TSTP Solution File: GRP126-2.004 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP126-2.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.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 20:19:22 EDT 2024
% Result : Unsatisfiable 0.11s 0.34s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 67
% Syntax : Number of formulae : 282 ( 66 unt; 0 def)
% Number of atoms : 584 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 559 ( 257 ~; 257 |; 0 &)
% ( 45 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 49 ( 48 usr; 46 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 72 ( 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,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(f28,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2)
| product(Z1,Z2,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f45,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f46,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f47,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f48,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f49,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f50,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f51,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f52,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f53,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f54,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f55,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f56,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f57,plain,
~ equalish(e_4,e_1),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f58,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f59,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f60,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)],[f27]) ).
fof(f61,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f28]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f63,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f29]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f65,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f30]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f67,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f68,plain,
! [Y,Z1,Z2] :
( ! [X] :
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2) )
| product(Z1,Z2,Y) ),
inference(miniscoping,[status(esa)],[f32]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X1,X0,X3)
| product(X2,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f72,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f62,f67]) ).
fof(f74,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f64,f67]) ).
fof(f76,plain,
! [X0,X1] :
( ~ product(X0,X1,X1)
| equalish(X1,X0) ),
inference(resolution,[status(thm)],[f66,f67]) ).
fof(f79,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)],[f60,f47]) ).
fof(f80,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| product(e_3,X0,e_3)
| product(e_3,X0,e_4) ),
inference(resolution,[status(thm)],[f60,f46]) ).
fof(f81,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)],[f60,f45]) ).
fof(f82,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)],[f60,f44]) ).
fof(f97,plain,
( spl0_4
<=> product(e_4,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f98,plain,
( product(e_4,e_3,e_1)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( spl0_5
<=> product(e_4,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f101,plain,
( product(e_4,e_3,e_2)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( spl0_6
<=> product(e_4,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f104,plain,
( product(e_4,e_3,e_3)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( spl0_7
<=> product(e_4,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f107,plain,
( product(e_4,e_3,e_4)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,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)],[f79,f46]) ).
fof(f110,plain,
( spl0_4
| spl0_5
| spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f109,f97,f100,f103,f106]) ).
fof(f114,plain,
( spl0_9
<=> product(e_4,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f115,plain,
( product(e_4,e_2,e_2)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f120,plain,
( spl0_11
<=> product(e_4,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f121,plain,
( product(e_4,e_2,e_4)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f125,plain,
( spl0_12
<=> product(e_4,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f126,plain,
( product(e_4,e_1,e_1)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( spl0_13
<=> product(e_4,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f129,plain,
( product(e_4,e_1,e_2)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f131,plain,
( spl0_14
<=> product(e_4,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f132,plain,
( product(e_4,e_1,e_3)
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( spl0_15
<=> product(e_4,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f135,plain,
( product(e_4,e_1,e_4)
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,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)],[f79,f44]) ).
fof(f138,plain,
( spl0_12
| spl0_13
| spl0_14
| spl0_15 ),
inference(split_clause,[status(thm)],[f137,f125,f128,f131,f134]) ).
fof(f141,plain,
( equalish(e_4,e_1)
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f135,f74]) ).
fof(f142,plain,
( $false
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f57]) ).
fof(f143,plain,
~ spl0_15,
inference(contradiction_clause,[status(thm)],[f142]) ).
fof(f148,plain,
! [X0] :
( ~ product(e_1,e_4,X0)
| product(e_3,X0,e_1)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f132,f69]) ).
fof(f156,plain,
( equalish(e_1,e_4)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f126,f76]) ).
fof(f157,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f50]) ).
fof(f158,plain,
~ spl0_12,
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f161,plain,
! [X0] :
( ~ product(e_4,X0,e_2)
| equalish(e_1,X0)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f129,f64]) ).
fof(f165,plain,
( equalish(e_4,e_2)
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f121,f74]) ).
fof(f166,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f58]) ).
fof(f167,plain,
~ spl0_11,
inference(contradiction_clause,[status(thm)],[f166]) ).
fof(f181,plain,
( equalish(e_4,e_3)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f107,f74]) ).
fof(f182,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f59]) ).
fof(f183,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f182]) ).
fof(f184,plain,
( equalish(e_3,e_4)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f104,f76]) ).
fof(f185,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f56]) ).
fof(f186,plain,
~ spl0_6,
inference(contradiction_clause,[status(thm)],[f185]) ).
fof(f187,plain,
( equalish(e_1,e_3)
| ~ spl0_5
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f101,f161]) ).
fof(f188,plain,
( $false
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f187,f49]) ).
fof(f189,plain,
( ~ spl0_5
| ~ spl0_13 ),
inference(contradiction_clause,[status(thm)],[f188]) ).
fof(f190,plain,
! [X0] :
( ~ product(X0,e_3,e_1)
| equalish(e_4,X0)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f98,f66]) ).
fof(f193,plain,
! [X0] :
( ~ product(e_3,e_4,X0)
| product(e_1,X0,e_3)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f98,f69]) ).
fof(f207,plain,
( spl0_16
<=> product(e_3,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f208,plain,
( product(e_3,e_4,e_1)
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,plain,
( spl0_17
<=> product(e_3,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f211,plain,
( product(e_3,e_4,e_2)
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f213,plain,
( spl0_18
<=> product(e_3,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f214,plain,
( product(e_3,e_4,e_3)
| ~ spl0_18 ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,plain,
( spl0_19
<=> product(e_3,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f217,plain,
( product(e_3,e_4,e_4)
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,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)],[f80,f47]) ).
fof(f220,plain,
( spl0_16
| spl0_17
| spl0_18
| spl0_19 ),
inference(split_clause,[status(thm)],[f219,f207,f210,f213,f216]) ).
fof(f221,plain,
( spl0_20
<=> product(e_3,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f222,plain,
( product(e_3,e_3,e_1)
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,plain,
( spl0_21
<=> product(e_3,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f225,plain,
( product(e_3,e_3,e_2)
| ~ spl0_21 ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,plain,
( spl0_22
<=> product(e_3,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f230,plain,
( spl0_23
<=> product(e_3,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f231,plain,
( product(e_3,e_3,e_4)
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f233,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_4) ),
inference(resolution,[status(thm)],[f80,f46]) ).
fof(f234,plain,
( spl0_20
| spl0_21
| spl0_22
| spl0_23 ),
inference(split_clause,[status(thm)],[f233,f221,f224,f227,f230]) ).
fof(f235,plain,
( spl0_24
<=> product(e_3,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f236,plain,
( product(e_3,e_2,e_1)
| ~ spl0_24 ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,plain,
( spl0_25
<=> product(e_3,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f239,plain,
( product(e_3,e_2,e_2)
| ~ spl0_25 ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,plain,
( spl0_26
<=> product(e_3,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f242,plain,
( product(e_3,e_2,e_3)
| ~ spl0_26 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f249,plain,
( spl0_28
<=> product(e_3,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f250,plain,
( product(e_3,e_1,e_1)
| ~ spl0_28 ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f255,plain,
( spl0_30
<=> product(e_3,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f256,plain,
( product(e_3,e_1,e_3)
| ~ spl0_30 ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f266,plain,
( spl0_33
<=> product(e_2,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f267,plain,
( product(e_2,e_4,e_2)
| ~ spl0_33 ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f272,plain,
( spl0_35
<=> product(e_2,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f273,plain,
( product(e_2,e_4,e_4)
| ~ spl0_35 ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f277,plain,
( spl0_36
<=> product(e_2,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f278,plain,
( product(e_2,e_3,e_1)
| ~ spl0_36 ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,plain,
( spl0_37
<=> product(e_2,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f281,plain,
( product(e_2,e_3,e_2)
| ~ spl0_37 ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f283,plain,
( spl0_38
<=> product(e_2,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f284,plain,
( product(e_2,e_3,e_3)
| ~ spl0_38 ),
inference(component_clause,[status(thm)],[f283]) ).
fof(f286,plain,
( spl0_39
<=> product(e_2,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f287,plain,
( product(e_2,e_3,e_4)
| ~ spl0_39 ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,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)],[f81,f46]) ).
fof(f290,plain,
( spl0_36
| spl0_37
| spl0_38
| spl0_39 ),
inference(split_clause,[status(thm)],[f289,f277,f280,f283,f286]) ).
fof(f291,plain,
( spl0_40
<=> product(e_2,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f292,plain,
( product(e_2,e_2,e_1)
| ~ spl0_40 ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f297,plain,
( spl0_42
<=> product(e_2,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f298,plain,
( product(e_2,e_2,e_3)
| ~ spl0_42 ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f305,plain,
( spl0_44
<=> product(e_2,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f306,plain,
( product(e_2,e_1,e_1)
| ~ spl0_44 ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f314,plain,
( spl0_47
<=> product(e_2,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f315,plain,
( product(e_2,e_1,e_4)
| ~ spl0_47 ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f319,plain,
( spl0_48
<=> product(e_1,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f320,plain,
( product(e_1,e_4,e_1)
| ~ spl0_48 ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f322,plain,
( spl0_49
<=> product(e_1,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f323,plain,
( product(e_1,e_4,e_2)
| ~ spl0_49 ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f325,plain,
( spl0_50
<=> product(e_1,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f326,plain,
( product(e_1,e_4,e_3)
| ~ spl0_50 ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f328,plain,
( spl0_51
<=> product(e_1,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f329,plain,
( product(e_1,e_4,e_4)
| ~ spl0_51 ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f331,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)],[f82,f47]) ).
fof(f332,plain,
( spl0_48
| spl0_49
| spl0_50
| spl0_51 ),
inference(split_clause,[status(thm)],[f331,f319,f322,f325,f328]) ).
fof(f333,plain,
( spl0_52
<=> product(e_1,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f334,plain,
( product(e_1,e_3,e_1)
| ~ spl0_52 ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f339,plain,
( spl0_54
<=> product(e_1,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f340,plain,
( product(e_1,e_3,e_3)
| ~ spl0_54 ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f347,plain,
( spl0_56
<=> product(e_1,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f348,plain,
( product(e_1,e_2,e_1)
| ~ spl0_56 ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f350,plain,
( spl0_57
<=> product(e_1,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f351,plain,
( product(e_1,e_2,e_2)
| ~ spl0_57 ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f361,plain,
( spl0_60
<=> product(e_1,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f364,plain,
( spl0_61
<=> product(e_1,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f365,plain,
( product(e_1,e_1,e_2)
| ~ spl0_61 ),
inference(component_clause,[status(thm)],[f364]) ).
fof(f367,plain,
( spl0_62
<=> product(e_1,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f368,plain,
( product(e_1,e_1,e_3)
| ~ spl0_62 ),
inference(component_clause,[status(thm)],[f367]) ).
fof(f370,plain,
( spl0_63
<=> product(e_1,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f371,plain,
( product(e_1,e_1,e_4)
| ~ spl0_63 ),
inference(component_clause,[status(thm)],[f370]) ).
fof(f373,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_4) ),
inference(resolution,[status(thm)],[f82,f44]) ).
fof(f374,plain,
( spl0_60
| spl0_61
| spl0_62
| spl0_63 ),
inference(split_clause,[status(thm)],[f373,f361,f364,f367,f370]) ).
fof(f398,plain,
( equalish(e_1,e_3)
| ~ spl0_28 ),
inference(resolution,[status(thm)],[f250,f76]) ).
fof(f399,plain,
( $false
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[status(thm)],[f398,f49]) ).
fof(f400,plain,
~ spl0_28,
inference(contradiction_clause,[status(thm)],[f399]) ).
fof(f403,plain,
( equalish(e_3,e_1)
| ~ spl0_30 ),
inference(resolution,[status(thm)],[f256,f74]) ).
fof(f404,plain,
( $false
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[status(thm)],[f403,f54]) ).
fof(f405,plain,
~ spl0_30,
inference(contradiction_clause,[status(thm)],[f404]) ).
fof(f412,plain,
( equalish(e_2,e_3)
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f239,f76]) ).
fof(f413,plain,
( $false
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[status(thm)],[f412,f52]) ).
fof(f414,plain,
~ spl0_25,
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f416,plain,
! [X0] :
( ~ product(e_3,X0,e_1)
| equalish(e_2,X0)
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f236,f64]) ).
fof(f427,plain,
( equalish(e_3,e_2)
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f225,f72]) ).
fof(f428,plain,
( $false
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[status(thm)],[f427,f55]) ).
fof(f429,plain,
~ spl0_21,
inference(contradiction_clause,[status(thm)],[f428]) ).
fof(f437,plain,
( equalish(e_3,e_4)
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f214,f74]) ).
fof(f438,plain,
( $false
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f437,f56]) ).
fof(f439,plain,
~ spl0_18,
inference(contradiction_clause,[status(thm)],[f438]) ).
fof(f440,plain,
! [X0] :
( ~ product(X0,e_4,e_2)
| equalish(e_3,X0)
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f211,f66]) ).
fof(f443,plain,
! [X0] :
( ~ product(e_4,e_3,X0)
| product(e_2,X0,e_4)
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f211,f69]) ).
fof(f450,plain,
( equalish(e_2,e_4)
| ~ spl0_16
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f208,f416]) ).
fof(f451,plain,
( $false
| ~ spl0_16
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[status(thm)],[f450,f53]) ).
fof(f452,plain,
( ~ spl0_16
| ~ spl0_24 ),
inference(contradiction_clause,[status(thm)],[f451]) ).
fof(f456,plain,
( product(e_2,e_1,e_4)
| ~ spl0_17
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f443,f98]) ).
fof(f457,plain,
( spl0_47
| ~ spl0_17
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f456,f314,f210,f97]) ).
fof(f462,plain,
! [X0] :
( ~ product(e_2,X0,e_4)
| equalish(e_1,X0)
| ~ spl0_47 ),
inference(resolution,[status(thm)],[f315,f64]) ).
fof(f488,plain,
( equalish(e_1,e_3)
| ~ spl0_39
| ~ spl0_47 ),
inference(resolution,[status(thm)],[f287,f462]) ).
fof(f489,plain,
( $false
| ~ spl0_39
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f49]) ).
fof(f490,plain,
( ~ spl0_39
| ~ spl0_47 ),
inference(contradiction_clause,[status(thm)],[f489]) ).
fof(f491,plain,
( equalish(e_3,e_2)
| ~ spl0_38 ),
inference(resolution,[status(thm)],[f284,f76]) ).
fof(f492,plain,
( $false
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f55]) ).
fof(f493,plain,
~ spl0_38,
inference(contradiction_clause,[status(thm)],[f492]) ).
fof(f495,plain,
( equalish(e_2,e_3)
| ~ spl0_37 ),
inference(resolution,[status(thm)],[f281,f74]) ).
fof(f496,plain,
( $false
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f52]) ).
fof(f497,plain,
~ spl0_37,
inference(contradiction_clause,[status(thm)],[f496]) ).
fof(f498,plain,
( equalish(e_4,e_2)
| ~ spl0_36
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f278,f190]) ).
fof(f499,plain,
( $false
| ~ spl0_36
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f498,f58]) ).
fof(f500,plain,
( ~ spl0_36
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f499]) ).
fof(f510,plain,
( equalish(e_3,e_2)
| ~ spl0_26 ),
inference(resolution,[status(thm)],[f242,f74]) ).
fof(f511,plain,
( $false
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f55]) ).
fof(f512,plain,
~ spl0_26,
inference(contradiction_clause,[status(thm)],[f511]) ).
fof(f513,plain,
( equalish(e_2,e_4)
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f115,f76]) ).
fof(f514,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f513,f53]) ).
fof(f515,plain,
~ spl0_9,
inference(contradiction_clause,[status(thm)],[f514]) ).
fof(f525,plain,
( equalish(e_2,e_1)
| ~ spl0_40 ),
inference(resolution,[status(thm)],[f292,f72]) ).
fof(f526,plain,
( $false
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[status(thm)],[f525,f51]) ).
fof(f527,plain,
~ spl0_40,
inference(contradiction_clause,[status(thm)],[f526]) ).
fof(f537,plain,
( equalish(e_4,e_3)
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f217,f76]) ).
fof(f538,plain,
( $false
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f537,f59]) ).
fof(f539,plain,
~ spl0_19,
inference(contradiction_clause,[status(thm)],[f538]) ).
fof(f542,plain,
( equalish(e_3,e_4)
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f231,f72]) ).
fof(f543,plain,
( $false
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[status(thm)],[f542,f56]) ).
fof(f544,plain,
~ spl0_23,
inference(contradiction_clause,[status(thm)],[f543]) ).
fof(f545,plain,
( equalish(e_4,e_2)
| ~ spl0_35 ),
inference(resolution,[status(thm)],[f273,f76]) ).
fof(f546,plain,
( $false
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[status(thm)],[f545,f58]) ).
fof(f547,plain,
~ spl0_35,
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f553,plain,
( equalish(e_2,e_4)
| ~ spl0_33 ),
inference(resolution,[status(thm)],[f267,f74]) ).
fof(f554,plain,
( $false
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[status(thm)],[f553,f53]) ).
fof(f555,plain,
~ spl0_33,
inference(contradiction_clause,[status(thm)],[f554]) ).
fof(f563,plain,
( equalish(e_1,e_4)
| ~ spl0_63 ),
inference(resolution,[status(thm)],[f371,f72]) ).
fof(f564,plain,
( $false
| ~ spl0_63 ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f50]) ).
fof(f565,plain,
~ spl0_63,
inference(contradiction_clause,[status(thm)],[f564]) ).
fof(f569,plain,
( equalish(e_1,e_3)
| ~ spl0_62 ),
inference(resolution,[status(thm)],[f368,f72]) ).
fof(f570,plain,
( $false
| ~ spl0_62 ),
inference(forward_subsumption_resolution,[status(thm)],[f569,f49]) ).
fof(f571,plain,
~ spl0_62,
inference(contradiction_clause,[status(thm)],[f570]) ).
fof(f572,plain,
( product(e_1,e_1,e_3)
| ~ spl0_16
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f208,f193]) ).
fof(f573,plain,
( spl0_62
| ~ spl0_16
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f572,f367,f207,f97]) ).
fof(f581,plain,
( equalish(e_2,e_3)
| ~ spl0_42 ),
inference(resolution,[status(thm)],[f298,f72]) ).
fof(f582,plain,
( $false
| ~ spl0_42 ),
inference(forward_subsumption_resolution,[status(thm)],[f581,f52]) ).
fof(f583,plain,
~ spl0_42,
inference(contradiction_clause,[status(thm)],[f582]) ).
fof(f587,plain,
( equalish(e_1,e_2)
| ~ spl0_61 ),
inference(resolution,[status(thm)],[f365,f72]) ).
fof(f588,plain,
( $false
| ~ spl0_61 ),
inference(forward_subsumption_resolution,[status(thm)],[f587,f48]) ).
fof(f589,plain,
~ spl0_61,
inference(contradiction_clause,[status(thm)],[f588]) ).
fof(f594,plain,
( equalish(e_3,e_1)
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f222,f72]) ).
fof(f595,plain,
( $false
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f594,f54]) ).
fof(f596,plain,
~ spl0_20,
inference(contradiction_clause,[status(thm)],[f595]) ).
fof(f604,plain,
( equalish(e_1,e_2)
| ~ spl0_44 ),
inference(resolution,[status(thm)],[f306,f76]) ).
fof(f605,plain,
( $false
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[status(thm)],[f604,f48]) ).
fof(f606,plain,
~ spl0_44,
inference(contradiction_clause,[status(thm)],[f605]) ).
fof(f623,plain,
( equalish(e_2,e_1)
| ~ spl0_57 ),
inference(resolution,[status(thm)],[f351,f76]) ).
fof(f624,plain,
( $false
| ~ spl0_57 ),
inference(forward_subsumption_resolution,[status(thm)],[f623,f51]) ).
fof(f625,plain,
~ spl0_57,
inference(contradiction_clause,[status(thm)],[f624]) ).
fof(f629,plain,
( equalish(e_1,e_2)
| ~ spl0_56 ),
inference(resolution,[status(thm)],[f348,f74]) ).
fof(f630,plain,
( $false
| ~ spl0_56 ),
inference(forward_subsumption_resolution,[status(thm)],[f629,f48]) ).
fof(f631,plain,
~ spl0_56,
inference(contradiction_clause,[status(thm)],[f630]) ).
fof(f636,plain,
( equalish(e_3,e_1)
| ~ spl0_54 ),
inference(resolution,[status(thm)],[f340,f76]) ).
fof(f637,plain,
( $false
| ~ spl0_54 ),
inference(forward_subsumption_resolution,[status(thm)],[f636,f54]) ).
fof(f638,plain,
~ spl0_54,
inference(contradiction_clause,[status(thm)],[f637]) ).
fof(f647,plain,
( equalish(e_1,e_3)
| ~ spl0_52 ),
inference(resolution,[status(thm)],[f334,f74]) ).
fof(f648,plain,
( $false
| ~ spl0_52 ),
inference(forward_subsumption_resolution,[status(thm)],[f647,f49]) ).
fof(f649,plain,
~ spl0_52,
inference(contradiction_clause,[status(thm)],[f648]) ).
fof(f650,plain,
( equalish(e_4,e_1)
| ~ spl0_51 ),
inference(resolution,[status(thm)],[f329,f76]) ).
fof(f651,plain,
( $false
| ~ spl0_51 ),
inference(forward_subsumption_resolution,[status(thm)],[f650,f57]) ).
fof(f652,plain,
~ spl0_51,
inference(contradiction_clause,[status(thm)],[f651]) ).
fof(f653,plain,
( product(e_3,e_3,e_1)
| ~ spl0_50
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f326,f148]) ).
fof(f654,plain,
( spl0_20
| ~ spl0_50
| ~ spl0_14 ),
inference(split_clause,[status(thm)],[f653,f221,f325,f131]) ).
fof(f670,plain,
( equalish(e_1,e_4)
| ~ spl0_48 ),
inference(resolution,[status(thm)],[f320,f74]) ).
fof(f671,plain,
( $false
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[status(thm)],[f670,f50]) ).
fof(f672,plain,
~ spl0_48,
inference(contradiction_clause,[status(thm)],[f671]) ).
fof(f690,plain,
( equalish(e_3,e_1)
| ~ spl0_17
| ~ spl0_49 ),
inference(resolution,[status(thm)],[f440,f323]) ).
fof(f691,plain,
( $false
| ~ spl0_17
| ~ spl0_49 ),
inference(forward_subsumption_resolution,[status(thm)],[f690,f54]) ).
fof(f692,plain,
( ~ spl0_17
| ~ spl0_49 ),
inference(contradiction_clause,[status(thm)],[f691]) ).
fof(f693,plain,
( product(e_3,e_2,e_1)
| ~ spl0_49
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f323,f148]) ).
fof(f694,plain,
( spl0_24
| ~ spl0_49
| ~ spl0_14 ),
inference(split_clause,[status(thm)],[f693,f235,f322,f131]) ).
fof(f696,plain,
$false,
inference(sat_refutation,[status(thm)],[f110,f138,f143,f158,f167,f183,f186,f189,f220,f234,f290,f332,f374,f400,f405,f414,f429,f439,f452,f457,f490,f493,f497,f500,f512,f515,f527,f539,f544,f547,f555,f565,f571,f573,f583,f589,f596,f606,f625,f631,f638,f649,f652,f654,f672,f692,f694]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.07 % Problem : GRP126-2.004 : TPTP v8.1.2. Released v1.2.0.
% 0.05/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26 % Computer : n024.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue Apr 30 00:25:06 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.07/0.26 % Drodi V3.6.0
% 0.11/0.34 % Refutation found
% 0.11/0.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.36 % Elapsed time: 0.093871 seconds
% 0.11/0.36 % CPU time: 0.673849 seconds
% 0.11/0.36 % Total memory used: 14.400 MB
% 0.11/0.36 % Net memory used: 13.322 MB
%------------------------------------------------------------------------------