TSTP Solution File: GRP126-4.004 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP126-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 12:10:34 EDT 2023
% Result : Unsatisfiable 0.15s 0.34s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 52
% Syntax : Number of formulae : 213 ( 40 unt; 0 def)
% Number of atoms : 521 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 514 ( 206 ~; 277 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 35 ( 34 usr; 32 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 98 (; 98 !; 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)
| product(e_4,X,Y) ),
file('/export/starexec/sandbox/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)
| product(X,e_4,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [X,Y,Z1,Z2] :
( product(X,Y,Z1)
| ~ product(Z1,Z2,Y)
| ~ product(Y,X,Z2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [Y,X,Z2,Z1] :
( product(Y,X,Z2)
| ~ product(Z1,Z2,Y)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3)
| product(X,Y,e_4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(e_1,X0,X1)
| product(e_2,X0,X1)
| product(e_3,X0,X1)
| product(e_4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f28,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,e_1,X1)
| product(X0,e_2,X1)
| product(X0,e_3,X1)
| product(X0,e_4,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f29,plain,
! [X,Y,Z2] :
( ! [Z1] :
( product(X,Y,Z1)
| ~ product(Z1,Z2,Y) )
| ~ product(Y,X,Z2) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( product(X0,X1,X2)
| ~ product(X2,X3,X1)
| ~ product(X1,X0,X3) ),
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f31,plain,
! [Y,X,Z1] :
( ! [Z2] :
( product(Y,X,Z2)
| ~ product(Z1,Z2,Y) )
| ~ product(X,Y,Z1) ),
inference(miniscoping,[status(esa)],[f4]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( product(X0,X1,X2)
| ~ product(X3,X2,X0)
| ~ product(X1,X0,X3) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f34,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f35,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f36,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f39,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f41,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f42,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f44,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f45,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f46,plain,
~ equalish(e_4,e_1),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f47,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f48,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f49,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3)
| product(X0,X1,e_4) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f50,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f54,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f24]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f56,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f65,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f51,f56]) ).
fof(f67,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f53,f56]) ).
fof(f69,plain,
! [X0,X1] :
( ~ product(X0,X1,X1)
| equalish(X1,X0) ),
inference(resolution,[status(thm)],[f55,f56]) ).
fof(f72,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,e_1,X0)
| product(e_2,e_1,X0)
| product(e_3,e_1,X0)
| product(e_4,e_1,X0) ),
inference(resolution,[status(thm)],[f33,f27]) ).
fof(f73,plain,
! [X0] :
( ~ group_element(X0)
| product(e_2,e_1,X0)
| product(e_2,e_2,X0)
| product(e_2,e_3,X0)
| product(e_2,e_4,X0) ),
inference(resolution,[status(thm)],[f34,f28]) ).
fof(f74,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,e_2,X0)
| product(e_2,e_2,X0)
| product(e_3,e_2,X0)
| product(e_4,e_2,X0) ),
inference(resolution,[status(thm)],[f34,f27]) ).
fof(f75,plain,
! [X0] :
( ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| product(e_2,X0,e_3)
| product(e_2,X0,e_4) ),
inference(resolution,[status(thm)],[f49,f34]) ).
fof(f76,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2)
| product(e_1,X0,e_3)
| product(e_1,X0,e_4) ),
inference(resolution,[status(thm)],[f49,f33]) ).
fof(f86,plain,
( spl0_3
<=> product(e_1,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f87,plain,
( product(e_1,e_4,e_2)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f100,plain,
( spl0_7
<=> product(e_1,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f101,plain,
( product(e_1,e_4,e_1)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f111,plain,
( spl0_10
<=> product(e_4,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f112,plain,
( product(e_4,e_1,e_2)
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f122,plain,
( spl0_13
<=> product(e_4,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f123,plain,
( product(e_4,e_1,e_1)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f133,plain,
( spl0_16
<=> product(e_2,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f134,plain,
( product(e_2,e_4,e_2)
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f144,plain,
( spl0_19
<=> product(e_2,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f145,plain,
( product(e_2,e_4,e_1)
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f152,plain,
( spl0_21
<=> product(e_4,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f153,plain,
( product(e_4,e_2,e_2)
| ~ spl0_21 ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f160,plain,
( spl0_23
<=> product(e_4,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f161,plain,
( product(e_4,e_2,e_1)
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f168,plain,
( spl0_25
<=> product(e_2,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f169,plain,
( product(e_2,e_2,e_4)
| ~ spl0_25 ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f176,plain,
( spl0_27
<=> product(e_2,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f177,plain,
( product(e_2,e_1,e_4)
| ~ spl0_27 ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f184,plain,
( spl0_29
<=> product(e_1,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f185,plain,
( product(e_1,e_2,e_4)
| ~ spl0_29 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f192,plain,
( spl0_31
<=> product(e_1,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f193,plain,
( product(e_1,e_1,e_4)
| ~ spl0_31 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f200,plain,
( spl0_33
<=> product(e_1,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f201,plain,
( product(e_1,e_3,e_4)
| ~ spl0_33 ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f208,plain,
( spl0_35
<=> product(e_2,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f209,plain,
( product(e_2,e_3,e_4)
| ~ spl0_35 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f216,plain,
( spl0_37
<=> product(e_4,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f217,plain,
( product(e_4,e_2,e_3)
| ~ spl0_37 ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f221,plain,
( spl0_38
<=> product(e_2,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f222,plain,
( product(e_2,e_4,e_3)
| ~ spl0_38 ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f229,plain,
( spl0_40
<=> product(e_4,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f230,plain,
( product(e_4,e_1,e_3)
| ~ spl0_40 ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f234,plain,
( spl0_41
<=> product(e_1,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f235,plain,
( product(e_1,e_4,e_3)
| ~ spl0_41 ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f241,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,e_3,X0)
| product(e_2,e_3,X0)
| product(e_3,e_3,X0)
| product(e_4,e_3,X0) ),
inference(resolution,[status(thm)],[f35,f27]) ).
fof(f251,plain,
( spl0_45
<=> product(e_3,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f252,plain,
( product(e_3,e_3,e_4)
| ~ spl0_45 ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f256,plain,
( spl0_46
<=> product(e_3,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f257,plain,
( product(e_3,e_2,e_4)
| ~ spl0_46 ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f261,plain,
( spl0_47
<=> product(e_3,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f262,plain,
( product(e_3,e_1,e_4)
| ~ spl0_47 ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f281,plain,
( spl0_51
<=> product(e_4,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f282,plain,
( product(e_4,e_3,e_3)
| ~ spl0_51 ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f286,plain,
( spl0_52
<=> product(e_4,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f287,plain,
( product(e_4,e_3,e_2)
| ~ spl0_52 ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f291,plain,
( spl0_53
<=> product(e_4,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f292,plain,
( product(e_4,e_3,e_1)
| ~ spl0_53 ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f296,plain,
( spl0_54
<=> product(e_4,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f297,plain,
( product(e_4,e_3,e_4)
| ~ spl0_54 ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_3,e_4) ),
inference(resolution,[status(thm)],[f36,f241]) ).
fof(f300,plain,
( spl0_33
| spl0_35
| spl0_45
| spl0_54 ),
inference(split_clause,[status(thm)],[f299,f200,f208,f251,f296]) ).
fof(f301,plain,
( spl0_55
<=> product(e_3,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f302,plain,
( product(e_3,e_4,e_4)
| ~ spl0_55 ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f308,plain,
( spl0_56
<=> product(e_1,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f309,plain,
( product(e_1,e_4,e_4)
| ~ spl0_56 ),
inference(component_clause,[status(thm)],[f308]) ).
fof(f311,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(resolution,[status(thm)],[f36,f76]) ).
fof(f312,plain,
( spl0_7
| spl0_3
| spl0_41
| spl0_56 ),
inference(split_clause,[status(thm)],[f311,f100,f86,f234,f308]) ).
fof(f313,plain,
( spl0_57
<=> product(e_2,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f314,plain,
( product(e_2,e_4,e_4)
| ~ spl0_57 ),
inference(component_clause,[status(thm)],[f313]) ).
fof(f316,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4) ),
inference(resolution,[status(thm)],[f36,f75]) ).
fof(f317,plain,
( spl0_19
| spl0_16
| spl0_38
| spl0_57 ),
inference(split_clause,[status(thm)],[f316,f144,f133,f221,f313]) ).
fof(f318,plain,
( spl0_58
<=> product(e_4,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f319,plain,
( product(e_4,e_2,e_4)
| ~ spl0_58 ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f321,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_4,e_2,e_4) ),
inference(resolution,[status(thm)],[f36,f74]) ).
fof(f322,plain,
( spl0_29
| spl0_25
| spl0_46
| spl0_58 ),
inference(split_clause,[status(thm)],[f321,f184,f168,f256,f318]) ).
fof(f323,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_2,e_4)
| product(e_2,e_3,e_4)
| product(e_2,e_4,e_4) ),
inference(resolution,[status(thm)],[f36,f73]) ).
fof(f324,plain,
( spl0_27
| spl0_25
| spl0_35
| spl0_57 ),
inference(split_clause,[status(thm)],[f323,f176,f168,f208,f313]) ).
fof(f325,plain,
( spl0_59
<=> product(e_4,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f326,plain,
( product(e_4,e_1,e_4)
| ~ spl0_59 ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f328,plain,
( product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_1,e_4) ),
inference(resolution,[status(thm)],[f36,f72]) ).
fof(f329,plain,
( spl0_31
| spl0_27
| spl0_47
| spl0_59 ),
inference(split_clause,[status(thm)],[f328,f192,f176,f261,f325]) ).
fof(f332,plain,
! [X0] :
( ~ group_element(X0)
| product(e_4,X0,e_1)
| product(e_4,X0,e_2)
| product(e_4,X0,e_3)
| product(e_4,X0,e_4) ),
inference(resolution,[status(thm)],[f36,f49]) ).
fof(f334,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,e_4,X0)
| product(e_2,e_4,X0)
| product(e_3,e_4,X0)
| product(e_4,e_4,X0) ),
inference(resolution,[status(thm)],[f36,f27]) ).
fof(f344,plain,
( spl0_63
<=> product(e_4,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f349,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(resolution,[status(thm)],[f332,f35]) ).
fof(f350,plain,
( spl0_53
| spl0_52
| spl0_51
| spl0_54 ),
inference(split_clause,[status(thm)],[f349,f291,f286,f281,f296]) ).
fof(f351,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_4) ),
inference(resolution,[status(thm)],[f332,f34]) ).
fof(f352,plain,
( spl0_23
| spl0_21
| spl0_37
| spl0_58 ),
inference(split_clause,[status(thm)],[f351,f160,f152,f216,f318]) ).
fof(f353,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(resolution,[status(thm)],[f332,f33]) ).
fof(f354,plain,
( spl0_13
| spl0_10
| spl0_40
| spl0_59 ),
inference(split_clause,[status(thm)],[f353,f122,f111,f229,f325]) ).
fof(f363,plain,
( product(e_1,e_4,e_4)
| product(e_2,e_4,e_4)
| product(e_3,e_4,e_4)
| product(e_4,e_4,e_4) ),
inference(resolution,[status(thm)],[f334,f36]) ).
fof(f364,plain,
( spl0_56
| spl0_57
| spl0_55
| spl0_63 ),
inference(split_clause,[status(thm)],[f363,f308,f313,f301,f344]) ).
fof(f376,plain,
! [X0] :
( product(X0,e_4,e_1)
| ~ product(e_4,X0,e_3)
| ~ spl0_33 ),
inference(resolution,[status(thm)],[f201,f30]) ).
fof(f382,plain,
! [X0] :
( product(e_4,X0,e_2)
| ~ product(X0,e_4,e_1)
| ~ spl0_29 ),
inference(resolution,[status(thm)],[f185,f32]) ).
fof(f389,plain,
( equalish(e_1,e_4)
| ~ spl0_31 ),
inference(resolution,[status(thm)],[f193,f65]) ).
fof(f390,plain,
( $false
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[status(thm)],[f389,f39]) ).
fof(f391,plain,
~ spl0_31,
inference(contradiction_clause,[status(thm)],[f390]) ).
fof(f392,plain,
! [X0] :
( ~ product(X0,e_1,e_4)
| equalish(e_3,X0)
| ~ spl0_47 ),
inference(resolution,[status(thm)],[f262,f55]) ).
fof(f399,plain,
( equalish(e_3,e_2)
| ~ spl0_27
| ~ spl0_47 ),
inference(resolution,[status(thm)],[f177,f392]) ).
fof(f400,plain,
( $false
| ~ spl0_27
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[status(thm)],[f399,f44]) ).
fof(f401,plain,
( ~ spl0_27
| ~ spl0_47 ),
inference(contradiction_clause,[status(thm)],[f400]) ).
fof(f407,plain,
! [X0] :
( product(X0,e_4,e_2)
| ~ product(e_4,X0,e_3)
| ~ spl0_35 ),
inference(resolution,[status(thm)],[f209,f30]) ).
fof(f415,plain,
! [X0] :
( ~ product(e_3,X0,e_4)
| equalish(e_2,X0)
| ~ spl0_46 ),
inference(resolution,[status(thm)],[f257,f53]) ).
fof(f423,plain,
( equalish(e_2,e_3)
| ~ spl0_45
| ~ spl0_46 ),
inference(resolution,[status(thm)],[f252,f415]) ).
fof(f424,plain,
( $false
| ~ spl0_45
| ~ spl0_46 ),
inference(forward_subsumption_resolution,[status(thm)],[f423,f41]) ).
fof(f425,plain,
( ~ spl0_45
| ~ spl0_46 ),
inference(contradiction_clause,[status(thm)],[f424]) ).
fof(f426,plain,
( equalish(e_4,e_1)
| ~ spl0_56 ),
inference(resolution,[status(thm)],[f309,f69]) ).
fof(f427,plain,
( $false
| ~ spl0_56 ),
inference(forward_subsumption_resolution,[status(thm)],[f426,f46]) ).
fof(f428,plain,
~ spl0_56,
inference(contradiction_clause,[status(thm)],[f427]) ).
fof(f429,plain,
( equalish(e_4,e_2)
| ~ spl0_57 ),
inference(resolution,[status(thm)],[f314,f69]) ).
fof(f430,plain,
( $false
| ~ spl0_57 ),
inference(forward_subsumption_resolution,[status(thm)],[f429,f47]) ).
fof(f431,plain,
~ spl0_57,
inference(contradiction_clause,[status(thm)],[f430]) ).
fof(f436,plain,
! [X0] :
( product(e_4,X0,e_1)
| ~ product(X0,e_4,e_2)
| ~ spl0_27 ),
inference(resolution,[status(thm)],[f177,f32]) ).
fof(f442,plain,
! [X0] :
( product(e_3,X0,e_4)
| ~ product(X0,e_3,e_2)
| ~ spl0_38 ),
inference(resolution,[status(thm)],[f222,f32]) ).
fof(f454,plain,
! [X0] :
( product(e_1,X0,e_4)
| ~ product(X0,e_1,e_2)
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f145,f32]) ).
fof(f461,plain,
! [X0] :
( product(e_3,X0,e_4)
| ~ product(X0,e_3,e_1)
| ~ spl0_41 ),
inference(resolution,[status(thm)],[f235,f32]) ).
fof(f471,plain,
! [X0] :
( product(e_2,X0,e_4)
| ~ product(X0,e_2,e_1)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f87,f32]) ).
fof(f479,plain,
( equalish(e_4,e_3)
| ~ spl0_55 ),
inference(resolution,[status(thm)],[f302,f69]) ).
fof(f480,plain,
( $false
| ~ spl0_55 ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f48]) ).
fof(f481,plain,
~ spl0_55,
inference(contradiction_clause,[status(thm)],[f480]) ).
fof(f484,plain,
( equalish(e_2,e_4)
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f169,f65]) ).
fof(f485,plain,
( $false
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[status(thm)],[f484,f42]) ).
fof(f486,plain,
~ spl0_25,
inference(contradiction_clause,[status(thm)],[f485]) ).
fof(f501,plain,
( product(e_1,e_4,e_4)
| ~ spl0_10
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f112,f454]) ).
fof(f502,plain,
( spl0_56
| ~ spl0_10
| ~ spl0_19 ),
inference(split_clause,[status(thm)],[f501,f308,f111,f144]) ).
fof(f510,plain,
( equalish(e_1,e_4)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f123,f69]) ).
fof(f511,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f39]) ).
fof(f512,plain,
~ spl0_13,
inference(contradiction_clause,[status(thm)],[f511]) ).
fof(f513,plain,
( product(e_1,e_4,e_2)
| ~ spl0_35
| ~ spl0_40 ),
inference(resolution,[status(thm)],[f407,f230]) ).
fof(f514,plain,
( spl0_3
| ~ spl0_35
| ~ spl0_40 ),
inference(split_clause,[status(thm)],[f513,f86,f208,f229]) ).
fof(f515,plain,
( product(e_1,e_4,e_1)
| ~ spl0_33
| ~ spl0_40 ),
inference(resolution,[status(thm)],[f376,f230]) ).
fof(f516,plain,
( spl0_7
| ~ spl0_33
| ~ spl0_40 ),
inference(split_clause,[status(thm)],[f515,f100,f200,f229]) ).
fof(f519,plain,
( equalish(e_1,e_4)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f101,f67]) ).
fof(f520,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f39]) ).
fof(f521,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f520]) ).
fof(f525,plain,
( equalish(e_4,e_2)
| ~ spl0_58 ),
inference(resolution,[status(thm)],[f319,f67]) ).
fof(f526,plain,
( $false
| ~ spl0_58 ),
inference(forward_subsumption_resolution,[status(thm)],[f525,f47]) ).
fof(f527,plain,
~ spl0_58,
inference(contradiction_clause,[status(thm)],[f526]) ).
fof(f530,plain,
( product(e_2,e_4,e_2)
| ~ spl0_37
| ~ spl0_35 ),
inference(resolution,[status(thm)],[f217,f407]) ).
fof(f531,plain,
( spl0_16
| ~ spl0_37
| ~ spl0_35 ),
inference(split_clause,[status(thm)],[f530,f133,f216,f208]) ).
fof(f539,plain,
( equalish(e_2,e_4)
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f134,f67]) ).
fof(f540,plain,
( $false
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f42]) ).
fof(f541,plain,
~ spl0_16,
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f546,plain,
( equalish(e_4,e_1)
| ~ spl0_59 ),
inference(resolution,[status(thm)],[f326,f67]) ).
fof(f547,plain,
( $false
| ~ spl0_59 ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f46]) ).
fof(f548,plain,
~ spl0_59,
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f558,plain,
( product(e_2,e_4,e_4)
| ~ spl0_3
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f471,f161]) ).
fof(f559,plain,
( spl0_57
| ~ spl0_3
| ~ spl0_23 ),
inference(split_clause,[status(thm)],[f558,f313,f86,f160]) ).
fof(f563,plain,
( equalish(e_3,e_4)
| ~ spl0_51 ),
inference(resolution,[status(thm)],[f282,f69]) ).
fof(f564,plain,
( $false
| ~ spl0_51 ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f45]) ).
fof(f565,plain,
~ spl0_51,
inference(contradiction_clause,[status(thm)],[f564]) ).
fof(f566,plain,
( product(e_3,e_4,e_4)
| ~ spl0_52
| ~ spl0_38 ),
inference(resolution,[status(thm)],[f287,f442]) ).
fof(f567,plain,
( spl0_55
| ~ spl0_52
| ~ spl0_38 ),
inference(split_clause,[status(thm)],[f566,f301,f286,f221]) ).
fof(f583,plain,
( equalish(e_2,e_4)
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f153,f69]) ).
fof(f584,plain,
( $false
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[status(thm)],[f583,f42]) ).
fof(f585,plain,
~ spl0_21,
inference(contradiction_clause,[status(thm)],[f584]) ).
fof(f586,plain,
( product(e_4,e_2,e_2)
| ~ spl0_19
| ~ spl0_29 ),
inference(resolution,[status(thm)],[f145,f382]) ).
fof(f587,plain,
( spl0_21
| ~ spl0_19
| ~ spl0_29 ),
inference(split_clause,[status(thm)],[f586,f152,f144,f184]) ).
fof(f589,plain,
( equalish(e_4,e_3)
| ~ spl0_54 ),
inference(resolution,[status(thm)],[f297,f67]) ).
fof(f590,plain,
( $false
| ~ spl0_54 ),
inference(forward_subsumption_resolution,[status(thm)],[f589,f48]) ).
fof(f591,plain,
~ spl0_54,
inference(contradiction_clause,[status(thm)],[f590]) ).
fof(f592,plain,
( product(e_3,e_4,e_4)
| ~ spl0_53
| ~ spl0_41 ),
inference(resolution,[status(thm)],[f292,f461]) ).
fof(f593,plain,
( spl0_55
| ~ spl0_53
| ~ spl0_41 ),
inference(split_clause,[status(thm)],[f592,f301,f291,f234]) ).
fof(f594,plain,
( product(e_4,e_1,e_1)
| ~ spl0_3
| ~ spl0_27 ),
inference(resolution,[status(thm)],[f87,f436]) ).
fof(f595,plain,
( spl0_13
| ~ spl0_3
| ~ spl0_27 ),
inference(split_clause,[status(thm)],[f594,f122,f86,f176]) ).
fof(f596,plain,
$false,
inference(sat_refutation,[status(thm)],[f300,f312,f317,f322,f324,f329,f350,f352,f354,f364,f391,f401,f425,f428,f431,f481,f486,f502,f512,f514,f516,f521,f527,f531,f541,f548,f559,f565,f567,f585,f587,f591,f593,f595]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GRP126-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.03/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n019.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 11:35:40 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.31 % Drodi V3.5.1
% 0.15/0.34 % Refutation found
% 0.15/0.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.38 % Elapsed time: 0.071341 seconds
% 0.15/0.38 % CPU time: 0.079785 seconds
% 0.15/0.38 % Memory used: 1.974 MB
%------------------------------------------------------------------------------