TSTP Solution File: HEN011-2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : HEN011-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n018.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 : 300s
% DateTime : Wed May 31 12:12:52 EDT 2023
% Result : Unsatisfiable 8.11s 1.48s
% Output : CNFRefutation 8.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 29
% Syntax : Number of formulae : 134 ( 29 unt; 0 def)
% Number of atoms : 312 ( 21 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 341 ( 163 ~; 166 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 13 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 165 (; 165 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4)
| ~ quotient(V1,Z,V5)
| less_equal(V4,V5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| 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] :
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W)
| Z = W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : quotient(X,X,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y,W1,Z,W2] :
( ~ quotient(X,Y,W1)
| ~ less_equal(W1,Z)
| ~ quotient(X,Z,W2)
| less_equal(W2,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,Z,W1,W2] :
( ~ less_equal(X,Y)
| ~ quotient(Z,Y,W1)
| ~ quotient(Z,X,W2)
| less_equal(W1,W2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
quotient(identity,b,idQb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
quotient(identity,idQb,idQ_idQb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,plain,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f29,plain,
! [X,Z] :
( ! [Y] : ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f31,plain,
! [V4,V5] :
( ! [V1,Z] :
( ! [V2,V3] :
( ! [X] :
( ! [Y] :
( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2) )
| ~ quotient(X,Z,V3) )
| ~ quotient(V3,V2,V4) )
| ~ quotient(V1,Z,V5) )
| less_equal(V4,V5) ),
inference(miniscoping,[status(esa)],[f4]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X3,X5)
| ~ quotient(X5,X4,X6)
| ~ quotient(X2,X3,X7)
| less_equal(X6,X7) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f34,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f36,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f37,plain,
! [Z,W] :
( ! [X,Y] :
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W) )
| Z = W ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f41,plain,
! [X0] : quotient(X0,X0,zero),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f43,plain,
! [X,Z] :
( ! [Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z) )
| less_equal(X,Z) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X2)
| less_equal(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f45,plain,
! [Y,W2] :
( ! [X,Z] :
( ! [W1] :
( ~ quotient(X,Y,W1)
| ~ less_equal(W1,Z) )
| ~ quotient(X,Z,W2) )
| less_equal(W2,Y) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4] :
( ~ quotient(X0,X1,X2)
| ~ less_equal(X2,X3)
| ~ quotient(X0,X3,X4)
| less_equal(X4,X1) ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f47,plain,
! [W1,W2] :
( ! [X,Z] :
( ! [Y] :
( ~ less_equal(X,Y)
| ~ quotient(Z,Y,W1) )
| ~ quotient(Z,X,W2) )
| less_equal(W1,W2) ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f48,plain,
! [X0,X1,X2,X3,X4] :
( ~ less_equal(X0,X1)
| ~ quotient(X2,X1,X3)
| ~ quotient(X2,X0,X4)
| less_equal(X3,X4) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f55,plain,
quotient(identity,a,idQa),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f56,plain,
quotient(identity,b,idQb),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f57,plain,
quotient(identity,idQb,idQ_idQb),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f58,plain,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f59,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f60,plain,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f61,plain,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f67,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[status(thm)],[f28,f41]) ).
fof(f76,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f30,f36]) ).
fof(f116,plain,
! [X0] :
( ~ quotient(identity,idQb,X0)
| idQ_idQb = X0 ),
inference(resolution,[status(thm)],[f38,f57]) ).
fof(f131,plain,
! [X0,X1,X2,X3,X4] :
( ~ quotient(idQa,X0,X1)
| ~ quotient(identity,X0,X2)
| ~ quotient(X2,X1,X3)
| ~ quotient(idQ_idQa,X0,X4)
| less_equal(X3,X4) ),
inference(resolution,[status(thm)],[f32,f59]) ).
fof(f132,plain,
! [X0,X1,X2,X3,X4] :
( ~ quotient(idQb,X0,X1)
| ~ quotient(identity,X0,X2)
| ~ quotient(X2,X1,X3)
| ~ quotient(idQ_idQb,X0,X4)
| less_equal(X3,X4) ),
inference(resolution,[status(thm)],[f32,f57]) ).
fof(f153,plain,
! [X0,X1] :
( ~ less_equal(idQ_idQa,X0)
| ~ quotient(identity,X0,X1)
| less_equal(X1,idQa) ),
inference(resolution,[status(thm)],[f46,f59]) ).
fof(f155,plain,
! [X0,X1] :
( ~ less_equal(idQb,X0)
| ~ quotient(identity,X0,X1)
| less_equal(X1,b) ),
inference(resolution,[status(thm)],[f46,f56]) ).
fof(f156,plain,
! [X0,X1] :
( ~ less_equal(idQa,X0)
| ~ quotient(identity,X0,X1)
| less_equal(X1,a) ),
inference(resolution,[status(thm)],[f46,f55]) ).
fof(f163,plain,
! [X0,X1,X2,X3] :
( ~ less_equal(divide(X0,X1),X2)
| ~ quotient(X0,X2,X3)
| less_equal(X3,X1) ),
inference(resolution,[status(thm)],[f46,f36]) ).
fof(f535,plain,
idQ_idQb = divide(identity,idQb),
inference(resolution,[status(thm)],[f116,f36]) ).
fof(f553,plain,
! [X0,X1,X2,X3,X4] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X0,divide(X1,X3),X4)
| less_equal(X2,X4) ),
inference(resolution,[status(thm)],[f48,f76]) ).
fof(f1324,plain,
! [X0,X1,X2] :
( ~ quotient(identity,idQ_idQb,X0)
| ~ quotient(X0,idQa_Q__idQ_idQb,X1)
| ~ quotient(idQ_idQa,idQ_idQb,X2)
| less_equal(X1,X2) ),
inference(resolution,[status(thm)],[f131,f58]) ).
fof(f1329,plain,
! [X0,X1,X2] :
( ~ quotient(identity,idQ_idQa,X0)
| ~ quotient(X0,idQb_Q__idQ_idQa,X1)
| ~ quotient(idQ_idQb,idQ_idQa,X2)
| less_equal(X1,X2) ),
inference(resolution,[status(thm)],[f132,f60]) ).
fof(f3418,plain,
( spl0_105
<=> less_equal(idQ_idQa,a) ),
introduced(split_symbol_definition) ).
fof(f3419,plain,
( less_equal(idQ_idQa,a)
| ~ spl0_105 ),
inference(component_clause,[status(thm)],[f3418]) ).
fof(f3421,plain,
( spl0_106
<=> less_equal(idQa,idQa) ),
introduced(split_symbol_definition) ).
fof(f3423,plain,
( ~ less_equal(idQa,idQa)
| spl0_106 ),
inference(component_clause,[status(thm)],[f3421]) ).
fof(f3436,plain,
! [X0] :
( ~ less_equal(idQ_idQa,X0)
| less_equal(divide(identity,X0),idQa) ),
inference(resolution,[status(thm)],[f153,f36]) ).
fof(f3448,plain,
( spl0_110
<=> less_equal(idQ_idQb,b) ),
introduced(split_symbol_definition) ).
fof(f3449,plain,
( less_equal(idQ_idQb,b)
| ~ spl0_110 ),
inference(component_clause,[status(thm)],[f3448]) ).
fof(f3451,plain,
( spl0_111
<=> less_equal(idQb,idQb) ),
introduced(split_symbol_definition) ).
fof(f3453,plain,
( ~ less_equal(idQb,idQb)
| spl0_111 ),
inference(component_clause,[status(thm)],[f3451]) ).
fof(f3886,plain,
less_equal(divide(identity,idQ_idQa),idQa),
inference(resolution,[status(thm)],[f3436,f67]) ).
fof(f3889,plain,
( ~ less_equal(idQb,idQb)
| less_equal(idQ_idQb,b) ),
inference(resolution,[status(thm)],[f155,f57]) ).
fof(f3890,plain,
( ~ spl0_111
| spl0_110 ),
inference(split_clause,[status(thm)],[f3889,f3451,f3448]) ).
fof(f3919,plain,
( $false
| spl0_111 ),
inference(forward_subsumption_resolution,[status(thm)],[f3453,f67]) ).
fof(f3920,plain,
spl0_111,
inference(contradiction_clause,[status(thm)],[f3919]) ).
fof(f3921,plain,
( ~ less_equal(idQa,idQa)
| less_equal(idQ_idQa,a) ),
inference(resolution,[status(thm)],[f156,f59]) ).
fof(f3922,plain,
( ~ spl0_106
| spl0_105 ),
inference(split_clause,[status(thm)],[f3921,f3421,f3418]) ).
fof(f3947,plain,
( $false
| spl0_106 ),
inference(forward_subsumption_resolution,[status(thm)],[f3423,f67]) ).
fof(f3948,plain,
spl0_106,
inference(contradiction_clause,[status(thm)],[f3947]) ).
fof(f3971,plain,
! [X0,X1,X2] :
( ~ quotient(X0,divide(X0,X1),X2)
| less_equal(X2,X1) ),
inference(resolution,[status(thm)],[f163,f67]) ).
fof(f4014,plain,
! [X0,X1,X2] :
( ~ quotient(X0,b,X1)
| ~ quotient(X0,idQ_idQb,X2)
| less_equal(X1,X2)
| ~ spl0_110 ),
inference(resolution,[status(thm)],[f3449,f48]) ).
fof(f4231,plain,
! [X0,X1,X2] :
( ~ quotient(X0,a,X1)
| ~ quotient(X0,idQ_idQa,X2)
| less_equal(X1,X2)
| ~ spl0_105 ),
inference(resolution,[status(thm)],[f3419,f48]) ).
fof(f4381,plain,
! [X0] :
( ~ quotient(identity,idQ_idQb,X0)
| less_equal(idQb,X0)
| ~ spl0_110 ),
inference(resolution,[status(thm)],[f4014,f56]) ).
fof(f4483,plain,
( spl0_143
<=> less_equal(idQa,divide(identity,idQ_idQa)) ),
introduced(split_symbol_definition) ).
fof(f4485,plain,
( ~ less_equal(idQa,divide(identity,idQ_idQa))
| spl0_143 ),
inference(component_clause,[status(thm)],[f4483]) ).
fof(f4486,plain,
( spl0_144
<=> divide(identity,idQ_idQa) = idQa ),
introduced(split_symbol_definition) ).
fof(f4487,plain,
( divide(identity,idQ_idQa) = idQa
| ~ spl0_144 ),
inference(component_clause,[status(thm)],[f4486]) ).
fof(f4489,plain,
( ~ less_equal(idQa,divide(identity,idQ_idQa))
| divide(identity,idQ_idQa) = idQa ),
inference(resolution,[status(thm)],[f3886,f34]) ).
fof(f4490,plain,
( ~ spl0_143
| spl0_144 ),
inference(split_clause,[status(thm)],[f4489,f4483,f4486]) ).
fof(f4536,plain,
! [X0,X1] : less_equal(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[f3971,f36]) ).
fof(f4592,plain,
less_equal(divide(identity,idQ_idQb),idQb),
inference(paramodulation,[status(thm)],[f535,f4536]) ).
fof(f4640,plain,
( spl0_145
<=> less_equal(idQb,divide(identity,idQ_idQb)) ),
introduced(split_symbol_definition) ).
fof(f4642,plain,
( ~ less_equal(idQb,divide(identity,idQ_idQb))
| spl0_145 ),
inference(component_clause,[status(thm)],[f4640]) ).
fof(f4643,plain,
( spl0_146
<=> divide(identity,idQ_idQb) = idQb ),
introduced(split_symbol_definition) ).
fof(f4644,plain,
( divide(identity,idQ_idQb) = idQb
| ~ spl0_146 ),
inference(component_clause,[status(thm)],[f4643]) ).
fof(f4646,plain,
( ~ less_equal(idQb,divide(identity,idQ_idQb))
| divide(identity,idQ_idQb) = idQb ),
inference(resolution,[status(thm)],[f4592,f34]) ).
fof(f4647,plain,
( ~ spl0_145
| spl0_146 ),
inference(split_clause,[status(thm)],[f4646,f4640,f4643]) ).
fof(f4963,plain,
! [X0] :
( ~ quotient(identity,idQ_idQa,X0)
| less_equal(idQa,X0)
| ~ spl0_105 ),
inference(resolution,[status(thm)],[f4231,f55]) ).
fof(f6043,plain,
( less_equal(idQb,divide(identity,idQ_idQb))
| ~ spl0_110 ),
inference(resolution,[status(thm)],[f4381,f36]) ).
fof(f6044,plain,
( $false
| spl0_145
| ~ spl0_110 ),
inference(forward_subsumption_resolution,[status(thm)],[f6043,f4642]) ).
fof(f6045,plain,
( spl0_145
| ~ spl0_110 ),
inference(contradiction_clause,[status(thm)],[f6044]) ).
fof(f7776,plain,
( less_equal(idQa,divide(identity,idQ_idQa))
| ~ spl0_105 ),
inference(resolution,[status(thm)],[f4963,f36]) ).
fof(f7777,plain,
( $false
| spl0_143
| ~ spl0_105 ),
inference(forward_subsumption_resolution,[status(thm)],[f7776,f4485]) ).
fof(f7778,plain,
( spl0_143
| ~ spl0_105 ),
inference(contradiction_clause,[status(thm)],[f7777]) ).
fof(f11114,plain,
! [X0,X1] :
( ~ quotient(divide(identity,idQ_idQa),idQb_Q__idQ_idQa,X0)
| ~ quotient(idQ_idQb,idQ_idQa,X1)
| less_equal(X0,X1) ),
inference(resolution,[status(thm)],[f1329,f36]) ).
fof(f11115,plain,
! [X0,X1] :
( ~ quotient(idQa,idQb_Q__idQ_idQa,X0)
| ~ quotient(idQ_idQb,idQ_idQa,X1)
| less_equal(X0,X1)
| ~ spl0_144 ),
inference(forward_demodulation,[status(thm)],[f4487,f11114]) ).
fof(f11441,plain,
! [X0] :
( ~ quotient(idQ_idQb,idQ_idQa,X0)
| less_equal(divide(idQa,idQb_Q__idQ_idQa),X0)
| ~ spl0_144 ),
inference(resolution,[status(thm)],[f11115,f36]) ).
fof(f11573,plain,
( less_equal(divide(idQa,idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa))
| ~ spl0_144 ),
inference(resolution,[status(thm)],[f11441,f36]) ).
fof(f12448,plain,
! [X0,X1] :
( ~ quotient(idQb,divide(idQ_idQa,X0),X1)
| less_equal(idQb_Q__idQ_idQa,X1) ),
inference(resolution,[status(thm)],[f553,f60]) ).
fof(f12721,plain,
! [X0] :
( ~ less_equal(divide(idQ_idQb,idQ_idQa),X0)
| less_equal(divide(idQa,idQb_Q__idQ_idQa),X0)
| ~ spl0_144 ),
inference(resolution,[status(thm)],[f11573,f44]) ).
fof(f22109,plain,
( less_equal(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb)
| ~ spl0_144 ),
inference(resolution,[status(thm)],[f12721,f76]) ).
fof(f22129,plain,
! [X0] :
( ~ quotient(idQa,idQ_idQb,X0)
| less_equal(X0,idQb_Q__idQ_idQa)
| ~ spl0_144 ),
inference(resolution,[status(thm)],[f22109,f163]) ).
fof(f22631,plain,
( less_equal(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa)
| ~ spl0_144 ),
inference(resolution,[status(thm)],[f22129,f58]) ).
fof(f22640,plain,
! [X0] :
( ~ less_equal(idQb_Q__idQ_idQa,X0)
| less_equal(idQa_Q__idQ_idQb,X0)
| ~ spl0_144 ),
inference(resolution,[status(thm)],[f22631,f44]) ).
fof(f22641,plain,
( spl0_347
<=> less_equal(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb) ),
introduced(split_symbol_definition) ).
fof(f22643,plain,
( ~ less_equal(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb)
| spl0_347 ),
inference(component_clause,[status(thm)],[f22641]) ).
fof(f22644,plain,
( spl0_348
<=> idQa_Q__idQ_idQb = idQb_Q__idQ_idQa ),
introduced(split_symbol_definition) ).
fof(f22645,plain,
( idQa_Q__idQ_idQb = idQb_Q__idQ_idQa
| ~ spl0_348 ),
inference(component_clause,[status(thm)],[f22644]) ).
fof(f22647,plain,
( ~ less_equal(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb)
| idQa_Q__idQ_idQb = idQb_Q__idQ_idQa
| ~ spl0_144 ),
inference(resolution,[status(thm)],[f22631,f34]) ).
fof(f22648,plain,
( ~ spl0_347
| spl0_348
| ~ spl0_144 ),
inference(split_clause,[status(thm)],[f22647,f22641,f22644,f4486]) ).
fof(f26862,plain,
! [X0,X1] :
( ~ quotient(divide(identity,idQ_idQb),idQa_Q__idQ_idQb,X0)
| ~ quotient(idQ_idQa,idQ_idQb,X1)
| less_equal(X0,X1) ),
inference(resolution,[status(thm)],[f1324,f36]) ).
fof(f26863,plain,
! [X0,X1] :
( ~ quotient(idQb,idQa_Q__idQ_idQb,X0)
| ~ quotient(idQ_idQa,idQ_idQb,X1)
| less_equal(X0,X1)
| ~ spl0_146 ),
inference(forward_demodulation,[status(thm)],[f4644,f26862]) ).
fof(f26998,plain,
! [X0] :
( ~ quotient(idQ_idQa,idQ_idQb,X0)
| less_equal(divide(idQb,idQa_Q__idQ_idQb),X0)
| ~ spl0_146 ),
inference(resolution,[status(thm)],[f26863,f36]) ).
fof(f27028,plain,
( less_equal(divide(idQb,idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb))
| ~ spl0_146 ),
inference(resolution,[status(thm)],[f26998,f36]) ).
fof(f27029,plain,
! [X0] :
( ~ quotient(idQb,divide(idQ_idQa,idQ_idQb),X0)
| less_equal(X0,idQa_Q__idQ_idQb)
| ~ spl0_146 ),
inference(resolution,[status(thm)],[f27028,f163]) ).
fof(f51773,plain,
! [X0] : less_equal(idQb_Q__idQ_idQa,divide(idQb,divide(idQ_idQa,X0))),
inference(resolution,[status(thm)],[f12448,f36]) ).
fof(f51788,plain,
! [X0] :
( less_equal(idQa_Q__idQ_idQb,divide(idQb,divide(idQ_idQa,X0)))
| ~ spl0_144 ),
inference(resolution,[status(thm)],[f51773,f22640]) ).
fof(f52786,plain,
( less_equal(divide(idQb,divide(idQ_idQa,idQ_idQb)),idQa_Q__idQ_idQb)
| ~ spl0_146 ),
inference(resolution,[status(thm)],[f27029,f36]) ).
fof(f52889,plain,
( spl0_715
<=> less_equal(idQa_Q__idQ_idQb,divide(idQb,divide(idQ_idQa,idQ_idQb))) ),
introduced(split_symbol_definition) ).
fof(f52891,plain,
( ~ less_equal(idQa_Q__idQ_idQb,divide(idQb,divide(idQ_idQa,idQ_idQb)))
| spl0_715 ),
inference(component_clause,[status(thm)],[f52889]) ).
fof(f52892,plain,
( spl0_716
<=> divide(idQb,divide(idQ_idQa,idQ_idQb)) = idQa_Q__idQ_idQb ),
introduced(split_symbol_definition) ).
fof(f52893,plain,
( divide(idQb,divide(idQ_idQa,idQ_idQb)) = idQa_Q__idQ_idQb
| ~ spl0_716 ),
inference(component_clause,[status(thm)],[f52892]) ).
fof(f52895,plain,
( ~ less_equal(idQa_Q__idQ_idQb,divide(idQb,divide(idQ_idQa,idQ_idQb)))
| divide(idQb,divide(idQ_idQa,idQ_idQb)) = idQa_Q__idQ_idQb
| ~ spl0_146 ),
inference(resolution,[status(thm)],[f52786,f34]) ).
fof(f52896,plain,
( ~ spl0_715
| spl0_716
| ~ spl0_146 ),
inference(split_clause,[status(thm)],[f52895,f52889,f52892,f4643]) ).
fof(f52898,plain,
( $false
| ~ spl0_144
| spl0_715 ),
inference(forward_subsumption_resolution,[status(thm)],[f52891,f51788]) ).
fof(f52899,plain,
( ~ spl0_144
| spl0_715 ),
inference(contradiction_clause,[status(thm)],[f52898]) ).
fof(f52902,plain,
( less_equal(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb)
| ~ spl0_716 ),
inference(paramodulation,[status(thm)],[f52893,f51773]) ).
fof(f52903,plain,
( $false
| spl0_347
| ~ spl0_716 ),
inference(forward_subsumption_resolution,[status(thm)],[f52902,f22643]) ).
fof(f52904,plain,
( spl0_347
| ~ spl0_716 ),
inference(contradiction_clause,[status(thm)],[f52903]) ).
fof(f52941,plain,
( $false
| ~ spl0_348 ),
inference(forward_subsumption_resolution,[status(thm)],[f22645,f61]) ).
fof(f52942,plain,
~ spl0_348,
inference(contradiction_clause,[status(thm)],[f52941]) ).
fof(f52943,plain,
$false,
inference(sat_refutation,[status(thm)],[f3890,f3920,f3922,f3948,f4490,f4647,f6045,f7778,f22648,f52896,f52899,f52904,f52942]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : HEN011-2 : TPTP v8.1.2. Released v1.0.0.
% 0.05/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n018.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 09:40:55 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.31 % Drodi V3.5.1
% 8.11/1.48 % Refutation found
% 8.11/1.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.11/1.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.75/1.53 % Elapsed time: 1.200939 seconds
% 8.75/1.53 % CPU time: 8.941724 seconds
% 8.75/1.53 % Memory used: 90.179 MB
%------------------------------------------------------------------------------