%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN007-1 : 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 : n018.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 07:31:46 AM UTC 2026
% Result : Unsatisfiable 32.46s 4.35s
% Output : CNFRefutation 32.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of clauses : 77 ( 41 unt; 0 nHn; 55 RR)
% Number of literals : 146 ( 26 equ; 71 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 4 ( 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 : 149 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(xLEy,hypothesis,
'less$uequal'(x,y) ).
cnf(zQy,hypothesis,
quotient(z,y,zQy) ).
cnf(zQx,hypothesis,
quotient(z,x,zQx) ).
cnf(prove_zQyLEzQx,negated_conjecture,
~ 'less$uequal'(zQy,zQx) ).
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$uequal'(X0,X1) ) ).
cnf(closure,axiom,
quotient(X0,X1,divide(X0,X1)) ).
cnf(well_defined,axiom,
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ) ).
cnf(c0,plain,
'less$uequal'(x,y),
inference(clausification,[status(esa)],[xLEy]) ).
cnf(c1,plain,
quotient(z,y,zQy),
inference(clausification,[status(esa)],[zQy]) ).
cnf(c2,plain,
quotient(z,x,zQx),
inference(clausification,[status(esa)],[zQx]) ).
cnf(c3,plain,
~ 'less$uequal'(zQy,zQx),
inference(clausification,[status(esa)],[prove_zQyLEzQx]) ).
cnf(c4,plain,
( quotient(X0,X1,zero)
| ~ 'less$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(c12,plain,
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(clausification,[status(esa)],[well_defined]) ).
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,
( ~ 'less$uequal'(X0,divide(X0,X1))
| X0 = divide(X0,X1) ),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
divide(zero,X0) = zero,
inference(resolution,[status(thm)],[d0,d1]) ).
cnf(d4,plain,
quotient(zero,X0,zero),
inference(superposition,[status(thm)],[d3,c11]) ).
cnf(d5,plain,
( ~ quotient(X6,X2,X5)
| ~ quotient(divide(X6,X3),X4,X0)
| ~ quotient(X5,X3,X1)
| ~ quotient(X2,X3,X4)
| 'less$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[c7,c11]) ).
cnf(d6,plain,
( ~ quotient(X4,X1,X2)
| ~ quotient(X5,X1,X3)
| ~ quotient(X0,X4,X5)
| 'less$uequal'(divide(divide(X0,X1),X2),X3) ),
inference(resolution,[status(thm)],[d5,c11]) ).
cnf(d7,plain,
( ~ quotient(X4,X1,X2)
| ~ quotient(divide(X0,X4),X1,X3)
| 'less$uequal'(divide(divide(X0,X1),X2),X3) ),
inference(resolution,[status(thm)],[d6,c11]) ).
cnf(d8,plain,
( ~ 'less$uequal'(divide(X0,X3),X1)
| ~ quotient(X3,X1,X2)
| 'less$uequal'(divide(divide(X0,X1),X2),zero) ),
inference(resolution,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
( ~ quotient(X2,X0,X1)
| 'less$uequal'(divide(divide(X0,X0),X1),zero) ),
inference(resolution,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
'less$uequal'(divide(divide(X0,X0),zero),zero),
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
divide(divide(X0,X0),zero) = zero,
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
quotient(divide(X0,X0),zero,zero),
inference(superposition,[status(thm)],[d11,c11]) ).
cnf(d13,plain,
'less$uequal'(divide(X0,X0),zero),
inference(resolution,[status(thm)],[d12,c5]) ).
cnf(d14,plain,
divide(X0,X0) = zero,
inference(resolution,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
( ~ quotient(X3,X1,X2)
| 'less$uequal'(divide(divide(X0,X1),X2),divide(divide(X0,X3),X1)) ),
inference(resolution,[status(thm)],[d7,c11]) ).
cnf(d16,plain,
( ~ 'less$uequal'(divide(divide(X3,X0),X1),divide(divide(X3,X1),X2))
| divide(divide(X3,X0),X1) = divide(divide(X3,X1),X2)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[d15,c9]) ).
cnf(d17,plain,
( ~ quotient(X1,divide(X0,X1),X2)
| divide(divide(X0,X1),divide(X0,X1)) = divide(divide(X0,divide(X0,X1)),X2)
| ~ 'less$uequal'(zero,divide(divide(X0,divide(X0,X1)),X2)) ),
inference(superposition,[status(thm)],[d14,d16]) ).
cnf(d18,plain,
( ~ quotient(X1,divide(X0,X1),X2)
| ~ 'less$uequal'(zero,divide(divide(X0,divide(X0,X1)),X2))
| zero = divide(divide(X0,divide(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[d17,d14]) ).
cnf(d19,plain,
( ~ quotient(X1,divide(X0,X1),X2)
| zero = divide(divide(X0,divide(X0,X1)),X2) ),
inference(resolution,[status(thm)],[c8,d18]) ).
cnf(d20,plain,
zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[d19,d4]) ).
cnf(d21,plain,
quotient(divide(X0,divide(X0,zero)),zero,zero),
inference(superposition,[status(thm)],[d20,c11]) ).
cnf(d22,plain,
'less$uequal'(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[d21,c5]) ).
cnf(d23,plain,
divide(X0,divide(X0,zero)) = zero,
inference(resolution,[status(thm)],[d22,d0]) ).
cnf(d24,plain,
quotient(X0,divide(X0,zero),zero),
inference(superposition,[status(thm)],[d23,c11]) ).
cnf(d25,plain,
'less$uequal'(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d24,c5]) ).
cnf(d26,plain,
X0 = divide(X0,zero),
inference(resolution,[status(thm)],[d25,d2]) ).
cnf(d27,plain,
( ~ 'less$uequal'(X0,X4)
| ~ quotient(X4,X1,X2)
| ~ quotient(zero,X1,X3)
| 'less$uequal'(divide(divide(X0,X1),X2),X3) ),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d28,plain,
( ~ quotient(X1,X2,X3)
| 'less$uequal'(divide(divide(X0,X2),X3),zero)
| ~ 'less$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[d27,d4]) ).
cnf(d29,plain,
( ~ 'less$uequal'(X1,X2)
| ~ quotient(X1,X2,X0)
| X0 = zero ),
inference(resolution,[status(thm)],[c12,c4]) ).
cnf(d30,plain,
( ~ 'less$uequal'(X0,X1)
| divide(X0,X1) = zero ),
inference(resolution,[status(thm)],[d29,c11]) ).
cnf(d31,plain,
divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[d30,d1]) ).
cnf(d32,plain,
quotient(divide(X0,X1),X0,zero),
inference(superposition,[status(thm)],[d31,c11]) ).
cnf(d33,plain,
( 'less$uequal'(divide(divide(X0,X1),zero),zero)
| ~ 'less$uequal'(X0,divide(X1,X2)) ),
inference(resolution,[status(thm)],[d32,d28]) ).
cnf(d34,plain,
divide(x,y) = zero,
inference(resolution,[status(thm)],[d30,c0]) ).
cnf(d35,plain,
quotient(x,y,zero),
inference(superposition,[status(thm)],[d34,c11]) ).
cnf(d36,plain,
( ~ quotient(X1,X2,X0)
| X0 = divide(X1,X2) ),
inference(resolution,[status(thm)],[c12,c11]) ).
cnf(d37,plain,
( ~ 'less$uequal'(X0,X1)
| zero = divide(X0,X1) ),
inference(resolution,[status(thm)],[d36,c4]) ).
cnf(d38,plain,
( ~ quotient(z,X2,X4)
| ~ quotient(zQy,X3,X0)
| ~ quotient(X4,y,X1)
| ~ quotient(X2,y,X3)
| 'less$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d39,plain,
( ~ quotient(z,X3,X2)
| ~ quotient(X3,y,X0)
| ~ quotient(X2,y,X1)
| 'less$uequal'(divide(zQy,X0),X1) ),
inference(resolution,[status(thm)],[d38,c11]) ).
cnf(d40,plain,
( ~ quotient(zQx,y,X1)
| ~ quotient(x,y,X0)
| 'less$uequal'(divide(zQy,X0),X1) ),
inference(resolution,[status(thm)],[d39,c2]) ).
cnf(d41,plain,
( zero = divide(divide(zQy,X0),X1)
| ~ quotient(zQx,y,X1)
| ~ quotient(x,y,X0) ),
inference(resolution,[status(thm)],[d40,d37]) ).
cnf(d42,plain,
( ~ quotient(x,y,X0)
| zero = divide(divide(zQy,X0),divide(zQx,y)) ),
inference(resolution,[status(thm)],[d41,c11]) ).
cnf(d43,plain,
zero = divide(divide(zQy,zero),divide(zQx,y)),
inference(resolution,[status(thm)],[d42,d35]) ).
cnf(d44,plain,
quotient(divide(zQy,zero),divide(zQx,y),zero),
inference(superposition,[status(thm)],[d43,c11]) ).
cnf(d45,plain,
'less$uequal'(divide(zQy,zero),divide(zQx,y)),
inference(resolution,[status(thm)],[d44,c5]) ).
cnf(d46,plain,
'less$uequal'(divide(divide(divide(zQy,zero),zQx),zero),zero),
inference(resolution,[status(thm)],[d45,d33]) ).
cnf(d47,plain,
'less$uequal'(divide(divide(zQy,zero),zQx),zero),
inference(demodulation,[status(thm)],[d46,d26]) ).
cnf(d48,plain,
'less$uequal'(divide(zQy,zQx),zero),
inference(demodulation,[status(thm)],[d47,d26]) ).
cnf(d49,plain,
divide(zQy,zQx) = zero,
inference(resolution,[status(thm)],[d48,d0]) ).
cnf(d50,plain,
quotient(zQy,zQx,zero),
inference(superposition,[status(thm)],[d49,c11]) ).
cnf(d51,plain,
'less$uequal'(zQy,zQx),
inference(resolution,[status(thm)],[d50,c5]) ).
cnf(d52,plain,
$false,
inference(resolution,[status(thm)],[c3,d51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.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 15:59:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.46/4.35 % SZS status Unsatisfiable for theBenchmark.p
% 32.46/4.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------