%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP123-8.003 : 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 : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:22:24 AM UTC 2026
% Result : Unsatisfiable 10.87s 3.20s
% Output : CNFRefutation 10.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of clauses : 47 ( 22 unt; 12 nHn; 43 RR)
% Number of literals : 100 ( 0 equ; 40 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 50 ( 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_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(product1_total_function1,axiom,
( product1(X0,X1,'e$u3')
| product1(X0,X1,'e$u2')
| product1(X0,X1,'e$u1')
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ) ).
cnf(product1_right_cancellation,axiom,
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ) ).
cnf(product1_left_cancellation,axiom,
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ) ).
cnf(product1_idempotence,axiom,
product1(X0,X0,X0) ).
cnf(product2_total_function2,axiom,
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ) ).
cnf(product2_idempotence,axiom,
product2(X0,X0,X0) ).
cnf(qg1a,negated_conjecture,
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ) ).
cnf(c16,plain,
'group$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$u3'),
inference(clausification,[status(esa)],[element_3]) ).
cnf(c21,plain,
~ equalish('e$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$u2'),
inference(clausification,[status(esa)],[e_3_is_not_e_2]) ).
cnf(c25,plain,
( ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0)
| product1(X0,X1,'e$u3')
| product1(X0,X1,'e$u2')
| product1(X0,X1,'e$u1') ),
inference(clausification,[status(esa)],[product1_total_function1]) ).
cnf(c27,plain,
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(clausification,[status(esa)],[product1_right_cancellation]) ).
cnf(c28,plain,
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(clausification,[status(esa)],[product1_left_cancellation]) ).
cnf(c29,plain,
product1(X0,X0,X0),
inference(clausification,[status(esa)],[product1_idempotence]) ).
cnf(c31,plain,
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(clausification,[status(esa)],[product2_total_function2]) ).
cnf(c34,plain,
product2(X0,X0,X0),
inference(clausification,[status(esa)],[product2_idempotence]) ).
cnf(c35,plain,
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg1a]) ).
cnf(d0,plain,
( ~ product1(X1,X0,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c28,c29]) ).
cnf(d1,plain,
( ~ product1(X1,X0,X1)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c27,c29]) ).
cnf(d2,plain,
( product1('e$u3',X0,'e$u2')
| product1('e$u3',X0,'e$u1')
| ~ 'group$uelement'(X0)
| ~ 'group$uelement'('e$u3')
| equalish(X0,'e$u3') ),
inference(resolution,[status(thm)],[d1,c25]) ).
cnf(d3,plain,
( product1('e$u3',X0,'e$u2')
| product1('e$u3',X0,'e$u1')
| ~ 'group$uelement'(X0)
| equalish(X0,'e$u3') ),
inference(resolution,[status(thm)],[c18,d2]) ).
cnf(d4,plain,
( equalish('e$u2','e$u3')
| product1('e$u3','e$u2','e$u1')
| ~ 'group$uelement'('e$u2')
| equalish('e$u2','e$u3') ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( product1('e$u3','e$u2','e$u1')
| equalish('e$u2','e$u3') ),
inference(resolution,[status(thm)],[c17,d4]) ).
cnf(d6,plain,
product1('e$u3','e$u2','e$u1'),
inference(resolution,[status(thm)],[c22,d5]) ).
cnf(d7,plain,
( ~ product1(X0,'e$u2','e$u1')
| equalish('e$u3',X0) ),
inference(resolution,[status(thm)],[d6,c28]) ).
cnf(d8,plain,
( ~ product2(X0,X0,X1)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c31,c34]) ).
cnf(d9,plain,
( product2(X0,'e$u3','e$u2')
| ~ product1('e$u1','e$u2',X0) ),
inference(resolution,[status(thm)],[d6,c35]) ).
cnf(d10,plain,
( product1('e$u1','e$u2','e$u2')
| product1('e$u1','e$u2','e$u1')
| ~ 'group$uelement'('e$u2')
| ~ 'group$uelement'('e$u1')
| product2('e$u3','e$u3','e$u2') ),
inference(resolution,[status(thm)],[d9,c25]) ).
cnf(d11,plain,
( product2('e$u3','e$u3','e$u2')
| product1('e$u1','e$u2','e$u2')
| product1('e$u1','e$u2','e$u1')
| ~ 'group$uelement'('e$u2') ),
inference(resolution,[status(thm)],[c16,d10]) ).
cnf(d12,plain,
( product2('e$u3','e$u3','e$u2')
| product1('e$u1','e$u2','e$u2')
| product1('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[c17,d11]) ).
cnf(d13,plain,
( equalish('e$u3','e$u2')
| product1('e$u1','e$u2','e$u2')
| product1('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( product1('e$u1','e$u2','e$u2')
| product1('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[c24,d13]) ).
cnf(d15,plain,
( equalish('e$u2','e$u1')
| product1('e$u1','e$u2','e$u1') ),
inference(resolution,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
product1('e$u1','e$u2','e$u1'),
inference(resolution,[status(thm)],[c21,d15]) ).
cnf(d17,plain,
equalish('e$u3','e$u1'),
inference(resolution,[status(thm)],[d16,d7]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[c23,d17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP123-8.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n011.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 14:24:28 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.87/3.20 % SZS status Unsatisfiable for theBenchmark.p
% 10.87/3.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------