TSTP Solution File: GRP124-1.004 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP124-1.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n023.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 20:19:19 EDT 2024
% Result : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 58
% Syntax : Number of formulae : 266 ( 62 unt; 0 def)
% Number of atoms : 567 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 601 ( 300 ~; 260 |; 0 &)
% ( 41 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 45 ( 44 usr; 42 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 125 ( 125 !; 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,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,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(f18,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
! [X1,Y1,Z1,X2,Y2,Z2] :
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,X1,Y1)
| ~ product(Z2,X2,Y2)
| equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
! [X1,Y1,Z1,X2,Y2,Z2] :
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,X1,Y1)
| ~ product(Z2,X2,Y2)
| equalish(Y1,Y2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f25,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f26,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f27,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f28,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f29,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f30,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f32,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f33,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f36,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f40,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)],[f17]) ).
fof(f41,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f18]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f45,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f47,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f48,plain,
! [X1,X2] :
( ! [Y2,Z2] :
( ! [Y1] :
( ! [Z1] :
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1) )
| ~ product(Z2,X1,Y1) )
| ~ product(Z2,X2,Y2) )
| equalish(X1,X2) ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X0,X1)
| ~ product(X5,X3,X4)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f50,plain,
! [Y1,Y2] :
( ! [X2,Z2] :
( ! [X1] :
( ! [Z1] :
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1) )
| ~ product(Z2,X1,Y1) )
| ~ product(Z2,X2,Y2) )
| equalish(Y1,Y2) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X0,X1)
| ~ product(X5,X3,X4)
| equalish(X1,X4) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f28,f46]) ).
fof(f53,plain,
! [X0,X1] :
( ~ product(X0,e_1,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f28,f44]) ).
fof(f54,plain,
! [X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f28,f42]) ).
fof(f57,plain,
~ product(e_1,e_2,e_2),
inference(resolution,[status(thm)],[f52,f47]) ).
fof(f58,plain,
~ product(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f53,f47]) ).
fof(f59,plain,
~ product(e_2,e_2,e_1),
inference(resolution,[status(thm)],[f54,f47]) ).
fof(f62,plain,
! [X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f29,f46]) ).
fof(f63,plain,
! [X0,X1] :
( ~ product(X0,e_1,X1)
| ~ product(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f29,f44]) ).
fof(f64,plain,
! [X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_3) ),
inference(resolution,[status(thm)],[f29,f42]) ).
fof(f67,plain,
! [X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(e_4,X0,X1) ),
inference(resolution,[status(thm)],[f30,f46]) ).
fof(f68,plain,
! [X0,X1] :
( ~ product(X0,e_1,X1)
| ~ product(X0,e_4,X1) ),
inference(resolution,[status(thm)],[f30,f44]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,e_1,X1)
| ~ product(X2,e_4,X1)
| ~ product(X3,X0,e_1)
| ~ product(X3,X2,e_4) ),
inference(resolution,[status(thm)],[f30,f51]) ).
fof(f77,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f32,f46]) ).
fof(f78,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f32,f44]) ).
fof(f79,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_3) ),
inference(resolution,[status(thm)],[f32,f42]) ).
fof(f82,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_4,X0,X1) ),
inference(resolution,[status(thm)],[f33,f46]) ).
fof(f83,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_4,X1) ),
inference(resolution,[status(thm)],[f33,f44]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( ~ product(e_2,X0,X1)
| ~ product(e_4,X2,X1)
| ~ product(X3,e_2,X0)
| ~ product(X3,e_4,X2) ),
inference(resolution,[status(thm)],[f33,f49]) ).
fof(f97,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_4,X0,X1) ),
inference(resolution,[status(thm)],[f36,f46]) ).
fof(f98,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_4,X1) ),
inference(resolution,[status(thm)],[f36,f44]) ).
fof(f117,plain,
~ product(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f62,f47]) ).
fof(f118,plain,
~ product(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f63,f47]) ).
fof(f119,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_4,e_1)
| product(X0,e_4,e_2)
| product(X0,e_4,e_3)
| product(X0,e_4,e_4) ),
inference(resolution,[status(thm)],[f40,f27]) ).
fof(f120,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| product(X0,e_3,e_3)
| product(X0,e_3,e_4) ),
inference(resolution,[status(thm)],[f40,f26]) ).
fof(f121,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2)
| product(X0,e_2,e_3)
| product(X0,e_2,e_4) ),
inference(resolution,[status(thm)],[f40,f25]) ).
fof(f123,plain,
~ product(e_3,e_3,e_1),
inference(resolution,[status(thm)],[f64,f47]) ).
fof(f131,plain,
! [X0,X1] :
( ~ product(e_2,X0,e_4)
| ~ product(X1,e_2,X0)
| ~ product(X1,e_4,e_4) ),
inference(resolution,[status(thm)],[f86,f47]) ).
fof(f134,plain,
~ product(e_1,e_4,e_4),
inference(resolution,[status(thm)],[f67,f47]) ).
fof(f135,plain,
~ product(e_4,e_1,e_4),
inference(resolution,[status(thm)],[f68,f47]) ).
fof(f137,plain,
~ product(e_2,e_3,e_3),
inference(resolution,[status(thm)],[f77,f47]) ).
fof(f138,plain,
~ product(e_3,e_2,e_3),
inference(resolution,[status(thm)],[f78,f47]) ).
fof(f139,plain,
~ product(e_3,e_3,e_2),
inference(resolution,[status(thm)],[f79,f47]) ).
fof(f140,plain,
~ product(e_2,e_4,e_4),
inference(resolution,[status(thm)],[f82,f47]) ).
fof(f141,plain,
~ product(e_4,e_2,e_4),
inference(resolution,[status(thm)],[f83,f47]) ).
fof(f143,plain,
~ product(e_3,e_4,e_4),
inference(resolution,[status(thm)],[f97,f47]) ).
fof(f144,plain,
~ product(e_4,e_3,e_4),
inference(resolution,[status(thm)],[f98,f47]) ).
fof(f160,plain,
( spl0_4
<=> product(e_3,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f161,plain,
( product(e_3,e_4,e_1)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( spl0_5
<=> product(e_3,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f164,plain,
( product(e_3,e_4,e_2)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( spl0_6
<=> product(e_3,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f167,plain,
( product(e_3,e_4,e_3)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,plain,
( spl0_7
<=> product(e_3,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f170,plain,
( product(e_3,e_4,e_4)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_4) ),
inference(resolution,[status(thm)],[f119,f26]) ).
fof(f173,plain,
( spl0_4
| spl0_5
| spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f172,f160,f163,f166,f169]) ).
fof(f174,plain,
( spl0_8
<=> product(e_2,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f175,plain,
( product(e_2,e_4,e_1)
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( spl0_9
<=> product(e_2,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f178,plain,
( product(e_2,e_4,e_2)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,plain,
( spl0_10
<=> product(e_2,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f181,plain,
( product(e_2,e_4,e_3)
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f183,plain,
( spl0_11
<=> product(e_2,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f184,plain,
( product(e_2,e_4,e_4)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,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)],[f119,f25]) ).
fof(f187,plain,
( spl0_8
| spl0_9
| spl0_10
| spl0_11 ),
inference(split_clause,[status(thm)],[f186,f174,f177,f180,f183]) ).
fof(f188,plain,
( spl0_12
<=> product(e_1,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f189,plain,
( product(e_1,e_4,e_1)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,plain,
( spl0_13
<=> product(e_1,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f192,plain,
( product(e_1,e_4,e_2)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f194,plain,
( spl0_14
<=> product(e_1,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f195,plain,
( product(e_1,e_4,e_3)
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,plain,
( spl0_15
<=> product(e_1,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f198,plain,
( product(e_1,e_4,e_4)
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,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)],[f119,f24]) ).
fof(f201,plain,
( spl0_12
| spl0_13
| spl0_14
| spl0_15 ),
inference(split_clause,[status(thm)],[f200,f188,f191,f194,f197]) ).
fof(f202,plain,
( $false
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f134]) ).
fof(f203,plain,
~ spl0_15,
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f204,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f140]) ).
fof(f205,plain,
~ spl0_11,
inference(contradiction_clause,[status(thm)],[f204]) ).
fof(f206,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f143]) ).
fof(f207,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f206]) ).
fof(f210,plain,
( ~ product(e_1,e_2,e_3)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f195,f83]) ).
fof(f221,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f189,f68]) ).
fof(f222,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f221,f47]) ).
fof(f223,plain,
~ spl0_12,
inference(contradiction_clause,[status(thm)],[f222]) ).
fof(f238,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f178,f83]) ).
fof(f239,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f47]) ).
fof(f240,plain,
~ spl0_9,
inference(contradiction_clause,[status(thm)],[f239]) ).
fof(f243,plain,
( ~ product(e_2,e_3,e_1)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f175,f98]) ).
fof(f255,plain,
( ~ product(e_1,e_4,e_2)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f164,f62]) ).
fof(f257,plain,
( ~ product(e_3,e_2,e_2)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f164,f83]) ).
fof(f263,plain,
( ~ product(e_2,e_4,e_1)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f161,f77]) ).
fof(f264,plain,
( $false
| ~ spl0_8
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f175]) ).
fof(f265,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f264]) ).
fof(f267,plain,
( ~ product(e_1,e_3,e_2)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f192,f98]) ).
fof(f273,plain,
( $false
| ~ spl0_13
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f255,f192]) ).
fof(f274,plain,
( ~ spl0_13
| ~ spl0_5 ),
inference(contradiction_clause,[status(thm)],[f273]) ).
fof(f282,plain,
! [X0,X1] :
( ~ product(X0,e_1,e_1)
| ~ product(X1,X0,e_1)
| ~ product(X1,e_3,e_4)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f161,f70]) ).
fof(f298,plain,
( spl0_18
<=> product(e_4,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f299,plain,
( product(e_4,e_3,e_3)
| ~ spl0_18 ),
inference(component_clause,[status(thm)],[f298]) ).
fof(f301,plain,
( spl0_19
<=> product(e_4,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f302,plain,
( product(e_4,e_3,e_4)
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f306,plain,
( spl0_20
<=> product(e_3,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f307,plain,
( product(e_3,e_3,e_1)
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,plain,
( spl0_21
<=> product(e_3,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f310,plain,
( product(e_3,e_3,e_2)
| ~ spl0_21 ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f320,plain,
( spl0_24
<=> product(e_2,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f321,plain,
( product(e_2,e_3,e_1)
| ~ spl0_24 ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,plain,
( spl0_25
<=> product(e_2,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f324,plain,
( product(e_2,e_3,e_2)
| ~ spl0_25 ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f326,plain,
( spl0_26
<=> product(e_2,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f327,plain,
( product(e_2,e_3,e_3)
| ~ spl0_26 ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f329,plain,
( spl0_27
<=> product(e_2,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f330,plain,
( product(e_2,e_3,e_4)
| ~ spl0_27 ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f332,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(resolution,[status(thm)],[f120,f25]) ).
fof(f333,plain,
( spl0_24
| spl0_25
| spl0_26
| spl0_27 ),
inference(split_clause,[status(thm)],[f332,f320,f323,f326,f329]) ).
fof(f334,plain,
( spl0_28
<=> product(e_1,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f335,plain,
( product(e_1,e_3,e_1)
| ~ spl0_28 ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,plain,
( spl0_29
<=> product(e_1,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f338,plain,
( product(e_1,e_3,e_2)
| ~ spl0_29 ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f340,plain,
( spl0_30
<=> product(e_1,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f341,plain,
( product(e_1,e_3,e_3)
| ~ spl0_30 ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f343,plain,
( spl0_31
<=> product(e_1,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f344,plain,
( product(e_1,e_3,e_4)
| ~ spl0_31 ),
inference(component_clause,[status(thm)],[f343]) ).
fof(f346,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[f120,f24]) ).
fof(f347,plain,
( spl0_28
| spl0_29
| spl0_30
| spl0_31 ),
inference(split_clause,[status(thm)],[f346,f334,f337,f340,f343]) ).
fof(f348,plain,
( $false
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[status(thm)],[f341,f117]) ).
fof(f349,plain,
~ spl0_30,
inference(contradiction_clause,[status(thm)],[f348]) ).
fof(f350,plain,
( $false
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f137]) ).
fof(f351,plain,
~ spl0_26,
inference(contradiction_clause,[status(thm)],[f350]) ).
fof(f352,plain,
( $false
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f139]) ).
fof(f353,plain,
~ spl0_21,
inference(contradiction_clause,[status(thm)],[f352]) ).
fof(f354,plain,
( $false
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f307,f123]) ).
fof(f355,plain,
~ spl0_20,
inference(contradiction_clause,[status(thm)],[f354]) ).
fof(f356,plain,
( $false
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f302,f144]) ).
fof(f357,plain,
~ spl0_19,
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f358,plain,
( spl0_32
<=> product(e_4,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f359,plain,
( product(e_4,e_2,e_1)
| ~ spl0_32 ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f361,plain,
( spl0_33
<=> product(e_4,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f362,plain,
( product(e_4,e_2,e_2)
| ~ spl0_33 ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,plain,
( spl0_34
<=> product(e_4,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f365,plain,
( product(e_4,e_2,e_3)
| ~ spl0_34 ),
inference(component_clause,[status(thm)],[f364]) ).
fof(f367,plain,
( spl0_35
<=> product(e_4,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f368,plain,
( product(e_4,e_2,e_4)
| ~ spl0_35 ),
inference(component_clause,[status(thm)],[f367]) ).
fof(f370,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)],[f121,f27]) ).
fof(f371,plain,
( spl0_32
| spl0_33
| spl0_34
| spl0_35 ),
inference(split_clause,[status(thm)],[f370,f358,f361,f364,f367]) ).
fof(f372,plain,
( spl0_36
<=> product(e_3,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f373,plain,
( product(e_3,e_2,e_1)
| ~ spl0_36 ),
inference(component_clause,[status(thm)],[f372]) ).
fof(f375,plain,
( spl0_37
<=> product(e_3,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f376,plain,
( product(e_3,e_2,e_2)
| ~ spl0_37 ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,plain,
( spl0_38
<=> product(e_3,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f379,plain,
( product(e_3,e_2,e_3)
| ~ spl0_38 ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,plain,
( spl0_39
<=> product(e_3,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f382,plain,
( product(e_3,e_2,e_4)
| ~ spl0_39 ),
inference(component_clause,[status(thm)],[f381]) ).
fof(f384,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4) ),
inference(resolution,[status(thm)],[f121,f26]) ).
fof(f385,plain,
( spl0_36
| spl0_37
| spl0_38
| spl0_39 ),
inference(split_clause,[status(thm)],[f384,f372,f375,f378,f381]) ).
fof(f386,plain,
( spl0_40
<=> product(e_2,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f387,plain,
( product(e_2,e_2,e_1)
| ~ spl0_40 ),
inference(component_clause,[status(thm)],[f386]) ).
fof(f392,plain,
( spl0_42
<=> product(e_2,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f393,plain,
( product(e_2,e_2,e_3)
| ~ spl0_42 ),
inference(component_clause,[status(thm)],[f392]) ).
fof(f400,plain,
( spl0_44
<=> product(e_1,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f401,plain,
( product(e_1,e_2,e_1)
| ~ spl0_44 ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f403,plain,
( spl0_45
<=> product(e_1,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f404,plain,
( product(e_1,e_2,e_2)
| ~ spl0_45 ),
inference(component_clause,[status(thm)],[f403]) ).
fof(f406,plain,
( spl0_46
<=> product(e_1,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f407,plain,
( product(e_1,e_2,e_3)
| ~ spl0_46 ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f409,plain,
( spl0_47
<=> product(e_1,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f410,plain,
( product(e_1,e_2,e_4)
| ~ spl0_47 ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f412,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[f121,f24]) ).
fof(f413,plain,
( spl0_44
| spl0_45
| spl0_46
| spl0_47 ),
inference(split_clause,[status(thm)],[f412,f400,f403,f406,f409]) ).
fof(f414,plain,
( $false
| ~ spl0_45 ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f57]) ).
fof(f415,plain,
~ spl0_45,
inference(contradiction_clause,[status(thm)],[f414]) ).
fof(f416,plain,
( $false
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[status(thm)],[f387,f59]) ).
fof(f417,plain,
~ spl0_40,
inference(contradiction_clause,[status(thm)],[f416]) ).
fof(f418,plain,
( $false
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[status(thm)],[f379,f138]) ).
fof(f419,plain,
~ spl0_38,
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f420,plain,
( $false
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[status(thm)],[f368,f141]) ).
fof(f421,plain,
~ spl0_35,
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f431,plain,
( spl0_51
<=> product(e_4,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f432,plain,
( product(e_4,e_1,e_4)
| ~ spl0_51 ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f442,plain,
( spl0_54
<=> product(e_3,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f443,plain,
( product(e_3,e_1,e_3)
| ~ spl0_54 ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f453,plain,
( spl0_57
<=> product(e_2,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f454,plain,
( product(e_2,e_1,e_2)
| ~ spl0_57 ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f478,plain,
( $false
| ~ spl0_57 ),
inference(forward_subsumption_resolution,[status(thm)],[f454,f58]) ).
fof(f479,plain,
~ spl0_57,
inference(contradiction_clause,[status(thm)],[f478]) ).
fof(f480,plain,
( $false
| ~ spl0_54 ),
inference(forward_subsumption_resolution,[status(thm)],[f443,f118]) ).
fof(f481,plain,
~ spl0_54,
inference(contradiction_clause,[status(thm)],[f480]) ).
fof(f482,plain,
( $false
| ~ spl0_51 ),
inference(forward_subsumption_resolution,[status(thm)],[f432,f135]) ).
fof(f483,plain,
~ spl0_51,
inference(contradiction_clause,[status(thm)],[f482]) ).
fof(f493,plain,
! [X0] :
( ~ product(X0,e_1,e_1)
| ~ product(e_1,X0,e_1)
| ~ spl0_31
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f344,f282]) ).
fof(f504,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_31
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f493,f47]) ).
fof(f505,plain,
( $false
| ~ spl0_31
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f47]) ).
fof(f506,plain,
( ~ spl0_31
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f507,plain,
( $false
| ~ spl0_13
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[status(thm)],[f338,f267]) ).
fof(f508,plain,
( ~ spl0_13
| ~ spl0_29 ),
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f512,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_28 ),
inference(resolution,[status(thm)],[f335,f63]) ).
fof(f513,plain,
( $false
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f47]) ).
fof(f514,plain,
~ spl0_28,
inference(contradiction_clause,[status(thm)],[f513]) ).
fof(f517,plain,
( ~ product(e_3,e_3,e_3)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f167,f98]) ).
fof(f518,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f517,f47]) ).
fof(f519,plain,
~ spl0_6,
inference(contradiction_clause,[status(thm)],[f518]) ).
fof(f520,plain,
( ~ product(e_1,e_4,e_3)
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f181,f52]) ).
fof(f521,plain,
( ~ spl0_14
| ~ spl0_10 ),
inference(split_clause,[status(thm)],[f520,f194,f180]) ).
fof(f524,plain,
! [X0] :
( ~ product(X0,e_2,e_3)
| ~ product(X0,e_4,e_4)
| ~ spl0_27 ),
inference(resolution,[status(thm)],[f330,f131]) ).
fof(f537,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f324,f78]) ).
fof(f538,plain,
( $false
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[status(thm)],[f537,f47]) ).
fof(f539,plain,
~ spl0_25,
inference(contradiction_clause,[status(thm)],[f538]) ).
fof(f540,plain,
( $false
| ~ spl0_8
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[status(thm)],[f321,f243]) ).
fof(f541,plain,
( ~ spl0_8
| ~ spl0_24 ),
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f546,plain,
( ~ product(e_3,e_3,e_3)
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f299,f97]) ).
fof(f547,plain,
( $false
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f47]) ).
fof(f548,plain,
~ spl0_18,
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f577,plain,
( $false
| ~ spl0_14
| ~ spl0_46 ),
inference(forward_subsumption_resolution,[status(thm)],[f407,f210]) ).
fof(f578,plain,
( ~ spl0_14
| ~ spl0_46 ),
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f580,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_44 ),
inference(resolution,[status(thm)],[f401,f53]) ).
fof(f581,plain,
( $false
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[status(thm)],[f580,f47]) ).
fof(f582,plain,
~ spl0_44,
inference(contradiction_clause,[status(thm)],[f581]) ).
fof(f594,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_42 ),
inference(resolution,[status(thm)],[f393,f79]) ).
fof(f595,plain,
( $false
| ~ spl0_42 ),
inference(forward_subsumption_resolution,[status(thm)],[f594,f47]) ).
fof(f596,plain,
~ spl0_42,
inference(contradiction_clause,[status(thm)],[f595]) ).
fof(f601,plain,
( ~ product(e_1,e_2,e_4)
| ~ spl0_39 ),
inference(resolution,[status(thm)],[f382,f62]) ).
fof(f602,plain,
( $false
| ~ spl0_47
| ~ spl0_39 ),
inference(forward_subsumption_resolution,[status(thm)],[f601,f410]) ).
fof(f603,plain,
( ~ spl0_47
| ~ spl0_39 ),
inference(contradiction_clause,[status(thm)],[f602]) ).
fof(f604,plain,
( $false
| ~ spl0_5
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[status(thm)],[f376,f257]) ).
fof(f605,plain,
( ~ spl0_5
| ~ spl0_37 ),
inference(contradiction_clause,[status(thm)],[f604]) ).
fof(f623,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_33 ),
inference(resolution,[status(thm)],[f362,f82]) ).
fof(f624,plain,
( $false
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[status(thm)],[f623,f47]) ).
fof(f625,plain,
~ spl0_33,
inference(contradiction_clause,[status(thm)],[f624]) ).
fof(f626,plain,
( ~ product(e_3,e_2,e_1)
| ~ spl0_32 ),
inference(resolution,[status(thm)],[f359,f97]) ).
fof(f627,plain,
( $false
| ~ spl0_36
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[status(thm)],[f626,f373]) ).
fof(f628,plain,
( ~ spl0_36
| ~ spl0_32 ),
inference(contradiction_clause,[status(thm)],[f627]) ).
fof(f629,plain,
( ~ product(e_4,e_2,e_3)
| ~ spl0_27 ),
inference(resolution,[status(thm)],[f524,f47]) ).
fof(f630,plain,
( $false
| ~ spl0_34
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[status(thm)],[f629,f365]) ).
fof(f631,plain,
( ~ spl0_34
| ~ spl0_27 ),
inference(contradiction_clause,[status(thm)],[f630]) ).
fof(f632,plain,
$false,
inference(sat_refutation,[status(thm)],[f173,f187,f201,f203,f205,f207,f223,f240,f265,f274,f333,f347,f349,f351,f353,f355,f357,f371,f385,f413,f415,f417,f419,f421,f479,f481,f483,f506,f508,f514,f519,f521,f539,f541,f548,f578,f582,f596,f603,f605,f625,f628,f631]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP124-1.004 : TPTP v8.1.2. Released v1.2.0.
% 0.08/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 30 00:41:10 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.060961 seconds
% 0.13/0.41 % CPU time: 0.409313 seconds
% 0.13/0.41 % Total memory used: 13.796 MB
% 0.13/0.41 % Net memory used: 13.289 MB
%------------------------------------------------------------------------------