%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP123-3.003 : 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 : n014.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 07:22:23 AM UTC 2026
% Result : Unsatisfiable 7.28s 3.54s
% Output : CNFRefutation 7.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 39 ( 19 unt; 9 nHn; 37 RR)
% Number of literals : 90 ( 0 equ; 43 neg)
% Maximal clause size : 6 ( 2 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 : 49 ( 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_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(product_total_function1,axiom,
( product(X0,X1,'e$u3')
| product(X0,X1,'e$u2')
| product(X0,X1,'e$u1')
| ~ 'group$uelement'(X1)
| ~ 'group$uelement'(X0) ) ).
cnf(product_right_cancellation,axiom,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ) ).
cnf(product_left_cancellation,axiom,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ) ).
cnf(product_idempotence,axiom,
product(X0,X0,X0) ).
cnf(qg1_2,negated_conjecture,
( equalish(X1,X4)
| ~ product(X5,X4,X3)
| ~ product(X5,X1,X0)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ) ).
cnf(c16,plain,
'group$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$u3'),
inference(clausification,[status(esa)],[element_3]) ).
cnf(c20,plain,
~ equalish('e$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$u3'),
inference(clausification,[status(esa)],[e_2_is_not_e_3]) ).
cnf(c25,plain,
( product(X0,X1,'e$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(c27,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_right_cancellation]) ).
cnf(c28,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_left_cancellation]) ).
cnf(c29,plain,
product(X0,X0,X0),
inference(clausification,[status(esa)],[product_idempotence]) ).
cnf(c31,plain,
( ~ product(X0,X3,X4)
| ~ product(X2,X1,X5)
| ~ product(X4,X3,X5)
| equalish(X3,X1)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[qg1_2]) ).
cnf(d0,plain,
( ~ product(X0,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c27,c29]) ).
cnf(d1,plain,
( product(X0,X2,'e$u2')
| product(X0,X2,'e$u1')
| ~ 'group$uelement'(X2)
| ~ 'group$uelement'(X0)
| ~ product(X1,X2,'e$u3')
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c28,c25]) ).
cnf(d2,plain,
( product(X0,'e$u3','e$u2')
| product(X0,'e$u3','e$u1')
| ~ 'group$uelement'(X0)
| ~ 'group$uelement'('e$u3')
| equalish(X0,'e$u3') ),
inference(resolution,[status(thm)],[d1,c29]) ).
cnf(d3,plain,
( product(X0,'e$u3','e$u2')
| product(X0,'e$u3','e$u1')
| ~ 'group$uelement'(X0)
| equalish(X0,'e$u3') ),
inference(resolution,[status(thm)],[c18,d2]) ).
cnf(d4,plain,
( equalish('e$u2','e$u3')
| product('e$u2','e$u3','e$u1')
| ~ 'group$uelement'('e$u2')
| equalish('e$u2','e$u3') ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( product('e$u2','e$u3','e$u1')
| equalish('e$u2','e$u3') ),
inference(resolution,[status(thm)],[c17,d4]) ).
cnf(d6,plain,
product('e$u2','e$u3','e$u1'),
inference(resolution,[status(thm)],[c22,d5]) ).
cnf(d7,plain,
( ~ product(X0,'e$u3','e$u1')
| equalish('e$u2',X0) ),
inference(resolution,[status(thm)],[d6,c28]) ).
cnf(d8,plain,
( ~ product(X3,X1,X0)
| ~ product(X2,X0,X0)
| ~ product(X2,X1,X3)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c31,c29]) ).
cnf(d9,plain,
( ~ product(X0,X1,X2)
| ~ product(X2,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[d8,c29]) ).
cnf(d10,plain,
( ~ product('e$u1','e$u3','e$u2')
| equalish('e$u2','e$u3') ),
inference(resolution,[status(thm)],[d6,d9]) ).
cnf(d11,plain,
~ product('e$u1','e$u3','e$u2'),
inference(resolution,[status(thm)],[c22,d10]) ).
cnf(d12,plain,
( product('e$u1','e$u3','e$u1')
| ~ 'group$uelement'('e$u1')
| equalish('e$u1','e$u3') ),
inference(resolution,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
( product('e$u1','e$u3','e$u1')
| equalish('e$u1','e$u3') ),
inference(resolution,[status(thm)],[c16,d12]) ).
cnf(d14,plain,
product('e$u1','e$u3','e$u1'),
inference(resolution,[status(thm)],[c20,d13]) ).
cnf(d15,plain,
equalish('e$u2','e$u1'),
inference(resolution,[status(thm)],[d14,d7]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[c21,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP123-3.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n014.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 14:23:33 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.28/3.54 % SZS status Unsatisfiable for theBenchmark.p
% 7.28/3.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------