TSTP Solution File: GRP131-2.002 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP131-2.002 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n028.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 : Tue Apr 30 20:19:28 EDT 2024
% Result : Unsatisfiable 0.07s 0.27s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 71 ( 7 unt; 0 def)
% Number of atoms : 176 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 213 ( 108 ~; 97 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 62 ( 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
! [X1,Y1,Z1,X2,Y2,Z2] :
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,Y1,X1)
| ~ product(Z2,Y2,X2)
| equalish(Y1,Y2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f19,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f20,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f22,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2) ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f25,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f31,plain,
! [Y1,Y2] :
( ! [X2,Z2] :
( ! [X1] :
( ! [Z1] :
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1) )
| ~ product(Z2,Y1,X1) )
| ~ product(Z2,Y2,X2) )
| equalish(Y1,Y2) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X5,X4,X3)
| equalish(X1,X4) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f20,f28]) ).
fof(f34,plain,
! [X0,X1] :
( ~ product(X0,e_1,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f20,f26]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,e_1,X1)
| ~ product(X2,e_2,X1)
| ~ product(X3,e_1,X0)
| ~ product(X3,e_2,X2) ),
inference(resolution,[status(thm)],[f20,f32]) ).
fof(f38,plain,
! [X0,X1] :
( ~ product(X0,e_1,X1)
| ~ product(X1,e_2,X1)
| ~ product(X1,e_1,X0) ),
inference(factoring,[status(esa)],[f36]) ).
fof(f44,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f22,f19]) ).
fof(f45,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_1)
| product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f22,f18]) ).
fof(f46,plain,
( spl0_0
<=> product(e_2,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f47,plain,
( product(e_2,e_2,e_1)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,plain,
( spl0_1
<=> product(e_2,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f50,plain,
( product(e_2,e_2,e_2)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f44,f19]) ).
fof(f53,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f52,f46,f49]) ).
fof(f54,plain,
( spl0_2
<=> product(e_1,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f55,plain,
( product(e_1,e_2,e_1)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( spl0_3
<=> product(e_1,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f58,plain,
( product(e_1,e_2,e_2)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f44,f18]) ).
fof(f61,plain,
( spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f60,f54,f57]) ).
fof(f62,plain,
( spl0_4
<=> product(e_2,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f63,plain,
( product(e_2,e_1,e_1)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,plain,
( spl0_5
<=> product(e_2,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f66,plain,
( product(e_2,e_1,e_2)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f45,f19]) ).
fof(f69,plain,
( spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f68,f62,f65]) ).
fof(f70,plain,
( spl0_6
<=> product(e_1,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f71,plain,
( product(e_1,e_1,e_1)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,plain,
( spl0_7
<=> product(e_1,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f74,plain,
( product(e_1,e_1,e_2)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f45,f18]) ).
fof(f77,plain,
( spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f76,f70,f73]) ).
fof(f78,plain,
! [X0] :
( ~ product(X0,e_1,e_1)
| ~ product(e_1,e_1,X0)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f55,f38]) ).
fof(f85,plain,
( ~ product(e_1,e_2,e_1)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f47,f33]) ).
fof(f86,plain,
( $false
| ~ spl0_2
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f85,f55]) ).
fof(f87,plain,
( ~ spl0_2
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f86]) ).
fof(f91,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f63,f33]) ).
fof(f92,plain,
( $false
| ~ spl0_6
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f71]) ).
fof(f93,plain,
( ~ spl0_6
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ~ product(X0,e_1,X1)
| ~ product(e_2,e_2,X1)
| ~ product(e_1,e_1,X0)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f58,f36]) ).
fof(f96,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f58,f34]) ).
fof(f100,plain,
( ~ product(e_1,e_2,e_2)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f50,f33]) ).
fof(f101,plain,
( $false
| ~ spl0_3
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f58]) ).
fof(f102,plain,
( ~ spl0_3
| ~ spl0_1 ),
inference(contradiction_clause,[status(thm)],[f101]) ).
fof(f108,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f50,f34]) ).
fof(f110,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_7
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f74,f78]) ).
fof(f115,plain,
( $false
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f66,f108]) ).
fof(f116,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(contradiction_clause,[status(thm)],[f115]) ).
fof(f121,plain,
( $false
| ~ spl0_7
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f96,f74]) ).
fof(f122,plain,
( ~ spl0_7
| ~ spl0_3 ),
inference(contradiction_clause,[status(thm)],[f121]) ).
fof(f142,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f63]) ).
fof(f143,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_2 ),
inference(contradiction_clause,[status(thm)],[f142]) ).
fof(f147,plain,
! [X0] :
( ~ product(X0,e_1,e_1)
| ~ product(e_1,e_1,X0)
| ~ spl0_0
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f47,f94]) ).
fof(f153,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_6
| ~ spl0_0
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f71,f147]) ).
fof(f154,plain,
( ~ spl0_6
| ~ spl0_0
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f153,f70,f46,f57]) ).
fof(f160,plain,
$false,
inference(sat_refutation,[status(thm)],[f53,f61,f69,f77,f87,f93,f102,f116,f122,f143,f154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07 % Problem : GRP131-2.002 : TPTP v8.1.2. Released v1.2.0.
% 0.04/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26 % Computer : n028.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue Apr 30 00:41:14 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.07/0.26 % Drodi V3.6.0
% 0.07/0.27 % Refutation found
% 0.07/0.27 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.28 % Elapsed time: 0.013859 seconds
% 0.07/0.28 % CPU time: 0.044525 seconds
% 0.07/0.28 % Total memory used: 2.770 MB
% 0.07/0.28 % Net memory used: 2.706 MB
%------------------------------------------------------------------------------