%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(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 : Thu Sep 24 12:45:20 PM UTC 2026
% Result : Unsatisfiable 3.22s 0.85s
% Output : CNFRefutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 45 unt; 0 def)
% Number of atoms : 137 ( 19 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 126 ( 64 ~; 62 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 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 : 148 ( 148 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : less_equal(zero,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
less_equal(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
quotient(z,y,zQy),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
quotient(z,x,zQx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ less_equal(zQy,zQx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X,Z] :
( less_equal(Z,X)
| ! [Y] : ~ quotient(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f17,plain,
! [X0,X1,X2] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [V4,V5] :
( less_equal(V4,V5)
| ! [V1,Z] :
( ~ quotient(V1,Z,V5)
| ! [V2,V3] :
( ~ quotient(V3,V2,V4)
| ! [X] :
( ~ quotient(X,Z,V3)
| ! [Y] :
( ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f19,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( less_equal(X6,X7)
| ~ quotient(X2,X3,X7)
| ~ quotient(X5,X4,X6)
| ~ quotient(X0,X3,X5)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
less_equal(x,y),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
quotient(z,y,zQy),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
quotient(z,x,zQx),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
~ less_equal(zQy,zQx),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(X3,X4)
| ~ quotient(zQx,X0,X4)
| ~ quotient(X2,X1,X3)
| ~ quotient(z,X0,X2)
| ~ quotient(x,X0,X1) ),
inference(resolution,[status(thm)],[f19,f28]) ).
fof(f36,plain,
! [X0] :
( zero = X0
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f20,f21]) ).
fof(f38,plain,
! [X0] : quotient(zero,X0,zero),
inference(resolution,[status(thm)],[f14,f20]) ).
fof(f43,plain,
quotient(x,y,zero),
inference(resolution,[status(thm)],[f26,f14]) ).
fof(f53,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( less_equal(X5,X6)
| ~ quotient(divide(X3,X0),X1,X6)
| ~ quotient(X4,X2,X5)
| ~ quotient(X3,X1,X4)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f23,f19]) ).
fof(f54,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f23,f17]) ).
fof(f55,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[status(thm)],[f54,f36]) ).
fof(f56,plain,
! [X0,X1] : quotient(divide(X0,X1),X0,zero),
inference(resolution,[status(thm)],[f54,f14]) ).
fof(f57,plain,
! [X0,X1] :
( divide(X0,X1) = X0
| ~ less_equal(X0,divide(X0,X1)) ),
inference(resolution,[status(thm)],[f54,f21]) ).
fof(f65,plain,
! [X0,X1,X2] :
( less_equal(X1,X2)
| ~ quotient(zQx,y,X2)
| ~ quotient(X0,zero,X1)
| ~ quotient(z,y,X0) ),
inference(resolution,[status(thm)],[f43,f32]) ).
fof(f77,plain,
! [X0,X1,X2] :
( zero = X2
| ~ quotient(divide(X0,X1),X0,X2) ),
inference(resolution,[status(thm)],[f25,f56]) ).
fof(f85,plain,
! [X0,X1,X2] :
( divide(X0,X1) = X2
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f25,f23]) ).
fof(f100,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(X3,X4)
| ~ quotient(divide(X0,zero),X1,X4)
| ~ quotient(X2,zero,X3)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f53,f38]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4,X5] :
( less_equal(X4,X5)
| ~ quotient(divide(X0,X3),X1,X5)
| ~ quotient(X2,divide(X3,X1),X4)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f53,f23]) ).
fof(f117,plain,
! [X0,X1] : zero = divide(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f77,f23]) ).
fof(f240,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(zQx,y,X1)
| ~ quotient(zQy,zero,X0) ),
inference(resolution,[status(thm)],[f65,f27]) ).
fof(f245,plain,
! [X0] :
( less_equal(divide(zQy,zero),X0)
| ~ quotient(zQx,y,X0) ),
inference(resolution,[status(thm)],[f240,f23]) ).
fof(f246,plain,
less_equal(divide(zQy,zero),divide(zQx,y)),
inference(resolution,[status(thm)],[f245,f23]) ).
fof(f247,plain,
quotient(divide(zQy,zero),divide(zQx,y),zero),
inference(resolution,[status(thm)],[f246,f14]) ).
fof(f250,plain,
divide(divide(zQy,zero),divide(zQx,y)) = zero,
inference(resolution,[status(thm)],[f247,f85]) ).
fof(f316,plain,
! [X0,X1,X2,X3] :
( less_equal(X2,X3)
| ~ quotient(divide(X0,zero),X1,X3)
| ~ quotient(divide(X0,X1),zero,X2) ),
inference(resolution,[status(thm)],[f100,f23]) ).
fof(f425,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(X3,X4)
| ~ quotient(divide(X0,X2),X1,X4)
| ~ quotient(divide(X0,X1),divide(X2,X1),X3) ),
inference(resolution,[status(thm)],[f104,f23]) ).
fof(f567,plain,
! [X0,X1,X2] :
( less_equal(divide(divide(X0,X1),zero),X2)
| ~ quotient(divide(X0,zero),X1,X2) ),
inference(resolution,[status(thm)],[f316,f23]) ).
fof(f588,plain,
! [X0] : less_equal(divide(divide(X0,X0),zero),zero),
inference(resolution,[status(thm)],[f567,f56]) ).
fof(f598,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(resolution,[status(thm)],[f588,f36]) ).
fof(f632,plain,
! [X0] : quotient(divide(X0,X0),zero,zero),
inference(paramodulation,[status(thm)],[f598,f23]) ).
fof(f638,plain,
! [X0] : less_equal(divide(X0,X0),zero),
inference(resolution,[status(thm)],[f632,f15]) ).
fof(f655,plain,
! [X0] : zero = divide(X0,X0),
inference(resolution,[status(thm)],[f638,f36]) ).
fof(f697,plain,
! [X0] : quotient(X0,X0,zero),
inference(paramodulation,[status(thm)],[f655,f23]) ).
fof(f718,plain,
! [X0] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(resolution,[status(thm)],[f697,f567]) ).
fof(f786,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[f718,f36]) ).
fof(f816,plain,
! [X0] : quotient(divide(X0,divide(X0,zero)),zero,zero),
inference(paramodulation,[status(thm)],[f786,f23]) ).
fof(f823,plain,
! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[f816,f15]) ).
fof(f846,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f823,f36]) ).
fof(f885,plain,
! [X0] : quotient(X0,divide(X0,zero),zero),
inference(paramodulation,[status(thm)],[f846,f23]) ).
fof(f907,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f885,f15]) ).
fof(f925,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[status(thm)],[f907,f57]) ).
fof(f951,plain,
divide(zQy,divide(zQx,y)) = zero,
inference(backward_demodulation,[status(thm)],[f925,f250]) ).
fof(f1769,plain,
! [X0,X1,X2,X3] :
( less_equal(divide(divide(X0,X2),divide(X1,X2)),X3)
| ~ quotient(divide(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f425,f23]) ).
fof(f2112,plain,
! [X0,X1,X2] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(resolution,[status(thm)],[f1769,f23]) ).
fof(f2180,plain,
! [X0,X1,X2] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,divide(X1,X2)),X1)),
inference(paramodulation,[status(thm)],[f117,f2112]) ).
fof(f2260,plain,
! [X0,X1,X2] : less_equal(divide(X0,X1),divide(divide(X0,divide(X1,X2)),X1)),
inference(forward_demodulation,[status(thm)],[f925,f2180]) ).
fof(f3203,plain,
less_equal(divide(zQy,zQx),divide(zero,zQx)),
inference(paramodulation,[status(thm)],[f951,f2260]) ).
fof(f3256,plain,
less_equal(divide(zQy,zQx),zero),
inference(forward_demodulation,[status(thm)],[f55,f3203]) ).
fof(f3287,plain,
zero = divide(zQy,zQx),
inference(resolution,[status(thm)],[f3256,f36]) ).
fof(f3323,plain,
quotient(zQy,zQx,zero),
inference(paramodulation,[status(thm)],[f3287,f23]) ).
fof(f3392,plain,
less_equal(zQy,zQx),
inference(resolution,[status(thm)],[f3323,f15]) ).
fof(f3406,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3392,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n020.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 : Sun Sep 20 20:46:47 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 3.22/0.85 % Refutation found
% 3.22/0.85 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.22/0.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.22/0.90 % Elapsed time: 0.513666 seconds
% 3.22/0.90 % CPU time: 3.625941 seconds
% 3.22/0.90 % Total memory used: 75.787 MB
% 3.22/0.90 % Net memory used: 69.034 MB
%------------------------------------------------------------------------------