TSTP Solution File: GRP123-9.003 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP123-9.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 12:10:29 EDT 2023
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 76 ( 24 unt; 0 def)
% Number of atoms : 160 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 173 ( 89 ~; 78 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 7 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 85 (; 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product1(X,Y,e_1)
| product1(X,Y,e_2)
| product1(X,Y,e_3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,W,Y,Z] :
( ~ product1(X,W,Y)
| ~ product1(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [W,Y,X,Z] :
( ~ product1(W,Y,X)
| ~ product1(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X] : product1(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,W,Z] :
( ~ product2(X,Y,W)
| ~ product2(X,Y,Z)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,W,Y,Z] :
( ~ product2(X,W,Y)
| ~ product2(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] : product2(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
! [X,Y,Z1,Z2] :
( ~ product1(X,Y,Z1)
| ~ product1(Z1,Y,Z2)
| product2(Z2,X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f26,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f27,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f28,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f29,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f31,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f34,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product1(X0,X1,e_1)
| product1(X0,X1,e_2)
| product1(X0,X1,e_3) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f37,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product1(X,W,Y)
| ~ product1(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( ~ product1(X0,X1,X2)
| ~ product1(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f39,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product1(W,Y,X)
| ~ product1(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( ~ product1(X0,X1,X2)
| ~ product1(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f41,plain,
! [X0] : product1(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f43,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product2(X,Y,W)
| ~ product2(X,Y,Z) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f18]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( ~ product2(X0,X1,X2)
| ~ product2(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f45,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product2(X,W,Y)
| ~ product2(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( ~ product2(X0,X1,X2)
| ~ product2(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f49,plain,
! [X0] : product2(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f50,plain,
! [X,Y,Z2] :
( ! [Z1] :
( ~ product1(X,Y,Z1)
| ~ product1(Z1,Y,Z2) )
| product2(Z2,X,Y) ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ~ product1(X0,X1,X2)
| ~ product1(X2,X1,X3)
| product2(X3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( ~ product1(X0,X1,X1)
| product2(X1,X0,X1) ),
inference(resolution,[status(thm)],[f41,f51]) ).
fof(f56,plain,
! [X0,X1] :
( ~ product1(e_1,X0,X1)
| ~ product1(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f28,f40]) ).
fof(f70,plain,
! [X0,X1] :
( ~ product2(X0,e_1,X1)
| ~ product2(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f29,f46]) ).
fof(f73,plain,
! [X0,X1] :
( ~ product1(X0,e_1,X1)
| ~ product1(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f29,f38]) ).
fof(f82,plain,
! [X0,X1] :
( ~ product2(X0,e_2,X1)
| ~ product2(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f31,f46]) ).
fof(f83,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_2)
| ~ product2(X0,X1,e_3) ),
inference(resolution,[status(thm)],[f31,f44]) ).
fof(f109,plain,
! [X0] :
( ~ group_element(X0)
| product1(X0,e_3,e_1)
| product1(X0,e_3,e_2)
| product1(X0,e_3,e_3) ),
inference(resolution,[status(thm)],[f34,f27]) ).
fof(f121,plain,
~ product2(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f70,f49]) ).
fof(f127,plain,
~ product1(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f121,f52]) ).
fof(f144,plain,
~ product2(e_3,e_2,e_3),
inference(resolution,[status(thm)],[f82,f49]) ).
fof(f148,plain,
~ product1(e_2,e_3,e_3),
inference(resolution,[status(thm)],[f144,f52]) ).
fof(f152,plain,
! [X0,X1,X2] :
( ~ product2(X0,X1,e_2)
| ~ product1(X1,e_3,X2)
| ~ product1(X2,e_3,X0) ),
inference(resolution,[status(thm)],[f83,f51]) ).
fof(f175,plain,
( spl0_3
<=> product1(e_2,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f176,plain,
( product1(e_2,e_3,e_1)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( spl0_4
<=> product1(e_2,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f179,plain,
( product1(e_2,e_3,e_2)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( spl0_5
<=> product1(e_2,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f182,plain,
( product1(e_2,e_3,e_3)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f109,f26]) ).
fof(f185,plain,
( spl0_3
| spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f184,f175,f178,f181]) ).
fof(f186,plain,
( spl0_6
<=> product1(e_1,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f187,plain,
( product1(e_1,e_3,e_1)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( spl0_7
<=> product1(e_1,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f190,plain,
( product1(e_1,e_3,e_2)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( spl0_8
<=> product1(e_1,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f193,plain,
( product1(e_1,e_3,e_3)
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( product1(e_1,e_3,e_1)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f109,f25]) ).
fof(f196,plain,
( spl0_6
| spl0_7
| spl0_8 ),
inference(split_clause,[status(thm)],[f195,f186,f189,f192]) ).
fof(f197,plain,
( $false
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f193,f127]) ).
fof(f198,plain,
~ spl0_8,
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f199,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f182,f148]) ).
fof(f200,plain,
~ spl0_5,
inference(contradiction_clause,[status(thm)],[f199]) ).
fof(f397,plain,
! [X0] :
( ~ product2(e_2,X0,e_2)
| ~ product1(X0,e_3,e_1)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f190,f152]) ).
fof(f409,plain,
( ~ product1(e_1,e_1,e_1)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f187,f73]) ).
fof(f410,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f409,f41]) ).
fof(f411,plain,
~ spl0_6,
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f417,plain,
( ~ product1(e_1,e_3,e_2)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f179,f56]) ).
fof(f418,plain,
( $false
| ~ spl0_7
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f417,f190]) ).
fof(f419,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f422,plain,
( ~ product2(e_2,e_2,e_2)
| ~ spl0_3
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f176,f397]) ).
fof(f423,plain,
( $false
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f422,f49]) ).
fof(f424,plain,
( ~ spl0_3
| ~ spl0_7 ),
inference(contradiction_clause,[status(thm)],[f423]) ).
fof(f425,plain,
$false,
inference(sat_refutation,[status(thm)],[f185,f196,f198,f200,f411,f419,f424]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP123-9.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 11:22:35 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.12/0.35 % Refutation found
% 0.12/0.35 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.37 % Elapsed time: 0.021452 seconds
% 0.19/0.37 % CPU time: 0.057824 seconds
% 0.19/0.37 % Memory used: 2.289 MB
%------------------------------------------------------------------------------