%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN009-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 07:31:48 AM UTC 2026
% Result : Unsatisfiable 13.61s 12.13s
% Output : CNFRefutation 13.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 31 ( 16 unt; 0 nHn; 28 RR)
% Number of literals : 59 ( 5 equ; 31 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 37 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(x_divide_x_is_zero,axiom,
quotient(X0,X0,zero) ).
cnf(xQyLEz_implies_xQzLEy,axiom,
( 'less$uequal'(X4,X1)
| ~ quotient(X0,X3,X4)
| ~ 'less$uequal'(X2,X3)
| ~ quotient(X0,X1,X2) ) ).
cnf(xLEy_implies_zQyLEzQx,axiom,
( 'less$uequal'(X3,X4)
| ~ quotient(X2,X0,X4)
| ~ quotient(X2,X1,X3)
| ~ 'less$uequal'(X0,X1) ) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,'idQ$uidQa') ).
cnf(identity_divide_idQ_idQa,hypothesis,
quotient(identity,'idQ$uidQa','idQ$u$uidQ$uidQa') ).
cnf(prove_one_inversion_equals_three,negated_conjecture,
idQa != 'idQ$u$uidQ$uidQa' ).
cnf(less_equal_quotient,axiom,
( 'less$uequal'(X0,X1)
| ~ quotient(X0,X1,zero) ) ).
cnf(less_equal_and_equal,axiom,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ) ).
cnf(c2,plain,
quotient(X0,X0,zero),
inference(clausification,[status(esa)],[x_divide_x_is_zero]) ).
cnf(c5,plain,
( 'less$uequal'(X4,X1)
| ~ quotient(X0,X3,X4)
| ~ 'less$uequal'(X2,X3)
| ~ quotient(X0,X1,X2) ),
inference(clausification,[status(esa)],[xQyLEz_implies_xQzLEy]) ).
cnf(c6,plain,
( 'less$uequal'(X3,X4)
| ~ quotient(X2,X0,X4)
| ~ quotient(X2,X1,X3)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[xLEy_implies_zQyLEzQx]) ).
cnf(c8,plain,
quotient(identity,a,idQa),
inference(clausification,[status(esa)],[identity_divide_a]) ).
cnf(c9,plain,
quotient(identity,idQa,'idQ$uidQa'),
inference(clausification,[status(esa)],[identity_divide_idQa]) ).
cnf(c10,plain,
quotient(identity,'idQ$uidQa','idQ$u$uidQ$uidQa'),
inference(clausification,[status(esa)],[identity_divide_idQ_idQa]) ).
cnf(c11,plain,
idQa != 'idQ$u$uidQ$uidQa',
inference(clausification,[status(esa)],[prove_one_inversion_equals_three]) ).
cnf(c13,plain,
( 'less$uequal'(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(clausification,[status(esa)],[less_equal_quotient]) ).
cnf(c17,plain,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[less_equal_and_equal]) ).
cnf(d0,plain,
( ~ 'less$uequal'('idQ$uidQa',X0)
| 'less$uequal'(X1,idQa)
| ~ quotient(identity,X0,X1) ),
inference(resolution,[status(thm)],[c9,c5]) ).
cnf(d1,plain,
( ~ 'less$uequal'('idQ$uidQa','idQ$uidQa')
| 'less$uequal'('idQ$u$uidQ$uidQa',idQa) ),
inference(resolution,[status(thm)],[d0,c10]) ).
cnf(d2,plain,
'less$uequal'(X0,X0),
inference(resolution,[status(thm)],[c13,c2]) ).
cnf(d3,plain,
'less$uequal'('idQ$u$uidQ$uidQa',idQa),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ 'less$uequal'(idQa,'idQ$u$uidQ$uidQa')
| idQa = 'idQ$u$uidQ$uidQa' ),
inference(resolution,[status(thm)],[d3,c17]) ).
cnf(d5,plain,
~ 'less$uequal'(idQa,'idQ$u$uidQ$uidQa'),
inference(resolution,[status(thm)],[c11,d4]) ).
cnf(d6,plain,
( ~ 'less$uequal'('idQ$uidQa',X0)
| 'less$uequal'(X1,'idQ$u$uidQ$uidQa')
| ~ quotient(identity,X0,X1) ),
inference(resolution,[status(thm)],[c10,c6]) ).
cnf(d7,plain,
( ~ 'less$uequal'('idQ$uidQa',a)
| 'less$uequal'(idQa,'idQ$u$uidQ$uidQa') ),
inference(resolution,[status(thm)],[d6,c8]) ).
cnf(d8,plain,
( ~ 'less$uequal'(idQa,X0)
| 'less$uequal'(X1,a)
| ~ quotient(identity,X0,X1) ),
inference(resolution,[status(thm)],[c5,c8]) ).
cnf(d9,plain,
( ~ 'less$uequal'(idQa,idQa)
| 'less$uequal'('idQ$uidQa',a) ),
inference(resolution,[status(thm)],[d8,c9]) ).
cnf(d10,plain,
'less$uequal'('idQ$uidQa',a),
inference(resolution,[status(thm)],[d2,d9]) ).
cnf(d11,plain,
'less$uequal'(idQa,'idQ$u$uidQ$uidQa'),
inference(resolution,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN009-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n020.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Fri Sep 25 15:58:30 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.61/12.13 % SZS status Unsatisfiable for theBenchmark.p
% 13.61/12.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------