TSTP Solution File: GRP127-1.004 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP127-1.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 0.16s 0.37s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 67
% Syntax : Number of formulae : 293 ( 58 unt; 0 def)
% Number of atoms : 649 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 645 ( 289 ~; 311 |; 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 : 79 (; 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
! [Y,X,Z1,Z2] :
( ~ product(Y,X,Z1)
| ~ product(Z1,Y,Z2)
| product(Z2,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f24,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f25,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f26,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f27,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f28,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f29,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f30,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f31,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f32,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f33,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f34,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f35,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f36,plain,
~ equalish(e_4,e_1),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f37,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f38,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f39,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(f40,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f18]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f42,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f46,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f47,plain,
! [Y,X,Z2] :
( ! [Z1] :
( ~ product(Y,X,Z1)
| ~ product(Z1,Y,Z2) )
| product(Z2,Y,X) ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X2,X0,X3)
| product(X3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f51,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f41,f46]) ).
fof(f53,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f43,f46]) ).
fof(f55,plain,
! [X0,X1] :
( ~ product(X0,X1,X1)
| equalish(X1,X0) ),
inference(resolution,[status(thm)],[f45,f46]) ).
fof(f57,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)],[f23,f39]) ).
fof(f67,plain,
( spl0_3
<=> product(e_1,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f68,plain,
( product(e_1,e_1,e_4)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f72,plain,
( spl0_4
<=> product(e_1,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f73,plain,
( product(e_1,e_2,e_1)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,plain,
( spl0_5
<=> product(e_1,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f76,plain,
( product(e_1,e_2,e_2)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( spl0_6
<=> product(e_1,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f79,plain,
( product(e_1,e_2,e_3)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( spl0_7
<=> product(e_1,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f82,plain,
( product(e_1,e_2,e_4)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,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)],[f24,f57]) ).
fof(f85,plain,
( spl0_4
| spl0_5
| spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f84,f72,f75,f78,f81]) ).
fof(f86,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)],[f24,f39]) ).
fof(f87,plain,
( spl0_8
<=> product(e_2,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f88,plain,
( product(e_2,e_2,e_1)
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f96,plain,
( spl0_11
<=> product(e_2,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f97,plain,
( product(e_2,e_2,e_4)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f101,plain,
( spl0_12
<=> product(e_2,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f102,plain,
( product(e_2,e_1,e_1)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( spl0_13
<=> product(e_2,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f105,plain,
( product(e_2,e_1,e_2)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,plain,
( spl0_14
<=> product(e_2,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f108,plain,
( product(e_2,e_1,e_3)
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( spl0_15
<=> product(e_2,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f111,plain,
( product(e_2,e_1,e_4)
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(resolution,[status(thm)],[f86,f23]) ).
fof(f114,plain,
( spl0_12
| spl0_13
| spl0_14
| spl0_15 ),
inference(split_clause,[status(thm)],[f113,f101,f104,f107,f110]) ).
fof(f115,plain,
( spl0_16
<=> product(e_2,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f116,plain,
( product(e_2,e_3,e_1)
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( spl0_17
<=> product(e_2,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f119,plain,
( product(e_2,e_3,e_2)
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( spl0_18
<=> product(e_2,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f122,plain,
( product(e_2,e_3,e_3)
| ~ spl0_18 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( spl0_19
<=> product(e_2,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f125,plain,
( product(e_2,e_3,e_4)
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,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)],[f25,f86]) ).
fof(f128,plain,
( spl0_16
| spl0_17
| spl0_18
| spl0_19 ),
inference(split_clause,[status(thm)],[f127,f115,f118,f121,f124]) ).
fof(f129,plain,
( spl0_20
<=> product(e_1,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f130,plain,
( product(e_1,e_3,e_1)
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( spl0_21
<=> product(e_1,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f133,plain,
( product(e_1,e_3,e_2)
| ~ spl0_21 ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f135,plain,
( spl0_22
<=> product(e_1,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f136,plain,
( product(e_1,e_3,e_3)
| ~ spl0_22 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( spl0_23
<=> product(e_1,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f139,plain,
( product(e_1,e_3,e_4)
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,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)],[f25,f57]) ).
fof(f142,plain,
( spl0_20
| spl0_21
| spl0_22
| spl0_23 ),
inference(split_clause,[status(thm)],[f141,f129,f132,f135,f138]) ).
fof(f143,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)],[f25,f39]) ).
fof(f144,plain,
( spl0_24
<=> product(e_2,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f145,plain,
( product(e_2,e_4,e_1)
| ~ spl0_24 ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( spl0_25
<=> product(e_2,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f148,plain,
( product(e_2,e_4,e_2)
| ~ spl0_25 ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( spl0_26
<=> product(e_2,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f151,plain,
( product(e_2,e_4,e_3)
| ~ spl0_26 ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,plain,
( spl0_27
<=> product(e_2,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f154,plain,
( product(e_2,e_4,e_4)
| ~ spl0_27 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,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)],[f26,f86]) ).
fof(f157,plain,
( spl0_24
| spl0_25
| spl0_26
| spl0_27 ),
inference(split_clause,[status(thm)],[f156,f144,f147,f150,f153]) ).
fof(f158,plain,
( spl0_28
<=> product(e_1,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f159,plain,
( product(e_1,e_4,e_1)
| ~ spl0_28 ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( spl0_29
<=> product(e_1,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f162,plain,
( product(e_1,e_4,e_2)
| ~ spl0_29 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( spl0_30
<=> product(e_1,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f165,plain,
( product(e_1,e_4,e_3)
| ~ spl0_30 ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,plain,
( spl0_31
<=> product(e_1,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f168,plain,
( product(e_1,e_4,e_4)
| ~ spl0_31 ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,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)],[f26,f57]) ).
fof(f171,plain,
( spl0_28
| spl0_29
| spl0_30
| spl0_31 ),
inference(split_clause,[status(thm)],[f170,f158,f161,f164,f167]) ).
fof(f172,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)],[f26,f39]) ).
fof(f179,plain,
( spl0_34
<=> product(e_3,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f180,plain,
( product(e_3,e_4,e_3)
| ~ spl0_34 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f190,plain,
( spl0_37
<=> product(e_3,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f191,plain,
( product(e_3,e_3,e_2)
| ~ spl0_37 ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f201,plain,
( spl0_40
<=> product(e_3,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f202,plain,
( product(e_3,e_2,e_1)
| ~ spl0_40 ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,plain,
( spl0_41
<=> product(e_3,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f205,plain,
( product(e_3,e_2,e_2)
| ~ spl0_41 ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,plain,
( spl0_42
<=> product(e_3,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f208,plain,
( product(e_3,e_2,e_3)
| ~ spl0_42 ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,plain,
( spl0_43
<=> product(e_3,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f211,plain,
( product(e_3,e_2,e_4)
| ~ spl0_43 ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f213,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)],[f143,f24]) ).
fof(f214,plain,
( spl0_40
| spl0_41
| spl0_42
| spl0_43 ),
inference(split_clause,[status(thm)],[f213,f201,f204,f207,f210]) ).
fof(f215,plain,
( spl0_44
<=> product(e_3,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f216,plain,
( product(e_3,e_1,e_1)
| ~ spl0_44 ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( spl0_45
<=> product(e_3,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f219,plain,
( product(e_3,e_1,e_2)
| ~ spl0_45 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,plain,
( spl0_46
<=> product(e_3,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f222,plain,
( product(e_3,e_1,e_3)
| ~ spl0_46 ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,plain,
( spl0_47
<=> product(e_3,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f225,plain,
( product(e_3,e_1,e_4)
| ~ spl0_47 ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[f143,f23]) ).
fof(f228,plain,
( spl0_44
| spl0_45
| spl0_46
| spl0_47 ),
inference(split_clause,[status(thm)],[f227,f215,f218,f221,f224]) ).
fof(f257,plain,
( spl0_56
<=> product(e_4,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f258,plain,
( product(e_4,e_2,e_1)
| ~ spl0_56 ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,plain,
( spl0_57
<=> product(e_4,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f261,plain,
( product(e_4,e_2,e_2)
| ~ spl0_57 ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( spl0_58
<=> product(e_4,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f264,plain,
( product(e_4,e_2,e_3)
| ~ spl0_58 ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,plain,
( spl0_59
<=> product(e_4,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f267,plain,
( product(e_4,e_2,e_4)
| ~ spl0_59 ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,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)],[f172,f24]) ).
fof(f270,plain,
( spl0_56
| spl0_57
| spl0_58
| spl0_59 ),
inference(split_clause,[status(thm)],[f269,f257,f260,f263,f266]) ).
fof(f271,plain,
( spl0_60
<=> product(e_4,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f272,plain,
( product(e_4,e_1,e_1)
| ~ spl0_60 ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,plain,
( spl0_61
<=> product(e_4,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f275,plain,
( product(e_4,e_1,e_2)
| ~ spl0_61 ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,plain,
( spl0_62
<=> product(e_4,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f278,plain,
( product(e_4,e_1,e_3)
| ~ spl0_62 ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,plain,
( spl0_63
<=> product(e_4,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f281,plain,
( product(e_4,e_1,e_4)
| ~ spl0_63 ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f283,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)],[f172,f23]) ).
fof(f284,plain,
( spl0_60
| spl0_61
| spl0_62
| spl0_63 ),
inference(split_clause,[status(thm)],[f283,f271,f274,f277,f280]) ).
fof(f287,plain,
( equalish(e_1,e_4)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f68,f51]) ).
fof(f288,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f287,f29]) ).
fof(f289,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f288]) ).
fof(f290,plain,
! [X0] :
( ~ product(X0,e_2,e_4)
| equalish(e_1,X0)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f82,f45]) ).
fof(f292,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| equalish(e_4,X0)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f82,f41]) ).
fof(f293,plain,
! [X0] :
( ~ product(e_4,e_1,X0)
| product(X0,e_1,e_2)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f82,f48]) ).
fof(f297,plain,
( equalish(e_4,e_3)
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f79,f292]) ).
fof(f298,plain,
( $false
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f297,f38]) ).
fof(f299,plain,
( ~ spl0_6
| ~ spl0_7 ),
inference(contradiction_clause,[status(thm)],[f298]) ).
fof(f300,plain,
( equalish(e_2,e_1)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f76,f55]) ).
fof(f301,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f300,f30]) ).
fof(f302,plain,
~ spl0_5,
inference(contradiction_clause,[status(thm)],[f301]) ).
fof(f304,plain,
( equalish(e_1,e_2)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f73,f53]) ).
fof(f305,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f304,f27]) ).
fof(f306,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f305]) ).
fof(f308,plain,
! [X0] :
( ~ product(e_1,X0,e_3)
| equalish(e_2,X0)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f79,f43]) ).
fof(f310,plain,
! [X0] :
( ~ product(e_3,e_1,X0)
| product(X0,e_1,e_2)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f79,f48]) ).
fof(f311,plain,
! [X0] :
( ~ product(X0,e_1,e_4)
| equalish(e_2,X0)
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f111,f45]) ).
fof(f314,plain,
! [X0] :
( ~ product(e_4,e_2,X0)
| product(X0,e_2,e_1)
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f111,f48]) ).
fof(f322,plain,
( equalish(e_2,e_1)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f105,f53]) ).
fof(f323,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f322,f30]) ).
fof(f324,plain,
~ spl0_13,
inference(contradiction_clause,[status(thm)],[f323]) ).
fof(f325,plain,
( equalish(e_1,e_2)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f102,f55]) ).
fof(f326,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f325,f27]) ).
fof(f327,plain,
~ spl0_12,
inference(contradiction_clause,[status(thm)],[f326]) ).
fof(f329,plain,
! [X0] :
( ~ product(e_2,X0,e_3)
| equalish(e_1,X0)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f108,f43]) ).
fof(f331,plain,
! [X0] :
( ~ product(e_3,e_2,X0)
| product(X0,e_2,e_1)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f108,f48]) ).
fof(f334,plain,
( equalish(e_2,e_4)
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f97,f51]) ).
fof(f335,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f334,f32]) ).
fof(f336,plain,
~ spl0_11,
inference(contradiction_clause,[status(thm)],[f335]) ).
fof(f342,plain,
( equalish(e_2,e_1)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f88,f51]) ).
fof(f343,plain,
( $false
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f342,f30]) ).
fof(f344,plain,
~ spl0_8,
inference(contradiction_clause,[status(thm)],[f343]) ).
fof(f348,plain,
! [X0] :
( ~ product(e_4,e_1,X0)
| product(X0,e_1,e_3)
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f139,f48]) ).
fof(f356,plain,
! [X0] :
( ~ product(e_1,X0,e_2)
| equalish(e_3,X0)
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f133,f43]) ).
fof(f368,plain,
! [X0] :
( ~ product(e_4,e_2,X0)
| product(X0,e_2,e_3)
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f125,f48]) ).
fof(f379,plain,
! [X0] :
( ~ product(e_2,X0,e_1)
| equalish(e_3,X0)
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f116,f43]) ).
fof(f385,plain,
( equalish(e_4,e_1)
| ~ spl0_31 ),
inference(resolution,[status(thm)],[f168,f55]) ).
fof(f386,plain,
( $false
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[status(thm)],[f385,f36]) ).
fof(f387,plain,
~ spl0_31,
inference(contradiction_clause,[status(thm)],[f386]) ).
fof(f388,plain,
( equalish(e_2,e_4)
| ~ spl0_30
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f165,f308]) ).
fof(f389,plain,
( $false
| ~ spl0_30
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f388,f32]) ).
fof(f390,plain,
( ~ spl0_30
| ~ spl0_6 ),
inference(contradiction_clause,[status(thm)],[f389]) ).
fof(f391,plain,
( equalish(e_3,e_4)
| ~ spl0_29
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f162,f356]) ).
fof(f392,plain,
( $false
| ~ spl0_29
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[status(thm)],[f391,f35]) ).
fof(f393,plain,
( ~ spl0_29
| ~ spl0_21 ),
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f395,plain,
( equalish(e_1,e_3)
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f130,f53]) ).
fof(f396,plain,
( $false
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f395,f28]) ).
fof(f397,plain,
~ spl0_20,
inference(contradiction_clause,[status(thm)],[f396]) ).
fof(f402,plain,
( equalish(e_1,e_4)
| ~ spl0_28 ),
inference(resolution,[status(thm)],[f159,f53]) ).
fof(f403,plain,
( $false
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[status(thm)],[f402,f29]) ).
fof(f404,plain,
~ spl0_28,
inference(contradiction_clause,[status(thm)],[f403]) ).
fof(f409,plain,
( equalish(e_4,e_2)
| ~ spl0_27 ),
inference(resolution,[status(thm)],[f154,f55]) ).
fof(f410,plain,
( $false
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[status(thm)],[f409,f37]) ).
fof(f411,plain,
~ spl0_27,
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f412,plain,
( equalish(e_1,e_4)
| ~ spl0_26
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f151,f329]) ).
fof(f413,plain,
( $false
| ~ spl0_26
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[status(thm)],[f412,f29]) ).
fof(f414,plain,
( ~ spl0_26
| ~ spl0_14 ),
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f418,plain,
( equalish(e_3,e_4)
| ~ spl0_24
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f145,f379]) ).
fof(f419,plain,
( $false
| ~ spl0_24
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f418,f35]) ).
fof(f420,plain,
( ~ spl0_24
| ~ spl0_16 ),
inference(contradiction_clause,[status(thm)],[f419]) ).
fof(f426,plain,
( equalish(e_2,e_3)
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f119,f53]) ).
fof(f427,plain,
( $false
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f426,f31]) ).
fof(f428,plain,
~ spl0_17,
inference(contradiction_clause,[status(thm)],[f427]) ).
fof(f429,plain,
( equalish(e_3,e_2)
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f122,f55]) ).
fof(f430,plain,
( $false
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f429,f34]) ).
fof(f431,plain,
~ spl0_18,
inference(contradiction_clause,[status(thm)],[f430]) ).
fof(f436,plain,
! [X0] :
( ~ product(e_3,X0,e_4)
| equalish(e_1,X0)
| ~ spl0_47 ),
inference(resolution,[status(thm)],[f225,f43]) ).
fof(f445,plain,
( product(e_2,e_1,e_2)
| ~ spl0_45
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f219,f310]) ).
fof(f446,plain,
( spl0_13
| ~ spl0_45
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f445,f104,f218,f78]) ).
fof(f452,plain,
( equalish(e_1,e_3)
| ~ spl0_44 ),
inference(resolution,[status(thm)],[f216,f55]) ).
fof(f453,plain,
( $false
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[status(thm)],[f452,f28]) ).
fof(f454,plain,
~ spl0_44,
inference(contradiction_clause,[status(thm)],[f453]) ).
fof(f460,plain,
( equalish(e_1,e_2)
| ~ spl0_43
| ~ spl0_47 ),
inference(resolution,[status(thm)],[f211,f436]) ).
fof(f461,plain,
( $false
| ~ spl0_43
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[status(thm)],[f460,f27]) ).
fof(f462,plain,
( ~ spl0_43
| ~ spl0_47 ),
inference(contradiction_clause,[status(thm)],[f461]) ).
fof(f468,plain,
( equalish(e_2,e_3)
| ~ spl0_41 ),
inference(resolution,[status(thm)],[f205,f55]) ).
fof(f469,plain,
( $false
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[status(thm)],[f468,f31]) ).
fof(f470,plain,
~ spl0_41,
inference(contradiction_clause,[status(thm)],[f469]) ).
fof(f471,plain,
( product(e_1,e_2,e_1)
| ~ spl0_40
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f202,f331]) ).
fof(f472,plain,
( spl0_4
| ~ spl0_40
| ~ spl0_14 ),
inference(split_clause,[status(thm)],[f471,f72,f201,f107]) ).
fof(f485,plain,
( equalish(e_3,e_2)
| ~ spl0_37 ),
inference(resolution,[status(thm)],[f191,f51]) ).
fof(f486,plain,
( $false
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[status(thm)],[f485,f34]) ).
fof(f487,plain,
~ spl0_37,
inference(contradiction_clause,[status(thm)],[f486]) ).
fof(f495,plain,
( equalish(e_3,e_4)
| ~ spl0_34 ),
inference(resolution,[status(thm)],[f180,f53]) ).
fof(f496,plain,
( $false
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f35]) ).
fof(f497,plain,
~ spl0_34,
inference(contradiction_clause,[status(thm)],[f496]) ).
fof(f511,plain,
( equalish(e_3,e_1)
| ~ spl0_22 ),
inference(resolution,[status(thm)],[f136,f55]) ).
fof(f512,plain,
( $false
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f33]) ).
fof(f513,plain,
~ spl0_22,
inference(contradiction_clause,[status(thm)],[f512]) ).
fof(f515,plain,
( equalish(e_3,e_2)
| ~ spl0_42 ),
inference(resolution,[status(thm)],[f208,f53]) ).
fof(f516,plain,
( $false
| ~ spl0_42 ),
inference(forward_subsumption_resolution,[status(thm)],[f515,f34]) ).
fof(f517,plain,
~ spl0_42,
inference(contradiction_clause,[status(thm)],[f516]) ).
fof(f523,plain,
( equalish(e_3,e_1)
| ~ spl0_46 ),
inference(resolution,[status(thm)],[f222,f53]) ).
fof(f524,plain,
( $false
| ~ spl0_46 ),
inference(forward_subsumption_resolution,[status(thm)],[f523,f33]) ).
fof(f525,plain,
~ spl0_46,
inference(contradiction_clause,[status(thm)],[f524]) ).
fof(f533,plain,
( equalish(e_2,e_4)
| ~ spl0_63
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f281,f311]) ).
fof(f534,plain,
( $false
| ~ spl0_63
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f32]) ).
fof(f535,plain,
( ~ spl0_63
| ~ spl0_15 ),
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f536,plain,
( product(e_3,e_1,e_3)
| ~ spl0_62
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f278,f348]) ).
fof(f537,plain,
( spl0_46
| ~ spl0_62
| ~ spl0_23 ),
inference(split_clause,[status(thm)],[f536,f221,f277,f138]) ).
fof(f539,plain,
! [X0] :
( ~ product(e_4,X0,e_3)
| equalish(e_1,X0)
| ~ spl0_62 ),
inference(resolution,[status(thm)],[f278,f43]) ).
fof(f542,plain,
( product(e_2,e_1,e_3)
| ~ spl0_61
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f275,f348]) ).
fof(f543,plain,
( spl0_14
| ~ spl0_61
| ~ spl0_23 ),
inference(split_clause,[status(thm)],[f542,f107,f274,f138]) ).
fof(f544,plain,
( product(e_2,e_1,e_2)
| ~ spl0_61
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f275,f293]) ).
fof(f545,plain,
( spl0_13
| ~ spl0_61
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f544,f104,f274,f81]) ).
fof(f550,plain,
( equalish(e_1,e_4)
| ~ spl0_60 ),
inference(resolution,[status(thm)],[f272,f55]) ).
fof(f551,plain,
( $false
| ~ spl0_60 ),
inference(forward_subsumption_resolution,[status(thm)],[f550,f29]) ).
fof(f552,plain,
~ spl0_60,
inference(contradiction_clause,[status(thm)],[f551]) ).
fof(f558,plain,
( equalish(e_2,e_4)
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f148,f53]) ).
fof(f559,plain,
( $false
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[status(thm)],[f558,f32]) ).
fof(f560,plain,
~ spl0_25,
inference(contradiction_clause,[status(thm)],[f559]) ).
fof(f568,plain,
( product(e_3,e_2,e_3)
| ~ spl0_58
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f264,f368]) ).
fof(f569,plain,
( spl0_42
| ~ spl0_58
| ~ spl0_19 ),
inference(split_clause,[status(thm)],[f568,f207,f263,f124]) ).
fof(f572,plain,
( equalish(e_1,e_2)
| ~ spl0_58
| ~ spl0_62 ),
inference(resolution,[status(thm)],[f264,f539]) ).
fof(f573,plain,
( $false
| ~ spl0_58
| ~ spl0_62 ),
inference(forward_subsumption_resolution,[status(thm)],[f572,f27]) ).
fof(f574,plain,
( ~ spl0_58
| ~ spl0_62 ),
inference(contradiction_clause,[status(thm)],[f573]) ).
fof(f578,plain,
( equalish(e_2,e_4)
| ~ spl0_57 ),
inference(resolution,[status(thm)],[f261,f55]) ).
fof(f579,plain,
( $false
| ~ spl0_57 ),
inference(forward_subsumption_resolution,[status(thm)],[f578,f32]) ).
fof(f580,plain,
~ spl0_57,
inference(contradiction_clause,[status(thm)],[f579]) ).
fof(f581,plain,
( product(e_1,e_2,e_3)
| ~ spl0_56
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f258,f368]) ).
fof(f582,plain,
( spl0_6
| ~ spl0_56
| ~ spl0_19 ),
inference(split_clause,[status(thm)],[f581,f78,f257,f124]) ).
fof(f583,plain,
( product(e_1,e_2,e_1)
| ~ spl0_56
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f258,f314]) ).
fof(f584,plain,
( spl0_4
| ~ spl0_56
| ~ spl0_15 ),
inference(split_clause,[status(thm)],[f583,f72,f257,f110]) ).
fof(f591,plain,
( equalish(e_1,e_4)
| ~ spl0_59
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f267,f290]) ).
fof(f592,plain,
( $false
| ~ spl0_59
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f591,f29]) ).
fof(f593,plain,
( ~ spl0_59
| ~ spl0_7 ),
inference(contradiction_clause,[status(thm)],[f592]) ).
fof(f594,plain,
$false,
inference(sat_refutation,[status(thm)],[f85,f114,f128,f142,f157,f171,f214,f228,f270,f284,f289,f299,f302,f306,f324,f327,f336,f344,f387,f390,f393,f397,f404,f411,f414,f420,f428,f431,f446,f454,f462,f470,f472,f487,f497,f513,f517,f525,f535,f537,f543,f545,f552,f560,f569,f574,f580,f582,f584,f593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP127-1.004 : TPTP v8.1.2. Released v1.2.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue May 30 11:41:43 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.33 % Drodi V3.5.1
% 0.16/0.37 % Refutation found
% 0.16/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.31/0.61 % Elapsed time: 0.067155 seconds
% 0.31/0.61 % CPU time: 0.122551 seconds
% 0.31/0.61 % Memory used: 2.824 MB
%------------------------------------------------------------------------------