(X3,X0)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(clausification,[status(esa)],[product1_left_cancellation]) ).
cnf(c41,plain,
product1(X0,X0,X0),
inference(clausification,[status(esa)],[product1_idempotence]) ).
cnf(c43,plain,
( equalish(X3,X2)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(clausification,[status(esa)],[product2_total_function2]) ).
cnf(c44,plain,
( equalish(X3,X1)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(clausification,[status(esa)],[product2_right_cancellation]) ).
cnf(c46,plain,
product2(X0,X0,X0),
inference(clausification,[status(esa)],[product2_idempotence]) ).
cnf(c47,plain,
( product2(X2,X3,X1)
| ~ product1(X1,X3,X0)
| ~ product1(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg2a]) ).
cnf(d0,plain,
( ~ product2(X1,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c43,c46]) ).
cnf(d1,plain,
( ~ product1(X0,X1,X1)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c40,c41]) ).
cnf(d2,plain,
( ~ product1(X0,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c39,c41]) ).
cnf(d3,plain,
( product1('e$u2',X0,'e$u4')
| product1('e$u2',X0,'e$u3')
| product1('e$u2',X0,'e$u2')
| product1('e$u2',X0,'e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c37,c22]) ).
cnf(d4,plain,
( product1('e$u2','e$u1','e$u4')
| product1('e$u2','e$u1','e$u3')
| product1('e$u2','e$u1','e$u2')
| product1('e$u2','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d3,c21]) ).
cnf(d5,plain,
( equalish('e$u2','e$u1')
| product1('e$u2','e$u1','e$u4')
| product1('e$u2','e$u1','e$u3')
| product1('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( product1('e$u2','e$u1','e$u4')
| product1('e$u2','e$u1','e$u3')
| product1('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c28,d5]) ).
cnf(d7,plain,
( equalish('e$u2','e$u1')
| product1('e$u2','e$u1','e$u4')
| product1('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( product1('e$u2','e$u1','e$u4')
| product1('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c28,d7]) ).
cnf(d9,plain,
( product2('e$u3',X0,'e$u1')
| ~ product1('e$u1',X0,'e$u2')
| product1('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d8,c47]) ).
cnf(d10,plain,
( product1('e$u1',X0,'e$u4')
| product1('e$u1',X0,'e$u3')
| product1('e$u1',X0,'e$u2')
| product1('e$u1',X0,'e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c37,c21]) ).
cnf(d11,plain,
( product1('e$u1','e$u3','e$u4')
| product1('e$u1','e$u3','e$u3')
| product1('e$u1','e$u3','e$u2')
| product1('e$u1','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d10,c23]) ).
cnf(d12,plain,
( equalish('e$u1','e$u3')
| product1('e$u1','e$u3','e$u4')
| product1('e$u1','e$u3','e$u3')
| product1('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d11,d2]) ).
cnf(d13,plain,
( product1('e$u1','e$u3','e$u4')
| product1('e$u1','e$u3','e$u3')
| product1('e$u1','e$u3','e$u2') ),
inference(resolution,[status(thm)],[c26,d12]) ).
cnf(d14,plain,
( product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u1','e$u4')
| product1('e$u1','e$u3','e$u4')
| product1('e$u1','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
( equalish('e$u1','e$u3')
| product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u1','e$u4')
| product1('e$u1','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d14,d1]) ).
cnf(d16,plain,
( product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u1','e$u4')
| product1('e$u1','e$u3','e$u4') ),
inference(resolution,[status(thm)],[c26,d15]) ).
cnf(d17,plain,
( ~ product1('e$u1',X0,'e$u4')
| equalish('e$u3',X0)
| product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d16,c39]) ).
cnf(d18,plain,
( product1('e$u1','e$u2','e$u4')
| product1('e$u1','e$u2','e$u3')
| product1('e$u1','e$u2','e$u2')
| product1('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d10,c22]) ).
cnf(d19,plain,
( equalish('e$u1','e$u2')
| product1('e$u1','e$u2','e$u4')
| product1('e$u1','e$u2','e$u3')
| product1('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d18,d2]) ).
cnf(d20,plain,
( product1('e$u1','e$u2','e$u4')
| product1('e$u1','e$u2','e$u3')
| product1('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[c25,d19]) ).
cnf(d21,plain,
( equalish('e$u1','e$u2')
| product1('e$u1','e$u2','e$u4')
| product1('e$u1','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d20,d1]) ).
cnf(d22,plain,
( product1('e$u1','e$u2','e$u4')
| product1('e$u1','e$u2','e$u3') ),
inference(resolution,[status(thm)],[c25,d21]) ).
cnf(d23,plain,
( ~ product1('e$u1',X0,'e$u3')
| equalish('e$u2',X0)
| product1('e$u1','e$u2','e$u4') ),
inference(resolution,[status(thm)],[d22,c39]) ).
cnf(d24,plain,
( product1('e$u1','e$u4','e$u4')
| product1('e$u1','e$u4','e$u3')
| product1('e$u1','e$u4','e$u2')
| product1('e$u1','e$u4','e$u1') ),
inference(resolution,[status(thm)],[d10,c24]) ).
cnf(d25,plain,
( equalish('e$u1','e$u4')
| product1('e$u1','e$u4','e$u4')
| product1('e$u1','e$u4','e$u3')
| product1('e$u1','e$u4','e$u2') ),
inference(resolution,[status(thm)],[d24,d2]) ).
cnf(d26,plain,
( product1('e$u1','e$u4','e$u4')
| product1('e$u1','e$u4','e$u3')
| product1('e$u1','e$u4','e$u2') ),
inference(resolution,[status(thm)],[c27,d25]) ).
cnf(d27,plain,
( product2('e$u3','e$u4','e$u1')
| product1('e$u2','e$u1','e$u4')
| product1('e$u1','e$u4','e$u4')
| product1('e$u1','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d26,d9]) ).
cnf(d28,plain,
( product1('e$u1','e$u2','e$u4')
| equalish('e$u2','e$u4')
| product2('e$u3','e$u4','e$u1')
| product1('e$u2','e$u1','e$u4')
| product1('e$u1','e$u4','e$u4') ),
inference(resolution,[status(thm)],[d27,d23]) ).
cnf(d29,plain,
( product2('e$u3','e$u4','e$u1')
| product1('e$u2','e$u1','e$u4')
| product1('e$u1','e$u4','e$u4')
| product1('e$u1','e$u2','e$u4') ),
inference(resolution,[status(thm)],[c30,d28]) ).
cnf(d30,plain,
( product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u1','e$u4')
| equalish('e$u3','e$u2')
| product2('e$u3','e$u4','e$u1')
| product1('e$u2','e$u1','e$u4')
| product1('e$u1','e$u4','e$u4') ),
inference(resolution,[status(thm)],[d29,d17]) ).
cnf(d31,plain,
( product2('e$u3','e$u4','e$u1')
| product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u1','e$u4')
| product1('e$u1','e$u4','e$u4') ),
inference(resolution,[status(thm)],[c32,d30]) ).
cnf(d32,plain,
( product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u1','e$u4')
| equalish('e$u3','e$u4')
| product2('e$u3','e$u4','e$u1')
| product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d31,d17]) ).
cnf(d33,plain,
( product2('e$u3','e$u4','e$u1')
| product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[c33,d32]) ).
cnf(d34,plain,
( ~ product1(X0,'e$u1','e$u4')
| equalish(X0,'e$u2')
| product2('e$u3','e$u4','e$u1')
| product2('e$u3','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d33,c40]) ).
cnf(d35,plain,
( ~ product1('e$u2',X0,'e$u4')
| equalish('e$u1',X0)
| product2('e$u3','e$u4','e$u1')
| product2('e$u3','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d33,c39]) ).
cnf(d36,plain,
( product1('e$u2','e$u3','e$u4')
| product1('e$u2','e$u3','e$u3')
| product1('e$u2','e$u3','e$u2')
| product1('e$u2','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d3,c23]) ).
cnf(d37,plain,
( product2('e$u1',X0,'e$u3')
| ~ product1('e$u3',X0,'e$u2')
| product1('e$u2','e$u3','e$u4')
| product1('e$u2','e$u3','e$u3')
| product1('e$u2','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d36,c47]) ).
cnf(d38,plain,
( product1('e$u3',X0,'e$u4')
| product1('e$u3',X0,'e$u3')
| product1('e$u3',X0,'e$u2')
| product1('e$u3',X0,'e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c37,c23]) ).
cnf(d39,plain,
( product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3')
| product1('e$u3','e$u1','e$u2')
| product1('e$u3','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d38,c21]) ).
cnf(d40,plain,
( equalish('e$u3','e$u1')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3')
| product1('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d39,d1]) ).
cnf(d41,plain,
( product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3')
| product1('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c31,d40]) ).
cnf(d42,plain,
( product2('e$u1','e$u1','e$u3')
| product1('e$u2','e$u3','e$u4')
| product1('e$u2','e$u3','e$u3')
| product1('e$u2','e$u3','e$u2')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d41,d37]) ).
cnf(d43,plain,
( equalish('e$u2','e$u3')
| product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3')
| product1('e$u2','e$u3','e$u4')
| product1('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d42,d2]) ).
cnf(d44,plain,
( product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3')
| product1('e$u2','e$u3','e$u4')
| product1('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[c29,d43]) ).
cnf(d45,plain,
( equalish('e$u2','e$u3')
| product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3')
| product1('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d44,d1]) ).
cnf(d46,plain,
( product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3')
| product1('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[c29,d45]) ).
cnf(d47,plain,
( product2('e$u3','e$u4','e$u1')
| product2('e$u3','e$u3','e$u1')
| equalish('e$u1','e$u3')
| product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d46,d35]) ).
cnf(d48,plain,
( product2('e$u3','e$u4','e$u1')
| product2('e$u3','e$u3','e$u1')
| product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c26,d47]) ).
cnf(d49,plain,
( equalish('e$u3','e$u1')
| product2('e$u3','e$u4','e$u1')
| product2('e$u3','e$u3','e$u1')
| product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d48,d2]) ).
cnf(d50,plain,
( product2('e$u3','e$u4','e$u1')
| product2('e$u3','e$u3','e$u1')
| product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4') ),
inference(resolution,[status(thm)],[c31,d49]) ).
cnf(d51,plain,
( product2('e$u3','e$u4','e$u1')
| product2('e$u3','e$u3','e$u1')
| equalish('e$u3','e$u2')
| product2('e$u3','e$u4','e$u1')
| product2('e$u3','e$u3','e$u1')
| product2('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d50,d34]) ).
cnf(d52,plain,
( product2('e$u3','e$u4','e$u1')
| product2('e$u3','e$u3','e$u1')
| product2('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c32,d51]) ).
cnf(d53,plain,
( equalish('e$u3','e$u1')
| product2('e$u3','e$u4','e$u1')
| product2('e$u3','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d52,d0]) ).
cnf(d54,plain,
( product2('e$u3','e$u4','e$u1')
| product2('e$u3','e$u3','e$u1') ),
inference(resolution,[status(thm)],[c31,d53]) ).
cnf(d55,plain,
( equalish('e$u1','e$u3')
| product2('e$u3','e$u4','e$u1') ),
inference(resolution,[status(thm)],[d54,d0]) ).
cnf(d56,plain,
product2('e$u3','e$u4','e$u1'),
inference(resolution,[status(thm)],[c26,d55]) ).
cnf(d57,plain,
( ~ product2('e$u3',X0,'e$u1')
| equalish(X0,'e$u4') ),
inference(resolution,[status(thm)],[d56,c44]) ).
cnf(d58,plain,
( ~ product1(X0,'e$u1','e$u3')
| equalish(X0,'e$u2')
| product1('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d8,c40]) ).
cnf(d59,plain,
( product1('e$u4',X0,'e$u4')
| product1('e$u4',X0,'e$u3')
| product1('e$u4',X0,'e$u2')
| product1('e$u4',X0,'e$u1')
| ~ 'group$uelement'(X0) ),
inference(resolution,[status(thm)],[c37,c24]) ).
cnf(d60,plain,
( product1('e$u4','e$u1','e$u4')
| product1('e$u4','e$u1','e$u3')
| product1('e$u4','e$u1','e$u2')
| product1('e$u4','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d59,c21]) ).
cnf(d61,plain,
( equalish('e$u4','e$u1')
| product1('e$u4','e$u1','e$u4')
| product1('e$u4','e$u1','e$u3')
| product1('e$u4','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d60,d1]) ).
cnf(d62,plain,
( product1('e$u4','e$u1','e$u4')
| product1('e$u4','e$u1','e$u3')
| product1('e$u4','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c34,d61]) ).
cnf(d63,plain,
( ~ product1(X0,'e$u1','e$u2')
| equalish(X0,'e$u4')
| product1('e$u4','e$u1','e$u4')
| product1('e$u4','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d62,c40]) ).
cnf(d64,plain,
( product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3')
| product1('e$u4','e$u1','e$u4')
| product1('e$u4','e$u1','e$u3')
| equalish('e$u3','e$u4') ),
inference(resolution,[status(thm)],[d63,d41]) ).
cnf(d65,plain,
( product1('e$u4','e$u1','e$u4')
| product1('e$u4','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c33,d64]) ).
cnf(d66,plain,
( equalish('e$u3','e$u1')
| product1('e$u4','e$u1','e$u4')
| product1('e$u4','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d65,d2]) ).
cnf(d67,plain,
( product1('e$u4','e$u1','e$u4')
| product1('e$u4','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4') ),
inference(resolution,[status(thm)],[c31,d66]) ).
cnf(d68,plain,
( ~ product1(X0,'e$u1','e$u4')
| equalish(X0,'e$u3')
| product1('e$u4','e$u1','e$u4')
| product1('e$u4','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d67,c40]) ).
cnf(d69,plain,
( ~ product1('e$u2',X0,'e$u3')
| equalish('e$u1',X0)
| product1('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d8,c39]) ).
cnf(d70,plain,
( product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3')
| product1('e$u2','e$u4','e$u2')
| product1('e$u2','e$u4','e$u1') ),
inference(resolution,[status(thm)],[d3,c24]) ).
cnf(d71,plain,
( ~ product1('e$u2',X0,'e$u1')
| equalish('e$u4',X0)
| product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3')
| product1('e$u2','e$u4','e$u2') ),
inference(resolution,[status(thm)],[d70,c39]) ).
cnf(d72,plain,
( product1('e$u2','e$u3','e$u4')
| product1('e$u2','e$u3','e$u3')
| product1('e$u2','e$u3','e$u2')
| product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3')
| product1('e$u2','e$u4','e$u2')
| equalish('e$u4','e$u3') ),
inference(resolution,[status(thm)],[d71,d36]) ).
cnf(d73,plain,
( product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3')
| product1('e$u2','e$u4','e$u2')
| product1('e$u2','e$u3','e$u4')
| product1('e$u2','e$u3','e$u3')
| product1('e$u2','e$u3','e$u2') ),
inference(resolution,[status(thm)],[c36,d72]) ).
cnf(d74,plain,
( equalish('e$u2','e$u3')
| product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3')
| product1('e$u2','e$u4','e$u2')
| product1('e$u2','e$u3','e$u4')
| product1('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[d73,d2]) ).
cnf(d75,plain,
( product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3')
| product1('e$u2','e$u4','e$u2')
| product1('e$u2','e$u3','e$u4')
| product1('e$u2','e$u3','e$u3') ),
inference(resolution,[status(thm)],[c29,d74]) ).
cnf(d76,plain,
( equalish('e$u2','e$u3')
| product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3')
| product1('e$u2','e$u4','e$u2')
| product1('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[d75,d1]) ).
cnf(d77,plain,
( product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3')
| product1('e$u2','e$u4','e$u2')
| product1('e$u2','e$u3','e$u4') ),
inference(resolution,[status(thm)],[c29,d76]) ).
cnf(d78,plain,
( ~ product1('e$u2',X0,'e$u4')
| equalish('e$u3',X0)
| product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3')
| product1('e$u2','e$u4','e$u2') ),
inference(resolution,[status(thm)],[d77,c39]) ).
cnf(d79,plain,
( ~ product1(X0,'e$u3','e$u4')
| equalish(X0,'e$u1')
| product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d16,c40]) ).
cnf(d80,plain,
( product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u1','e$u4')
| equalish('e$u2','e$u1')
| product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3')
| product1('e$u2','e$u4','e$u2') ),
inference(resolution,[status(thm)],[d77,d79]) ).
cnf(d81,plain,
( product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3')
| product1('e$u2','e$u4','e$u2')
| product1('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[c28,d80]) ).
cnf(d82,plain,
( product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3')
| product1('e$u2','e$u4','e$u2')
| equalish('e$u3','e$u1')
| product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3')
| product1('e$u2','e$u4','e$u2') ),
inference(resolution,[status(thm)],[d81,d78]) ).
cnf(d83,plain,
( product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3')
| product1('e$u2','e$u4','e$u2') ),
inference(resolution,[status(thm)],[c31,d82]) ).
cnf(d84,plain,
( equalish('e$u2','e$u4')
| product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[d83,d2]) ).
cnf(d85,plain,
( product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u4','e$u3') ),
inference(resolution,[status(thm)],[c30,d84]) ).
cnf(d86,plain,
( product1('e$u2','e$u1','e$u4')
| equalish('e$u1','e$u4')
| product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u4','e$u4') ),
inference(resolution,[status(thm)],[d85,d69]) ).
cnf(d87,plain,
( product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u4','e$u4')
| product1('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[c27,d86]) ).
cnf(d88,plain,
( product1('e$u4','e$u1','e$u4')
| product1('e$u4','e$u1','e$u3')
| equalish('e$u2','e$u3')
| product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u4','e$u4') ),
inference(resolution,[status(thm)],[d87,d68]) ).
cnf(d89,plain,
( product2('e$u3','e$u3','e$u1')
| product1('e$u4','e$u1','e$u4')
| product1('e$u4','e$u1','e$u3')
| product1('e$u2','e$u4','e$u4') ),
inference(resolution,[status(thm)],[c29,d88]) ).
cnf(d90,plain,
( equalish('e$u2','e$u4')
| product2('e$u3','e$u3','e$u1')
| product1('e$u4','e$u1','e$u4')
| product1('e$u4','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d89,d1]) ).
cnf(d91,plain,
( product2('e$u3','e$u3','e$u1')
| product1('e$u4','e$u1','e$u4')
| product1('e$u4','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c30,d90]) ).
cnf(d92,plain,
( product1('e$u2','e$u1','e$u4')
| equalish('e$u4','e$u2')
| product2('e$u3','e$u3','e$u1')
| product1('e$u4','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d91,d58]) ).
cnf(d93,plain,
( product2('e$u3','e$u3','e$u1')
| product1('e$u4','e$u1','e$u4')
| product1('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[c35,d92]) ).
cnf(d94,plain,
( ~ product1(X0,'e$u1','e$u4')
| equalish(X0,'e$u2')
| product2('e$u3','e$u3','e$u1')
| product1('e$u4','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d93,c40]) ).
cnf(d95,plain,
( ~ product1('e$u2',X0,'e$u4')
| equalish('e$u3',X0)
| product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d46,c39]) ).
cnf(d96,plain,
( product2('e$u3','e$u3','e$u1')
| product1('e$u2','e$u1','e$u4')
| equalish('e$u2','e$u1')
| product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d46,d79]) ).
cnf(d97,plain,
( product2('e$u3','e$u3','e$u1')
| product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3')
| product1('e$u2','e$u1','e$u4') ),
inference(resolution,[status(thm)],[c28,d96]) ).
cnf(d98,plain,
( product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3')
| equalish('e$u3','e$u1')
| product2('e$u3','e$u3','e$u1')
| product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d97,d95]) ).
cnf(d99,plain,
( product2('e$u3','e$u3','e$u1')
| product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4')
| product1('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c31,d98]) ).
cnf(d100,plain,
( equalish('e$u3','e$u1')
| product2('e$u3','e$u3','e$u1')
| product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d99,d2]) ).
cnf(d101,plain,
( product2('e$u3','e$u3','e$u1')
| product2('e$u1','e$u1','e$u3')
| product1('e$u3','e$u1','e$u4') ),
inference(resolution,[status(thm)],[c31,d100]) ).
cnf(d102,plain,
( product2('e$u3','e$u3','e$u1')
| product1('e$u4','e$u1','e$u4')
| equalish('e$u3','e$u2')
| product2('e$u3','e$u3','e$u1')
| product2('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d101,d94]) ).
cnf(d103,plain,
( product2('e$u3','e$u3','e$u1')
| product2('e$u1','e$u1','e$u3')
| product1('e$u4','e$u1','e$u4') ),
inference(resolution,[status(thm)],[c32,d102]) ).
cnf(d104,plain,
( equalish('e$u4','e$u1')
| product2('e$u3','e$u3','e$u1')
| product2('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d103,d2]) ).
cnf(d105,plain,
( product2('e$u3','e$u3','e$u1')
| product2('e$u1','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c34,d104]) ).
cnf(d106,plain,
( equalish('e$u3','e$u1')
| product2('e$u3','e$u3','e$u1') ),
inference(resolution,[status(thm)],[d105,d0]) ).
cnf(d107,plain,
product2('e$u3','e$u3','e$u1'),
inference(resolution,[status(thm)],[c31,d106]) ).
cnf(d108,plain,
equalish('e$u3','e$u4'),
inference(resolution,[status(thm)],[d107,d57]) ).
cnf(d109,plain,
$false,
inference(resolution,[status(thm)],[c33,d108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP124-8.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n004.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 14:25:20 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.35/7.12 % SZS status Unsatisfiable for theBenchmark.p
% 49.35/7.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------