%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN008-1 : TPTP v9.3.1. Released v1.0.0.
% 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 07:31:47 AM UTC 2026
% Result : Unsatisfiable 12.05s 2.13s
% Output : CNFRefutation 12.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 20 unt; 0 nHn; 29 RR)
% Number of literals : 70 ( 5 equ; 36 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 59 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(aLEb,hypothesis,
'less$uequal'(a,b) ).
cnf(aQc,hypothesis,
quotient(a,c,aQc) ).
cnf(bQc,hypothesis,
quotient(b,c,bQc) ).
cnf(prove_aQcLEbQc,negated_conjecture,
~ 'less$uequal'(aQc,bQc) ).
cnf(quotient_less_equal,axiom,
( quotient(X0,X1,zero)
| ~ 'less$uequal'(X0,X1) ) ).
cnf(less_equal_quotient,axiom,
( 'less$uequal'(X0,X1)
| ~ quotient(X0,X1,zero) ) ).
cnf(divisor_existence,axiom,
( 'less$uequal'(X2,X0)
| ~ quotient(X0,X1,X2) ) ).
cnf(quotient_property,axiom,
( 'less$uequal'(X6,X7)
| ~ quotient(X2,X3,X7)
| ~ quotient(X5,X4,X6)
| ~ quotient(X0,X3,X5)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X1,X2) ) ).
cnf(zero_is_smallest,axiom,
'less$uequal'(zero,X0) ).
cnf(less_equal_and_equal,axiom,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ) ).
cnf(closure,axiom,
quotient(X0,X1,divide(X0,X1)) ).
cnf(c0,plain,
'less$uequal'(a,b),
inference(clausification,[status(esa)],[aLEb]) ).
cnf(c1,plain,
quotient(a,c,aQc),
inference(clausification,[status(esa)],[aQc]) ).
cnf(c2,plain,
quotient(b,c,bQc),
inference(clausification,[status(esa)],[bQc]) ).
cnf(c3,plain,
~ 'less$uequal'(aQc,bQc),
inference(clausification,[status(esa)],[prove_aQcLEbQc]) ).
cnf(c4,plain,
( quotient(X0,X1,zero)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[quotient_less_equal]) ).
cnf(c5,plain,
( 'less$uequal'(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(clausification,[status(esa)],[less_equal_quotient]) ).
cnf(c6,plain,
( 'less$uequal'(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(clausification,[status(esa)],[divisor_existence]) ).
cnf(c7,plain,
( ~ quotient(X7,X5,X3)
| ~ quotient(X6,X5,X2)
| ~ quotient(X6,X7,X4)
| ~ quotient(X4,X5,X1)
| ~ quotient(X2,X3,X0)
| 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c8,plain,
'less$uequal'(zero,X0),
inference(clausification,[status(esa)],[zero_is_smallest]) ).
cnf(c9,plain,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[less_equal_and_equal]) ).
cnf(c11,plain,
quotient(X0,X1,divide(X0,X1)),
inference(clausification,[status(esa)],[closure]) ).
cnf(d0,plain,
( ~ 'less$uequal'(X0,zero)
| X0 = zero ),
inference(resolution,[status(thm)],[c9,c8]) ).
cnf(d1,plain,
'less$uequal'(divide(X0,X1),X0),
inference(resolution,[status(thm)],[c6,c11]) ).
cnf(d2,plain,
divide(zero,X0) = zero,
inference(resolution,[status(thm)],[d0,d1]) ).
cnf(d3,plain,
quotient(zero,X0,zero),
inference(superposition,[status(thm)],[d2,c11]) ).
cnf(d4,plain,
( ~ quotient(a,X2,X4)
| ~ quotient(aQc,X3,X0)
| ~ quotient(X4,c,X1)
| ~ quotient(X2,c,X3)
| 'less$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d5,plain,
( ~ quotient(a,X3,X2)
| ~ quotient(X3,c,X0)
| ~ quotient(X2,c,X1)
| 'less$uequal'(divide(aQc,X0),X1) ),
inference(resolution,[status(thm)],[d4,c11]) ).
cnf(d6,plain,
( ~ 'less$uequal'(a,X2)
| ~ quotient(zero,c,X1)
| ~ quotient(X2,c,X0)
| 'less$uequal'(divide(aQc,X0),X1) ),
inference(resolution,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
( ~ quotient(X0,c,X1)
| 'less$uequal'(divide(aQc,X1),zero)
| ~ 'less$uequal'(a,X0) ),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
( 'less$uequal'(divide(aQc,bQc),zero)
| ~ 'less$uequal'(a,b) ),
inference(resolution,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
'less$uequal'(divide(aQc,bQc),zero),
inference(resolution,[status(thm)],[c0,d8]) ).
cnf(d10,plain,
divide(aQc,bQc) = zero,
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
quotient(aQc,bQc,zero),
inference(superposition,[status(thm)],[d10,c11]) ).
cnf(d12,plain,
'less$uequal'(aQc,bQc),
inference(resolution,[status(thm)],[d11,c5]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c3,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n014.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 15:57:02 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.05/2.13 % SZS status Unsatisfiable for theBenchmark.p
% 12.05/2.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------