TSTP Solution File: GRP128-4.003 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP128-4.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 12:10:36 EDT 2023
% Result : Unsatisfiable 0.15s 0.37s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 37
% Syntax : Number of formulae : 171 ( 19 unt; 0 def)
% Number of atoms : 456 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 502 ( 217 ~; 265 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 24 ( 23 usr; 21 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 115 (; 115 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(e_1,X,Y)
| product(e_2,X,Y)
| product(e_3,X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,e_1,Y)
| product(X,e_2,Y)
| product(X,e_3,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [X,Y,Z1,Z2] :
( product(X,Y,Z1)
| ~ product(X,Z1,Z2)
| ~ product(Z1,Y,Z2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [Z1,Y,Z2,X] :
( product(Z1,Y,Z2)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(Z1,Y,Z2)
| product(X,Z1,Z2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(e_1,X0,X1)
| product(e_2,X0,X1)
| product(e_3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f20,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,e_1,X1)
| product(X0,e_2,X1)
| product(X0,e_3,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f21,plain,
! [Y,Z1,Z2] :
( ! [X] :
( product(X,Y,Z1)
| ~ product(X,Z1,Z2) )
| ~ product(Z1,Y,Z2) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( product(X0,X1,X2)
| ~ product(X0,X2,X3)
| ~ product(X2,X1,X3) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f23,plain,
! [Z1,Y,X] :
( ! [Z2] :
( product(Z1,Y,Z2)
| ~ product(X,Z1,Z2) )
| ~ product(X,Y,Z1) ),
inference(miniscoping,[status(esa)],[f4]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( product(X0,X1,X2)
| ~ product(X3,X0,X2)
| ~ product(X3,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f25,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f26,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f27,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f28,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f30,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f31,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f32,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f33,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f34,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f35,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f37,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f39,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f41,plain,
! [X,Z1,Z2] :
( ! [Y] :
( ~ product(X,Y,Z1)
| ~ product(Z1,Y,Z2) )
| product(X,Z1,Z2) ),
inference(miniscoping,[status(esa)],[f18]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X2,X1,X3)
| product(X0,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( product(X0,X0,X0)
| ~ product(X0,X0,X1) ),
inference(factoring,[status(esa)],[f22]) ).
fof(f44,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_2,X0,e_1)
| product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f19,f25]) ).
fof(f45,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_2)
| product(e_2,X0,e_2)
| product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f26,f19]) ).
fof(f47,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_3)
| product(X0,e_2,e_3)
| product(X0,e_3,e_3) ),
inference(resolution,[status(thm)],[f20,f27]) ).
fof(f48,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_2)
| product(X0,e_2,e_2)
| product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f20,f26]) ).
fof(f49,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_1)
| product(X0,e_2,e_1)
| product(X0,e_3,e_1) ),
inference(resolution,[status(thm)],[f20,f25]) ).
fof(f51,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2)
| product(X0,e_2,e_3) ),
inference(resolution,[status(thm)],[f34,f26]) ).
fof(f52,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_1)
| product(X0,e_1,e_2)
| product(X0,e_1,e_3) ),
inference(resolution,[status(thm)],[f34,f25]) ).
fof(f56,plain,
( spl0_1
<=> product(e_2,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f57,plain,
( product(e_2,e_3,e_1)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( spl0_2
<=> product(e_3,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f60,plain,
( product(e_3,e_3,e_1)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f67,plain,
( spl0_4
<=> product(e_2,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f68,plain,
( product(e_2,e_2,e_1)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( spl0_5
<=> product(e_3,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f71,plain,
( product(e_3,e_2,e_1)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f75,plain,
( spl0_6
<=> product(e_1,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f76,plain,
( product(e_1,e_1,e_1)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( spl0_7
<=> product(e_2,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f79,plain,
( product(e_2,e_1,e_1)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( spl0_8
<=> product(e_3,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f82,plain,
( product(e_3,e_1,e_1)
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f44,f25]) ).
fof(f85,plain,
( spl0_6
| spl0_7
| spl0_8 ),
inference(split_clause,[status(thm)],[f84,f75,f78,f81]) ).
fof(f86,plain,
( spl0_9
<=> product(e_1,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f87,plain,
( product(e_1,e_3,e_2)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,plain,
( spl0_10
<=> product(e_2,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f92,plain,
( spl0_11
<=> product(e_3,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f95,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f45,f27]) ).
fof(f96,plain,
( spl0_9
| spl0_10
| spl0_11 ),
inference(split_clause,[status(thm)],[f95,f86,f89,f92]) ).
fof(f97,plain,
( spl0_12
<=> product(e_1,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f98,plain,
( product(e_1,e_2,e_2)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( spl0_13
<=> product(e_2,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f101,plain,
( product(e_2,e_2,e_2)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f108,plain,
( spl0_15
<=> product(e_1,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f109,plain,
( product(e_1,e_1,e_2)
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,plain,
( spl0_16
<=> product(e_2,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f112,plain,
( product(e_2,e_1,e_2)
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( spl0_17
<=> product(e_3,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f115,plain,
( product(e_3,e_1,e_2)
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[f45,f25]) ).
fof(f118,plain,
( spl0_15
| spl0_16
| spl0_17 ),
inference(split_clause,[status(thm)],[f117,f108,f111,f114]) ).
fof(f119,plain,
( spl0_18
<=> product(e_1,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f120,plain,
( product(e_1,e_3,e_3)
| ~ spl0_18 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f136,plain,
( spl0_23
<=> product(e_3,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f137,plain,
( product(e_3,e_2,e_3)
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f141,plain,
( spl0_24
<=> product(e_1,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f142,plain,
( product(e_1,e_1,e_3)
| ~ spl0_24 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( spl0_25
<=> product(e_2,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f145,plain,
( product(e_2,e_1,e_3)
| ~ spl0_25 ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( spl0_26
<=> product(e_3,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f148,plain,
( product(e_3,e_1,e_3)
| ~ spl0_26 ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f160,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[f48,f26]) ).
fof(f161,plain,
( spl0_16
| spl0_13
| spl0_10 ),
inference(split_clause,[status(thm)],[f160,f111,f100,f89]) ).
fof(f162,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f48,f25]) ).
fof(f163,plain,
( spl0_15
| spl0_12
| spl0_9 ),
inference(split_clause,[status(thm)],[f162,f108,f97,f86]) ).
fof(f164,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f49,f27]) ).
fof(f165,plain,
( spl0_8
| spl0_5
| spl0_2 ),
inference(split_clause,[status(thm)],[f164,f81,f70,f59]) ).
fof(f166,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f49,f26]) ).
fof(f167,plain,
( spl0_7
| spl0_4
| spl0_1 ),
inference(split_clause,[status(thm)],[f166,f78,f67,f56]) ).
fof(f184,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f52,f26]) ).
fof(f185,plain,
( spl0_7
| spl0_16
| spl0_25 ),
inference(split_clause,[status(thm)],[f184,f78,f111,f144]) ).
fof(f192,plain,
! [X0] :
( product(e_1,e_1,X0)
| ~ product(e_3,e_1,X0)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f82,f24]) ).
fof(f195,plain,
( product(e_1,e_1,e_1)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f192,f82]) ).
fof(f196,plain,
! [X0] :
( ~ product(X0,e_1,e_1)
| equalish(X0,e_1)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f195,f40]) ).
fof(f203,plain,
( equalish(e_3,e_1)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f196,f82]) ).
fof(f204,plain,
( $false
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f203,f32]) ).
fof(f205,plain,
~ spl0_8,
inference(contradiction_clause,[status(thm)],[f204]) ).
fof(f210,plain,
! [X0] :
( product(e_1,e_1,X0)
| ~ product(e_2,e_1,X0)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f79,f24]) ).
fof(f213,plain,
( product(e_1,e_1,e_1)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f210,f79]) ).
fof(f214,plain,
! [X0] :
( ~ product(X0,e_1,e_1)
| equalish(X0,e_1)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f213,f40]) ).
fof(f221,plain,
( equalish(e_2,e_1)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f214,f79]) ).
fof(f222,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f221,f30]) ).
fof(f223,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f222]) ).
fof(f236,plain,
! [X0] :
( product(e_3,X0,e_2)
| ~ product(e_2,X0,e_1)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f71,f22]) ).
fof(f237,plain,
( product(e_3,e_2,e_2)
| ~ spl0_4
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f68,f236]) ).
fof(f241,plain,
! [X0] :
( ~ product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f68,f42]) ).
fof(f243,plain,
( product(e_2,e_2,e_2)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f68,f43]) ).
fof(f243_001,plain,
( product(e_2,e_2,e_2)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f68,f43]) ).
fof(f248,plain,
! [X0] :
( ~ product(X0,e_2,e_2)
| equalish(X0,e_3)
| ~ spl0_4
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f237,f40]) ).
fof(f257,plain,
! [X0] :
( ~ product(e_2,e_2,X0)
| equalish(X0,e_2)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f243,f36]) ).
fof(f261,plain,
( equalish(e_2,e_3)
| ~ spl0_5
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f248,f243]) ).
fof(f262,plain,
( $false
| ~ spl0_5
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f261,f31]) ).
fof(f263,plain,
( ~ spl0_5
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f262]) ).
fof(f278,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_2,e_1)
| product(X0,e_2,e_3)
| ~ spl0_4 ),
inference(backward_subsumption_resolution,[status(thm)],[f51,f241]) ).
fof(f282,plain,
! [X0] :
( ~ product(X0,e_1,e_3)
| product(X0,e_3,e_2)
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f115,f42]) ).
fof(f291,plain,
! [X0] :
( product(X0,e_1,e_2)
| ~ product(X0,e_2,e_2)
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f112,f22]) ).
fof(f292,plain,
! [X0] :
( product(e_2,X0,e_1)
| ~ product(e_1,X0,e_2)
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f112,f22]) ).
fof(f296,plain,
! [X0] :
( ~ product(X0,e_1,e_1)
| product(X0,e_1,e_2)
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f109,f42]) ).
fof(f309,plain,
( product(e_2,e_2,e_1)
| ~ spl0_13
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f101,f241]) ).
fof(f348,plain,
! [X0] :
( ~ product(X0,e_3,e_1)
| product(X0,e_1,e_3)
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f120,f42]) ).
fof(f355,plain,
! [X0] :
( ~ product(X0,e_3,e_2)
| product(X0,e_2,e_1)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f57,f42]) ).
fof(f369,plain,
! [X0] :
( ~ product(X0,e_2,e_3)
| product(X0,e_3,e_3)
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f137,f42]) ).
fof(f376,plain,
! [X0] :
( ~ product(X0,e_1,e_2)
| product(X0,e_2,e_3)
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f145,f42]) ).
fof(f377,plain,
! [X0] :
( product(e_3,e_1,X0)
| ~ product(e_2,e_3,X0)
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f145,f24]) ).
fof(f379,plain,
! [X0] :
( product(e_2,X0,e_1)
| ~ product(e_1,X0,e_3)
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f145,f22]) ).
fof(f387,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_3)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f278,f27]) ).
fof(f388,plain,
( spl0_5
| spl0_23
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f387,f70,f136,f67]) ).
fof(f405,plain,
( product(e_2,e_3,e_2)
| ~ spl0_17
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f282,f145]) ).
fof(f406,plain,
( product(e_3,e_3,e_2)
| ~ spl0_17
| ~ spl0_26 ),
inference(resolution,[status(thm)],[f282,f148]) ).
fof(f407,plain,
! [X0] :
( ~ product(X0,e_3,e_2)
| equalish(X0,e_2)
| ~ spl0_17
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f405,f40]) ).
fof(f431,plain,
( equalish(e_3,e_2)
| ~ spl0_25
| ~ spl0_17
| ~ spl0_26 ),
inference(resolution,[status(thm)],[f407,f406]) ).
fof(f432,plain,
( $false
| ~ spl0_25
| ~ spl0_17
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f431,f33]) ).
fof(f433,plain,
( ~ spl0_25
| ~ spl0_17
| ~ spl0_26 ),
inference(contradiction_clause,[status(thm)],[f432]) ).
fof(f443,plain,
( product(e_2,e_1,e_1)
| ~ spl0_16
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f292,f109]) ).
fof(f444,plain,
( spl0_7
| ~ spl0_16
| ~ spl0_15 ),
inference(split_clause,[status(thm)],[f443,f78,f111,f108]) ).
fof(f476,plain,
( product(e_1,e_2,e_1)
| ~ spl0_1
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f355,f87]) ).
fof(f479,plain,
! [X0] :
( ~ product(e_1,X0,e_1)
| equalish(X0,e_2)
| ~ spl0_1
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f476,f38]) ).
fof(f487,plain,
( equalish(e_1,e_2)
| ~ spl0_1
| ~ spl0_9
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f479,f76]) ).
fof(f488,plain,
( $false
| ~ spl0_1
| ~ spl0_9
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f487,f28]) ).
fof(f489,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_6 ),
inference(contradiction_clause,[status(thm)],[f488]) ).
fof(f491,plain,
( product(e_1,e_3,e_2)
| ~ spl0_17
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f282,f142]) ).
fof(f492,plain,
( spl0_9
| ~ spl0_17
| ~ spl0_24 ),
inference(split_clause,[status(thm)],[f491,f86,f114,f141]) ).
fof(f510,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_3)
| product(X0,e_3,e_3)
| ~ spl0_23 ),
inference(backward_subsumption_resolution,[status(thm)],[f47,f369]) ).
fof(f515,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_3,e_3)
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f510,f25]) ).
fof(f516,plain,
( spl0_24
| spl0_18
| ~ spl0_23 ),
inference(split_clause,[status(thm)],[f515,f141,f119,f136]) ).
fof(f518,plain,
( equalish(e_1,e_2)
| ~ spl0_13
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f257,f309]) ).
fof(f519,plain,
( $false
| ~ spl0_13
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f28]) ).
fof(f520,plain,
( ~ spl0_13
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f522,plain,
( product(e_1,e_1,e_2)
| ~ spl0_15
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f296,f76]) ).
fof(f523,plain,
( product(e_1,e_2,e_3)
| ~ spl0_15
| ~ spl0_6
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f522,f376]) ).
fof(f534,plain,
( product(e_2,e_2,e_1)
| ~ spl0_15
| ~ spl0_6
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f523,f379]) ).
fof(f535,plain,
( spl0_4
| ~ spl0_15
| ~ spl0_6
| ~ spl0_25 ),
inference(split_clause,[status(thm)],[f534,f67,f108,f75,f144]) ).
fof(f540,plain,
( product(e_1,e_1,e_2)
| ~ spl0_16
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f291,f98]) ).
fof(f541,plain,
( spl0_15
| ~ spl0_16
| ~ spl0_12 ),
inference(split_clause,[status(thm)],[f540,f108,f111,f97]) ).
fof(f542,plain,
( spl0_13
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f243,f100,f67]) ).
fof(f553,plain,
( product(e_3,e_1,e_3)
| ~ spl0_2
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f60,f348]) ).
fof(f554,plain,
( spl0_26
| ~ spl0_2
| ~ spl0_18 ),
inference(split_clause,[status(thm)],[f553,f147,f59,f119]) ).
fof(f581,plain,
( product(e_3,e_1,e_1)
| ~ spl0_1
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f57,f377]) ).
fof(f582,plain,
( spl0_8
| ~ spl0_1
| ~ spl0_25 ),
inference(split_clause,[status(thm)],[f581,f81,f56,f144]) ).
fof(f590,plain,
$false,
inference(sat_refutation,[status(thm)],[f85,f96,f118,f161,f163,f165,f167,f185,f205,f223,f263,f388,f433,f444,f489,f492,f516,f520,f535,f541,f542,f554,f582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP128-4.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.15/0.34 % Computer : n004.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue May 30 11:28:52 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Drodi V3.5.1
% 0.15/0.37 % Refutation found
% 0.15/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.38 % Elapsed time: 0.031502 seconds
% 0.15/0.38 % CPU time: 0.121599 seconds
% 0.15/0.38 % Memory used: 3.664 MB
%------------------------------------------------------------------------------