TSTP Solution File: GRP775+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP775+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %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 : 300s
% DateTime : Wed May 31 12:12:40 EDT 2023
% Result : Theorem 2.89s 0.83s
% Output : CNFRefutation 2.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 85 ( 11 unt; 0 def)
% Number of atoms : 227 ( 102 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 245 ( 103 ~; 107 |; 24 &)
% ( 10 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 100 (; 93 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [C,B,A] : product(product(A,B),C) = product(A,product(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] : product(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X0,X1] :
( l(X0,X1)
<=> ( product(X0,X1) = X0
& product(X1,X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X2,X3] :
( r(X2,X3)
<=> ( product(X2,X3) = X3
& product(X3,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X4,X5] :
( d(X4,X5)
<=> ? [X6] :
( r(X4,X6)
& l(X6,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [X7,X8] :
( d(X7,X8)
<=> ( product(X7,product(X8,X7)) = X7
& product(X8,product(X7,X8)) = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [X7,X8] :
( d(X7,X8)
<=> ( product(X7,product(X8,X7)) = X7
& product(X8,product(X7,X8)) = X8 ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] : product(product(X0,X1),X2) = product(X0,product(X1,X2)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f9,plain,
! [X0] : product(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f10,plain,
! [X0,X1] :
( ( ~ l(X0,X1)
| ( product(X0,X1) = X0
& product(X1,X0) = X1 ) )
& ( l(X0,X1)
| product(X0,X1) != X0
| product(X1,X0) != X1 ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f11,plain,
( ! [X0,X1] :
( ~ l(X0,X1)
| ( product(X0,X1) = X0
& product(X1,X0) = X1 ) )
& ! [X0,X1] :
( l(X0,X1)
| product(X0,X1) != X0
| product(X1,X0) != X1 ) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ~ l(X0,X1)
| product(X0,X1) = X0 ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ~ l(X0,X1)
| product(X1,X0) = X1 ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( l(X0,X1)
| product(X0,X1) != X0
| product(X1,X0) != X1 ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f15,plain,
! [X2,X3] :
( ( ~ r(X2,X3)
| ( product(X2,X3) = X3
& product(X3,X2) = X2 ) )
& ( r(X2,X3)
| product(X2,X3) != X3
| product(X3,X2) != X2 ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f16,plain,
( ! [X2,X3] :
( ~ r(X2,X3)
| ( product(X2,X3) = X3
& product(X3,X2) = X2 ) )
& ! [X2,X3] :
( r(X2,X3)
| product(X2,X3) != X3
| product(X3,X2) != X2 ) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ~ r(X0,X1)
| product(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ~ r(X0,X1)
| product(X1,X0) = X0 ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( r(X0,X1)
| product(X0,X1) != X1
| product(X1,X0) != X0 ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f20,plain,
! [X4,X5] :
( ( ~ d(X4,X5)
| ? [X6] :
( r(X4,X6)
& l(X6,X5) ) )
& ( d(X4,X5)
| ! [X6] :
( ~ r(X4,X6)
| ~ l(X6,X5) ) ) ),
inference(NNF_transformation,[status(esa)],[f5]) ).
fof(f21,plain,
( ! [X4,X5] :
( ~ d(X4,X5)
| ? [X6] :
( r(X4,X6)
& l(X6,X5) ) )
& ! [X4,X5] :
( d(X4,X5)
| ! [X6] :
( ~ r(X4,X6)
| ~ l(X6,X5) ) ) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f22,plain,
( ! [X4,X5] :
( ~ d(X4,X5)
| ( r(X4,sk0_0(X5,X4))
& l(sk0_0(X5,X4),X5) ) )
& ! [X4,X5] :
( d(X4,X5)
| ! [X6] :
( ~ r(X4,X6)
| ~ l(X6,X5) ) ) ),
inference(skolemization,[status(esa)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ~ d(X0,X1)
| r(X0,sk0_0(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ~ d(X0,X1)
| l(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f25,plain,
! [X0,X1,X2] :
( d(X0,X1)
| ~ r(X0,X2)
| ~ l(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f26,plain,
? [X7,X8] :
( d(X7,X8)
<~> ( product(X7,product(X8,X7)) = X7
& product(X8,product(X7,X8)) = X8 ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f27,plain,
? [X7,X8] :
( ( d(X7,X8)
| ( product(X7,product(X8,X7)) = X7
& product(X8,product(X7,X8)) = X8 ) )
& ( ~ d(X7,X8)
| product(X7,product(X8,X7)) != X7
| product(X8,product(X7,X8)) != X8 ) ),
inference(NNF_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
( ( d(sk0_1,sk0_2)
| ( product(sk0_1,product(sk0_2,sk0_1)) = sk0_1
& product(sk0_2,product(sk0_1,sk0_2)) = sk0_2 ) )
& ( ~ d(sk0_1,sk0_2)
| product(sk0_1,product(sk0_2,sk0_1)) != sk0_1
| product(sk0_2,product(sk0_1,sk0_2)) != sk0_2 ) ),
inference(skolemization,[status(esa)],[f27]) ).
fof(f29,plain,
( d(sk0_1,sk0_2)
| product(sk0_1,product(sk0_2,sk0_1)) = sk0_1 ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f30,plain,
( d(sk0_1,sk0_2)
| product(sk0_2,product(sk0_1,sk0_2)) = sk0_2 ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f31,plain,
( ~ d(sk0_1,sk0_2)
| product(sk0_1,product(sk0_2,sk0_1)) != sk0_1
| product(sk0_2,product(sk0_1,sk0_2)) != sk0_2 ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f32,plain,
( spl0_0
<=> d(sk0_1,sk0_2) ),
introduced(split_symbol_definition) ).
fof(f33,plain,
( d(sk0_1,sk0_2)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f34,plain,
( ~ d(sk0_1,sk0_2)
| spl0_0 ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,plain,
( spl0_1
<=> product(sk0_1,product(sk0_2,sk0_1)) = sk0_1 ),
introduced(split_symbol_definition) ).
fof(f36,plain,
( product(sk0_1,product(sk0_2,sk0_1)) = sk0_1
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f37,plain,
( product(sk0_1,product(sk0_2,sk0_1)) != sk0_1
| spl0_1 ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f29,f32,f35]) ).
fof(f39,plain,
( spl0_2
<=> product(sk0_2,product(sk0_1,sk0_2)) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f42,plain,
( spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f30,f32,f39]) ).
fof(f43,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f31,f32,f35,f39]) ).
fof(f48,plain,
! [X0,X1] : product(X0,X1) = product(X0,product(X0,X1)),
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f50,plain,
! [X0,X1,X2] : product(product(X0,X1),X2) = product(X0,product(X1,product(product(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f8,f48]) ).
fof(f51,plain,
! [X0,X1,X2] : product(X0,product(X1,X2)) = product(X0,product(X1,product(product(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f8,f50]) ).
fof(f52,plain,
! [X0,X1,X2] : product(X0,product(X1,X2)) = product(X0,product(X1,product(X0,product(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f8,f51]) ).
fof(f586,plain,
! [X0,X1,X2] :
( product(X0,X1) != X1
| product(X1,X0) != X0
| d(X0,X2)
| ~ l(X1,X2) ),
inference(resolution,[status(thm)],[f19,f25]) ).
fof(f587,plain,
! [X0,X1,X2] :
( product(X0,X1) != X1
| product(X1,X0) != X0
| d(X0,X2)
| product(X1,X2) != X1
| product(X2,X1) != X2 ),
inference(resolution,[status(thm)],[f586,f14]) ).
fof(f893,plain,
( l(sk0_0(sk0_2,sk0_1),sk0_2)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f33,f24]) ).
fof(f894,plain,
( r(sk0_1,sk0_0(sk0_2,sk0_1))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f33,f23]) ).
fof(f896,plain,
( product(sk0_2,sk0_0(sk0_2,sk0_1)) = sk0_2
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f893,f13]) ).
fof(f897,plain,
( product(sk0_0(sk0_2,sk0_1),sk0_2) = sk0_0(sk0_2,sk0_1)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f893,f12]) ).
fof(f899,plain,
( product(sk0_0(sk0_2,sk0_1),sk0_1) = sk0_1
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f894,f18]) ).
fof(f900,plain,
( product(sk0_1,sk0_0(sk0_2,sk0_1)) = sk0_0(sk0_2,sk0_1)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f894,f17]) ).
fof(f944,plain,
! [X0] :
( product(sk0_1,X0) = product(sk0_0(sk0_2,sk0_1),product(sk0_1,X0))
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f899,f8]) ).
fof(f960,plain,
! [X0] :
( product(sk0_0(sk0_2,sk0_1),X0) = product(sk0_0(sk0_2,sk0_1),product(sk0_2,X0))
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f897,f8]) ).
fof(f969,plain,
! [X0] :
( product(X0,product(sk0_1,sk0_0(sk0_2,sk0_1))) = product(X0,product(sk0_1,product(X0,sk0_0(sk0_2,sk0_1))))
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f900,f52]) ).
fof(f970,plain,
! [X0] :
( product(X0,sk0_0(sk0_2,sk0_1)) = product(X0,product(sk0_1,product(X0,sk0_0(sk0_2,sk0_1))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f900,f969]) ).
fof(f1724,plain,
( product(sk0_2,sk0_0(sk0_2,sk0_1)) = product(sk0_2,product(sk0_1,sk0_2))
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f896,f970]) ).
fof(f1725,plain,
( sk0_2 = product(sk0_2,product(sk0_1,sk0_2))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f896,f1724]) ).
fof(f1725_001,plain,
( sk0_2 = product(sk0_2,product(sk0_1,sk0_2))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f896,f1724]) ).
fof(f1842,plain,
! [X0] :
( product(sk0_2,X0) = product(sk0_2,product(product(sk0_1,sk0_2),X0))
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f1725,f8]) ).
fof(f1843,plain,
! [X0] :
( product(sk0_2,X0) = product(sk0_2,product(sk0_1,product(sk0_2,X0)))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f8,f1842]) ).
fof(f1884,plain,
! [X0] :
( product(sk0_0(sk0_2,sk0_1),product(sk0_1,product(sk0_2,X0))) = product(sk0_0(sk0_2,sk0_1),product(sk0_2,X0))
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f1843,f960]) ).
fof(f1885,plain,
! [X0] :
( product(sk0_1,product(sk0_2,X0)) = product(sk0_0(sk0_2,sk0_1),product(sk0_2,X0))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f944,f1884]) ).
fof(f1886,plain,
! [X0] :
( product(sk0_1,product(sk0_2,X0)) = product(sk0_0(sk0_2,sk0_1),X0)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f960,f1885]) ).
fof(f1976,plain,
( product(sk0_1,product(sk0_2,sk0_1)) = sk0_1
| ~ spl0_0 ),
inference(backward_demodulation,[status(thm)],[f1886,f899]) ).
fof(f1977,plain,
( $false
| spl0_1
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f1976,f37]) ).
fof(f1978,plain,
( spl0_1
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f1977]) ).
fof(f1979,plain,
! [X0] :
( product(sk0_1,X0) != X0
| product(X0,sk0_1) != sk0_1
| product(X0,sk0_2) != X0
| product(sk0_2,X0) != sk0_2
| spl0_0 ),
inference(resolution,[status(thm)],[f34,f587]) ).
fof(f2562,plain,
! [X0,X1] :
( product(sk0_1,product(X0,X1)) != product(X0,X1)
| product(X0,product(X1,sk0_1)) != sk0_1
| product(product(X0,X1),sk0_2) != product(X0,X1)
| product(sk0_2,product(X0,X1)) != sk0_2
| spl0_0 ),
inference(paramodulation,[status(thm)],[f8,f1979]) ).
fof(f2563,plain,
! [X0,X1] :
( product(sk0_1,product(X0,X1)) != product(X0,X1)
| product(X0,product(X1,sk0_1)) != sk0_1
| product(X0,product(X1,sk0_2)) != product(X0,X1)
| product(sk0_2,product(X0,X1)) != sk0_2
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f8,f2562]) ).
fof(f2566,plain,
( spl0_2
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f1725,f39,f32]) ).
fof(f6905,plain,
( spl0_9
<=> product(sk0_1,product(sk0_1,sk0_2)) = product(sk0_1,sk0_2) ),
introduced(split_symbol_definition) ).
fof(f6907,plain,
( product(sk0_1,product(sk0_1,sk0_2)) != product(sk0_1,sk0_2)
| spl0_9 ),
inference(component_clause,[status(thm)],[f6905]) ).
fof(f6908,plain,
( spl0_10
<=> product(sk0_1,product(sk0_2,sk0_2)) = product(sk0_1,sk0_2) ),
introduced(split_symbol_definition) ).
fof(f6910,plain,
( product(sk0_1,product(sk0_2,sk0_2)) != product(sk0_1,sk0_2)
| spl0_10 ),
inference(component_clause,[status(thm)],[f6908]) ).
fof(f6911,plain,
( product(sk0_1,product(sk0_1,sk0_2)) != product(sk0_1,sk0_2)
| product(sk0_1,product(sk0_2,sk0_2)) != product(sk0_1,sk0_2)
| product(sk0_2,product(sk0_1,sk0_2)) != sk0_2
| spl0_0
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f2563,f36]) ).
fof(f6912,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_2
| spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f6911,f6905,f6908,f39,f32,f35]) ).
fof(f6937,plain,
( product(sk0_1,sk0_2) != product(sk0_1,sk0_2)
| spl0_9 ),
inference(forward_demodulation,[status(thm)],[f48,f6907]) ).
fof(f6938,plain,
( $false
| spl0_9 ),
inference(trivial_equality_resolution,[status(esa)],[f6937]) ).
fof(f6939,plain,
spl0_9,
inference(contradiction_clause,[status(thm)],[f6938]) ).
fof(f6940,plain,
( product(sk0_1,sk0_2) != product(sk0_1,sk0_2)
| spl0_10 ),
inference(forward_demodulation,[status(thm)],[f9,f6910]) ).
fof(f6941,plain,
( $false
| spl0_10 ),
inference(trivial_equality_resolution,[status(esa)],[f6940]) ).
fof(f6942,plain,
spl0_10,
inference(contradiction_clause,[status(thm)],[f6941]) ).
fof(f6943,plain,
$false,
inference(sat_refutation,[status(thm)],[f38,f42,f43,f1978,f2566,f6912,f6939,f6942]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP775+1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 11:49:49 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % Drodi V3.5.1
% 2.89/0.83 % Refutation found
% 2.89/0.83 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.89/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.89/0.85 % Elapsed time: 0.500108 seconds
% 2.89/0.85 % CPU time: 3.465813 seconds
% 2.89/0.85 % Memory used: 109.138 MB
%------------------------------------------------------------------------------