%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP124-2.004 : 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 : n001.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 07:22:24 AM UTC 2026
% Result : Unsatisfiable 16.72s 3.72s
% Output : CNFRefutation 16.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of clauses : 74 ( 29 unt; 27 nHn; 72 RR)
% Number of literals : 170 ( 0 equ; 55 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 57 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(e_2_then_e_3,axiom,
next('e$u2','e$u3') ).
cnf(e_4_greater_e_3,axiom,
greater('e$u4','e$u3') ).
cnf(no_redundancy,axiom,
( ~ greater(X1,X2)
| ~ next(X0,X2)
| ~ product(X0,'e$u1',X1) ) ).
cnf(element_1,axiom,
'group$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$u1') ).
cnf(product_total_function1,axiom,
( product(X0,X1,'e$u4')
| product(X0,X1,'e$u3')
| product(X0,X1,'e$u2')
| product(X0,X1,'e$u1')
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ) ).
cnf(product_right_cancellation,axiom,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ) ).
cnf(product_left_cancellation,axiom,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ) ).
cnf(product_idempotence,axiom,
product(X0,X0,X0) ).
cnf(qg2_2,negated_conjecture,
( equalish(X1,X4)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ) ).
cnf(c1,plain,
next('e$u2','e$u3'),
inference(clausification,[status(esa)],[e_2_then_e_3]) ).
cnf(c8,plain,
greater('e$u4','e$u3'),
inference(clausification,[status(esa)],[e_4_greater_e_3]) ).
cnf(c9,plain,
( ~ greater(X2,X1)
| ~ product(X0,'e$u1',X2)
| ~ next(X0,X1) ),
inference(clausification,[status(esa)],[no_redundancy]) ).
cnf(c10,plain,
'group$uelement'('e$u1'),
inference(clausification,[status(esa)],[element_1]) ).
cnf(c11,plain,
'group$uelement'('e$u2'),
inference(clausification,[status(esa)],[element_2]) ).
cnf(c12,plain,
'group$uelement'('e$u3'),
inference(clausification,[status(esa)],[element_3]) ).
cnf(c14,plain,
~ equalish('e$u1','e$u2'),
inference(clausification,[status(esa)],[e_1_is_not_e_2]) ).
cnf(c15,plain,
~ equalish('e$u1','e$u3'),
inference(clausification,[status(esa)],[e_1_is_not_e_3]) ).
cnf(c17,plain,
~ equalish('e$u2','e$u1'),
inference(clausification,[status(esa)],[e_2_is_not_e_1]) ).
cnf(c18,plain,
~ equalish('e$u2','e$u3'),
inference(clausification,[status(esa)],[e_2_is_not_e_3]) ).
cnf(c20,plain,
~ equalish('e$u3','e$u1'),
inference(clausification,[status(esa)],[e_3_is_not_e_1]) ).
cnf(c26,plain,
( ~ 'group$uelement'(X1)
| product(X0,X1,'e$u4')
| product(X0,X1,'e$u1')
| ~ 'group$uelement'(X0)
| product(X0,X1,'e$u3')
| product(X0,X1,'e$u2') ),
inference(clausification,[status(esa)],[product_total_function1]) ).
cnf(c28,plain,
( equalish(X3,X1)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_right_cancellation]) ).
cnf(c29,plain,
( equalish(X3,X0)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_left_cancellation]) ).
cnf(c30,plain,
product(X0,X0,X0),
inference(clausification,[status(esa)],[product_idempotence]) ).
cnf(c32,plain,
( ~ product(X5,X0,X1)
| equalish(X4,X1)
| ~ product(X5,X3,X4)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg2_2]) ).
cnf(d0,plain,
( equalish(X1,X0)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[c28,c30]) ).
cnf(d1,plain,
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[c29,c30]) ).
cnf(d2,plain,
( ~ 'group$uelement'(X0)
| product(X0,'e$u2','e$u4')
| product(X0,'e$u2','e$u3')
| product(X0,'e$u2','e$u2')
| product(X0,'e$u2','e$u1') ),
inference(resolution,[status(thm)],[c26,c11]) ).
cnf(d3,plain,
( product('e$u3','e$u2','e$u4')
| product('e$u3','e$u2','e$u3')
| product('e$u3','e$u2','e$u2')
| product('e$u3','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d2,c12]) ).
cnf(d4,plain,
( equalish(X1,X2)
| ~ product(X3,X0,X1)
| ~ product(X3,X2,X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c32,c30]) ).
cnf(d5,plain,
( equalish(X2,X0)
| ~ product(X1,X2,X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d4,c30]) ).
cnf(d6,plain,
( ~ 'group$uelement'(X0)
| product(X0,'e$u1','e$u4')
| product(X0,'e$u1','e$u3')
| product(X0,'e$u1','e$u2')
| product(X0,'e$u1','e$u1') ),
inference(resolution,[status(thm)],[c26,c10]) ).
cnf(d7,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)],[d6,c11]) ).
cnf(d8,plain,
( ~ product('e$u2','e$u1',X0)
| ~ greater(X0,'e$u3') ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d9,plain,
~ product('e$u2','e$u1','e$u4'),
inference(resolution,[status(thm)],[d8,c8]) ).
cnf(d10,plain,
( product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2')
| product('e$u2','e$u1','e$u1') ),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( equalish('e$u1','e$u2')
| product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
( product('e$u2','e$u1','e$u3')
| product('e$u2','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c14,d11]) ).
cnf(d13,plain,
( equalish('e$u1','e$u2')
| product('e$u2','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
product('e$u2','e$u1','e$u3'),
inference(resolution,[status(thm)],[c14,d13]) ).
cnf(d15,plain,
( equalish('e$u1','e$u3')
| ~ product('e$u3','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d14,d5]) ).
cnf(d16,plain,
~ product('e$u3','e$u2','e$u1'),
inference(resolution,[status(thm)],[c15,d15]) ).
cnf(d17,plain,
( product('e$u3','e$u2','e$u4')
| product('e$u3','e$u2','e$u3')
| product('e$u3','e$u2','e$u2') ),
inference(resolution,[status(thm)],[d16,d3]) ).
cnf(d18,plain,
( equalish('e$u2','e$u3')
| product('e$u3','e$u2','e$u4')
| product('e$u3','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
( product('e$u3','e$u2','e$u4')
| product('e$u3','e$u2','e$u3') ),
inference(resolution,[status(thm)],[c18,d18]) ).
cnf(d20,plain,
( equalish('e$u2','e$u3')
| product('e$u3','e$u2','e$u4') ),
inference(resolution,[status(thm)],[d19,d0]) ).
cnf(d21,plain,
product('e$u3','e$u2','e$u4'),
inference(resolution,[status(thm)],[c18,d20]) ).
cnf(d22,plain,
( equalish(X0,'e$u2')
| ~ product('e$u3',X0,'e$u4') ),
inference(resolution,[status(thm)],[d21,c28]) ).
cnf(d23,plain,
( equalish('e$u2',X0)
| ~ product(X0,'e$u1','e$u3') ),
inference(resolution,[status(thm)],[d14,c29]) ).
cnf(d24,plain,
( equalish('e$u3',X0)
| ~ product(X0,'e$u2','e$u4') ),
inference(resolution,[status(thm)],[d21,c29]) ).
cnf(d25,plain,
( product('e$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$u1') ),
inference(resolution,[status(thm)],[d6,c12]) ).
cnf(d26,plain,
( equalish('e$u1','e$u3')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[d25,d1]) ).
cnf(d27,plain,
( product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| product('e$u3','e$u1','e$u2') ),
inference(resolution,[status(thm)],[c15,d26]) ).
cnf(d28,plain,
( product('e$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$u1') ),
inference(resolution,[status(thm)],[d2,c10]) ).
cnf(d29,plain,
( equalish('e$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)],[d28,d0]) ).
cnf(d30,plain,
( product('e$u1','e$u2','e$u4')
| product('e$u1','e$u2','e$u3')
| product('e$u1','e$u2','e$u2') ),
inference(resolution,[status(thm)],[c17,d29]) ).
cnf(d31,plain,
( equalish('e$u2','e$u1')
| product('e$u1','e$u2','e$u4')
| product('e$u1','e$u2','e$u3') ),
inference(resolution,[status(thm)],[d30,d1]) ).
cnf(d32,plain,
( product('e$u1','e$u2','e$u4')
| product('e$u1','e$u2','e$u3') ),
inference(resolution,[status(thm)],[c17,d31]) ).
cnf(d33,plain,
( equalish('e$u2','e$u3')
| ~ product('e$u3','e$u1','e$u2')
| product('e$u1','e$u2','e$u4') ),
inference(resolution,[status(thm)],[d32,d5]) ).
cnf(d34,plain,
( ~ product('e$u3','e$u1','e$u2')
| product('e$u1','e$u2','e$u4') ),
inference(resolution,[status(thm)],[c18,d33]) ).
cnf(d35,plain,
( product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3')
| product('e$u1','e$u2','e$u4') ),
inference(resolution,[status(thm)],[d34,d27]) ).
cnf(d36,plain,
( equalish('e$u3','e$u1')
| product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[d35,d24]) ).
cnf(d37,plain,
( product('e$u3','e$u1','e$u4')
| product('e$u3','e$u1','e$u3') ),
inference(resolution,[status(thm)],[c20,d36]) ).
cnf(d38,plain,
( equalish('e$u2','e$u3')
| product('e$u3','e$u1','e$u4') ),
inference(resolution,[status(thm)],[d37,d23]) ).
cnf(d39,plain,
product('e$u3','e$u1','e$u4'),
inference(resolution,[status(thm)],[c18,d38]) ).
cnf(d40,plain,
equalish('e$u1','e$u2'),
inference(resolution,[status(thm)],[d39,d22]) ).
cnf(d41,plain,
$false,
inference(resolution,[status(thm)],[c14,d40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-2.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:30:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.72/3.72 % SZS status Unsatisfiable for theBenchmark.p
% 16.72/3.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------