TSTP Solution File: HEN007-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN007-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 12:58:38 EDT 2022
% Result : Unsatisfiable 0.19s 0.58s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 15 unt; 0 nHn; 26 RR)
% Number of literals : 61 ( 0 equ; 30 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(less_equal_quotient,axiom,
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ) ).
cnf(closure,axiom,
quotient(X,Y,divide(X,Y)) ).
cnf(x_divide_x_is_zero,axiom,
quotient(X,X,zero) ).
cnf(transitivity_of_less_equal,axiom,
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) ) ).
cnf(xQyLEz_implies_xQzLEy,axiom,
( ~ quotient(X,Y,W1)
| ~ less_equal(W1,Z)
| ~ quotient(X,Z,W2)
| less_equal(W2,Y) ) ).
cnf(xLEy,hypothesis,
less_equal(x,y) ).
cnf(zQy,hypothesis,
quotient(z,y,zQy) ).
cnf(zQx,hypothesis,
quotient(z,x,zQx) ).
cnf(prove_zQyLEzQx,negated_conjecture,
~ less_equal(zQy,zQx) ).
cnf(refute_0_0,plain,
( ~ less_equal(X_31,x)
| ~ less_equal(x,y)
| less_equal(X_31,y) ),
inference(subst,[],[transitivity_of_less_equal:[bind(X,$fot(X_31)),bind(Y,$fot(x)),bind(Z,$fot(y))]]) ).
cnf(refute_0_1,plain,
( ~ less_equal(X_31,x)
| less_equal(X_31,y) ),
inference(resolve,[$cnf( less_equal(x,y) )],[xLEy,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ less_equal(divide(z,zQx),x)
| less_equal(divide(z,zQx),y) ),
inference(subst,[],[refute_0_1:[bind(X_31,$fot(divide(z,zQx)))]]) ).
cnf(refute_0_3,plain,
quotient(X_9,X_9,zero),
inference(subst,[],[x_divide_x_is_zero:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_4,plain,
( ~ quotient(X_9,X_9,zero)
| less_equal(X_9,X_9) ),
inference(subst,[],[less_equal_quotient:[bind(X,$fot(X_9)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_5,plain,
less_equal(X_9,X_9),
inference(resolve,[$cnf( quotient(X_9,X_9,zero) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
less_equal(zQx,zQx),
inference(subst,[],[refute_0_5:[bind(X_9,$fot(zQx))]]) ).
cnf(refute_0_7,plain,
quotient(z,X_533,divide(z,X_533)),
inference(subst,[],[closure:[bind(X,$fot(z)),bind(Y,$fot(X_533))]]) ).
cnf(refute_0_8,plain,
( ~ less_equal(zQx,X_522)
| ~ quotient(z,X_522,X_519)
| ~ quotient(z,x,zQx)
| less_equal(X_519,x) ),
inference(subst,[],[xQyLEz_implies_xQzLEy:[bind(W1,$fot(zQx)),bind(W2,$fot(X_519)),bind(X,$fot(z)),bind(Y,$fot(x)),bind(Z,$fot(X_522))]]) ).
cnf(refute_0_9,plain,
( ~ less_equal(zQx,X_522)
| ~ quotient(z,X_522,X_519)
| less_equal(X_519,x) ),
inference(resolve,[$cnf( quotient(z,x,zQx) )],[zQx,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ less_equal(zQx,X_533)
| ~ quotient(z,X_533,divide(z,X_533))
| less_equal(divide(z,X_533),x) ),
inference(subst,[],[refute_0_9:[bind(X_519,$fot(divide(z,X_533))),bind(X_522,$fot(X_533))]]) ).
cnf(refute_0_11,plain,
( ~ less_equal(zQx,X_533)
| less_equal(divide(z,X_533),x) ),
inference(resolve,[$cnf( quotient(z,X_533,divide(z,X_533)) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ less_equal(zQx,zQx)
| less_equal(divide(z,zQx),x) ),
inference(subst,[],[refute_0_11:[bind(X_533,$fot(zQx))]]) ).
cnf(refute_0_13,plain,
less_equal(divide(z,zQx),x),
inference(resolve,[$cnf( less_equal(zQx,zQx) )],[refute_0_6,refute_0_12]) ).
cnf(refute_0_14,plain,
less_equal(divide(z,zQx),y),
inference(resolve,[$cnf( less_equal(divide(z,zQx),x) )],[refute_0_13,refute_0_2]) ).
cnf(refute_0_15,plain,
quotient(z,X_563,divide(z,X_563)),
inference(subst,[],[closure:[bind(X,$fot(z)),bind(Y,$fot(X_563))]]) ).
cnf(refute_0_16,plain,
( ~ less_equal(X_518,y)
| ~ quotient(z,X_521,X_518)
| ~ quotient(z,y,zQy)
| less_equal(zQy,X_521) ),
inference(subst,[],[xQyLEz_implies_xQzLEy:[bind(W1,$fot(X_518)),bind(W2,$fot(zQy)),bind(X,$fot(z)),bind(Y,$fot(X_521)),bind(Z,$fot(y))]]) ).
cnf(refute_0_17,plain,
( ~ less_equal(X_518,y)
| ~ quotient(z,X_521,X_518)
| less_equal(zQy,X_521) ),
inference(resolve,[$cnf( quotient(z,y,zQy) )],[zQy,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ less_equal(divide(z,X_563),y)
| ~ quotient(z,X_563,divide(z,X_563))
| less_equal(zQy,X_563) ),
inference(subst,[],[refute_0_17:[bind(X_518,$fot(divide(z,X_563))),bind(X_521,$fot(X_563))]]) ).
cnf(refute_0_19,plain,
( ~ less_equal(divide(z,X_563),y)
| less_equal(zQy,X_563) ),
inference(resolve,[$cnf( quotient(z,X_563,divide(z,X_563)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ less_equal(divide(z,zQx),y)
| less_equal(zQy,zQx) ),
inference(subst,[],[refute_0_19:[bind(X_563,$fot(zQx))]]) ).
cnf(refute_0_21,plain,
less_equal(zQy,zQx),
inference(resolve,[$cnf( less_equal(divide(z,zQx),y) )],[refute_0_14,refute_0_20]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( less_equal(zQy,zQx) )],[refute_0_21,prove_zQyLEzQx]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : HEN007-2 : TPTP v8.1.0. Released v1.0.0.
% 0.09/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 1 13:35:58 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.58
% 0.19/0.58 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.58
%------------------------------------------------------------------------------