TSTP Solution File: GRP131-1.002 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP131-1.002 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.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 0.13s 0.36s
% Output : CNFRefutation 0.21s
% 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(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,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/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f12,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f13,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f15,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2) ),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f18,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f7]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f20,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f24,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)],[f10]) ).
fof(f25,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)],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f13,f21]) ).
fof(f27,plain,
! [X0,X1] :
( ~ product(X0,e_1,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f13,f19]) ).
fof(f29,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)],[f13,f25]) ).
fof(f31,plain,
! [X0,X1] :
( ~ product(X0,e_1,X1)
| ~ product(X1,e_2,X1)
| ~ product(X1,e_1,X0) ),
inference(factoring,[status(esa)],[f29]) ).
fof(f37,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f15,f12]) ).
fof(f38,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_1)
| product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f15,f11]) ).
fof(f39,plain,
( spl0_0
<=> product(e_2,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f40,plain,
( product(e_2,e_2,e_1)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,plain,
( spl0_1
<=> product(e_2,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f43,plain,
( product(e_2,e_2,e_2)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f37,f12]) ).
fof(f46,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f45,f39,f42]) ).
fof(f47,plain,
( spl0_2
<=> product(e_1,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f48,plain,
( product(e_1,e_2,e_1)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( spl0_3
<=> product(e_1,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f51,plain,
( product(e_1,e_2,e_2)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f37,f11]) ).
fof(f54,plain,
( spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f53,f47,f50]) ).
fof(f55,plain,
( spl0_4
<=> product(e_2,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f56,plain,
( product(e_2,e_1,e_1)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( spl0_5
<=> product(e_2,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f59,plain,
( product(e_2,e_1,e_2)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f38,f12]) ).
fof(f62,plain,
( spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f61,f55,f58]) ).
fof(f63,plain,
( spl0_6
<=> product(e_1,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f64,plain,
( product(e_1,e_1,e_1)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( spl0_7
<=> product(e_1,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f67,plain,
( product(e_1,e_1,e_2)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f38,f11]) ).
fof(f70,plain,
( spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f69,f63,f66]) ).
fof(f71,plain,
! [X0] :
( ~ product(X0,e_1,e_1)
| ~ product(e_1,e_1,X0)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f48,f31]) ).
fof(f78,plain,
( ~ product(e_1,e_2,e_1)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f40,f26]) ).
fof(f79,plain,
( $false
| ~ spl0_2
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f78,f48]) ).
fof(f80,plain,
( ~ spl0_2
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f83,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f56,f26]) ).
fof(f84,plain,
( $false
| ~ spl0_6
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f83,f64]) ).
fof(f85,plain,
( ~ spl0_6
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f84]) ).
fof(f86,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)],[f51,f29]) ).
fof(f88,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f51,f27]) ).
fof(f92,plain,
( ~ product(e_1,e_2,e_2)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f43,f26]) ).
fof(f93,plain,
( $false
| ~ spl0_3
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f92,f51]) ).
fof(f94,plain,
( ~ spl0_3
| ~ spl0_1 ),
inference(contradiction_clause,[status(thm)],[f93]) ).
fof(f100,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f43,f27]) ).
fof(f102,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_7
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f67,f71]) ).
fof(f106,plain,
( $false
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f100]) ).
fof(f107,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(contradiction_clause,[status(thm)],[f106]) ).
fof(f112,plain,
( $false
| ~ spl0_7
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f67]) ).
fof(f113,plain,
( ~ spl0_7
| ~ spl0_3 ),
inference(contradiction_clause,[status(thm)],[f112]) ).
fof(f131,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f56]) ).
fof(f132,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_2 ),
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f136,plain,
! [X0] :
( ~ product(X0,e_1,e_1)
| ~ product(e_1,e_1,X0)
| ~ spl0_0
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f40,f86]) ).
fof(f141,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_6
| ~ spl0_0
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f64,f136]) ).
fof(f142,plain,
( ~ spl0_6
| ~ spl0_0
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f141,f63,f39,f50]) ).
fof(f147,plain,
$false,
inference(sat_refutation,[status(thm)],[f46,f54,f62,f70,f80,f85,f94,f107,f113,f132,f142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP131-1.002 : TPTP v8.1.2. Released v1.2.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 30 00:59:17 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 0.13/0.36 % Refutation found
% 0.13/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.37 % Elapsed time: 0.021744 seconds
% 0.21/0.37 % CPU time: 0.069423 seconds
% 0.21/0.37 % Total memory used: 2.794 MB
% 0.21/0.37 % Net memory used: 2.732 MB
%------------------------------------------------------------------------------