TSTP Solution File: GRP127-4.004 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP127-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 12:10:35 EDT 2023
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 66
% Syntax : Number of formulae : 262 ( 61 unt; 0 def)
% Number of atoms : 582 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 544 ( 224 ~; 279 |; 0 &)
% ( 41 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 94 (; 94 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(e_1,X,Y)
| product(e_2,X,Y)
| product(e_3,X,Y)
| product(e_4,X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,e_1,Y)
| product(X,e_2,Y)
| product(X,e_3,Y)
| product(X,e_4,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [Y,X,Z1,Z2] :
( product(Y,X,Z1)
| ~ product(Z2,Y,X)
| ~ product(Z1,Y,Z2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3)
| product(X,Y,e_4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
! [Y,X,Z1,Z2] :
( ~ product(Y,X,Z1)
| ~ product(Z1,Y,Z2)
| product(Z2,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(e_1,X0,X1)
| product(e_2,X0,X1)
| product(e_3,X0,X1)
| product(e_4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f28,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,e_1,X1)
| product(X0,e_2,X1)
| product(X0,e_3,X1)
| product(X0,e_4,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f29,plain,
! [Y,Z1,Z2] :
( ! [X] :
( product(Y,X,Z1)
| ~ product(Z2,Y,X) )
| ~ product(Z1,Y,Z2) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( product(X0,X1,X2)
| ~ product(X3,X0,X1)
| ~ product(X2,X0,X3) ),
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f33,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f34,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f35,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f36,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f37,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f38,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f39,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f40,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f41,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f42,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f43,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f44,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f45,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f46,plain,
~ equalish(e_4,e_1),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f47,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f48,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f49,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3)
| product(X0,X1,e_4) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f50,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f54,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f24]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f56,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f57,plain,
! [Y,X,Z2] :
( ! [Z1] :
( ~ product(Y,X,Z1)
| ~ product(Z1,Y,Z2) )
| product(Z2,Y,X) ),
inference(miniscoping,[status(esa)],[f26]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X2,X0,X3)
| product(X3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f66,plain,
! [X0,X1] :
( product(X0,X0,X1)
| ~ product(X1,X0,X0) ),
inference(resolution,[status(thm)],[f56,f30]) ).
fof(f71,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_4)
| product(e_2,X0,e_4)
| product(e_3,X0,e_4)
| product(e_4,X0,e_4) ),
inference(resolution,[status(thm)],[f27,f36]) ).
fof(f72,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_3)
| product(e_2,X0,e_3)
| product(e_3,X0,e_3)
| product(e_4,X0,e_3) ),
inference(resolution,[status(thm)],[f27,f35]) ).
fof(f74,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_2,X0,e_1)
| product(e_3,X0,e_1)
| product(e_4,X0,e_1) ),
inference(resolution,[status(thm)],[f27,f33]) ).
fof(f75,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_4)
| product(X0,e_2,e_4)
| product(X0,e_3,e_4)
| product(X0,e_4,e_4) ),
inference(resolution,[status(thm)],[f28,f36]) ).
fof(f76,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_3)
| product(X0,e_2,e_3)
| product(X0,e_3,e_3)
| product(X0,e_4,e_3) ),
inference(resolution,[status(thm)],[f28,f35]) ).
fof(f79,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| equalish(X1,X0) ),
inference(resolution,[status(thm)],[f51,f56]) ).
fof(f81,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| equalish(X1,X0) ),
inference(resolution,[status(thm)],[f53,f56]) ).
fof(f83,plain,
! [X0,X1] :
( ~ product(X0,X1,X1)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f55,f56]) ).
fof(f86,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)],[f49,f34]) ).
fof(f87,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_1)
| product(X0,e_1,e_2)
| product(X0,e_1,e_3)
| product(X0,e_1,e_4) ),
inference(resolution,[status(thm)],[f49,f33]) ).
fof(f88,plain,
( spl0_0
<=> product(e_1,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f89,plain,
( product(e_1,e_4,e_4)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f94,plain,
( spl0_2
<=> product(e_3,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f95,plain,
( product(e_3,e_4,e_4)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,plain,
( spl0_3
<=> product(e_4,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f102,plain,
( spl0_4
<=> product(e_1,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f103,plain,
( product(e_1,e_3,e_4)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f108,plain,
( spl0_6
<=> product(e_3,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f109,plain,
( product(e_3,e_3,e_4)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,plain,
( spl0_7
<=> product(e_4,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f112,plain,
( product(e_4,e_3,e_4)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f116,plain,
( spl0_8
<=> product(e_1,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f117,plain,
( product(e_1,e_2,e_4)
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( spl0_9
<=> product(e_2,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f120,plain,
( product(e_2,e_2,e_4)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( spl0_10
<=> product(e_3,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f123,plain,
( product(e_3,e_2,e_4)
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,plain,
( spl0_11
<=> product(e_4,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f126,plain,
( product(e_4,e_2,e_4)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_4,e_2,e_4) ),
inference(resolution,[status(thm)],[f71,f34]) ).
fof(f129,plain,
( spl0_8
| spl0_9
| spl0_10
| spl0_11 ),
inference(split_clause,[status(thm)],[f128,f116,f119,f122,f125]) ).
fof(f130,plain,
( spl0_12
<=> product(e_1,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f131,plain,
( product(e_1,e_1,e_4)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f136,plain,
( spl0_14
<=> product(e_3,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f137,plain,
( product(e_3,e_1,e_4)
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( spl0_15
<=> product(e_4,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f140,plain,
( product(e_4,e_1,e_4)
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f144,plain,
( spl0_16
<=> product(e_1,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f145,plain,
( product(e_1,e_4,e_3)
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f153,plain,
( spl0_19
<=> product(e_4,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f154,plain,
( product(e_4,e_4,e_3)
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f158,plain,
( spl0_20
<=> product(e_1,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f159,plain,
( product(e_1,e_3,e_3)
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( spl0_21
<=> product(e_2,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f162,plain,
( product(e_2,e_3,e_3)
| ~ spl0_21 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( spl0_22
<=> product(e_3,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f167,plain,
( spl0_23
<=> product(e_4,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f168,plain,
( product(e_4,e_3,e_3)
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( product(e_1,e_3,e_3)
| product(e_2,e_3,e_3)
| product(e_3,e_3,e_3)
| product(e_4,e_3,e_3) ),
inference(resolution,[status(thm)],[f72,f35]) ).
fof(f171,plain,
( spl0_20
| spl0_21
| spl0_22
| spl0_23 ),
inference(split_clause,[status(thm)],[f170,f158,f161,f164,f167]) ).
fof(f172,plain,
( spl0_24
<=> product(e_1,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f173,plain,
( product(e_1,e_2,e_3)
| ~ spl0_24 ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,plain,
( spl0_25
<=> product(e_2,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f176,plain,
( product(e_2,e_2,e_3)
| ~ spl0_25 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( spl0_26
<=> product(e_3,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f179,plain,
( product(e_3,e_2,e_3)
| ~ spl0_26 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( spl0_27
<=> product(e_4,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f182,plain,
( product(e_4,e_2,e_3)
| ~ spl0_27 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_2,e_3)
| product(e_4,e_2,e_3) ),
inference(resolution,[status(thm)],[f72,f34]) ).
fof(f185,plain,
( spl0_24
| spl0_25
| spl0_26
| spl0_27 ),
inference(split_clause,[status(thm)],[f184,f172,f175,f178,f181]) ).
fof(f186,plain,
( spl0_28
<=> product(e_1,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f187,plain,
( product(e_1,e_1,e_3)
| ~ spl0_28 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f192,plain,
( spl0_30
<=> product(e_3,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f193,plain,
( product(e_3,e_1,e_3)
| ~ spl0_30 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( spl0_31
<=> product(e_4,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f196,plain,
( product(e_4,e_1,e_3)
| ~ spl0_31 ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f201,plain,
( equalish(e_1,e_4)
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f140,f81]) ).
fof(f202,plain,
( $false
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f39]) ).
fof(f203,plain,
~ spl0_15,
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f207,plain,
! [X0] :
( ~ product(e_1,X0,e_3)
| product(e_4,e_1,X0)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f137,f58]) ).
fof(f220,plain,
( equalish(e_4,e_1)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f131,f79]) ).
fof(f221,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f220,f46]) ).
fof(f222,plain,
~ spl0_12,
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f224,plain,
( equalish(e_2,e_4)
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f126,f81]) ).
fof(f225,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f224,f42]) ).
fof(f226,plain,
~ spl0_11,
inference(contradiction_clause,[status(thm)],[f225]) ).
fof(f232,plain,
! [X0] :
( product(e_2,X0,e_3)
| ~ product(e_4,e_2,X0)
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f123,f30]) ).
fof(f236,plain,
( equalish(e_4,e_2)
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f120,f79]) ).
fof(f237,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f236,f47]) ).
fof(f238,plain,
~ spl0_9,
inference(contradiction_clause,[status(thm)],[f237]) ).
fof(f244,plain,
! [X0] :
( product(e_2,X0,e_1)
| ~ product(e_4,e_2,X0)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f117,f30]) ).
fof(f247,plain,
( equalish(e_3,e_4)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f112,f81]) ).
fof(f248,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f247,f45]) ).
fof(f249,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f252,plain,
( equalish(e_4,e_3)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f109,f79]) ).
fof(f253,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f48]) ).
fof(f254,plain,
~ spl0_6,
inference(contradiction_clause,[status(thm)],[f253]) ).
fof(f274,plain,
! [X0] :
( ~ product(e_1,X0,e_4)
| product(e_3,e_1,X0)
| ~ spl0_31 ),
inference(resolution,[status(thm)],[f196,f58]) ).
fof(f279,plain,
( equalish(e_1,e_3)
| ~ spl0_30 ),
inference(resolution,[status(thm)],[f193,f81]) ).
fof(f280,plain,
( $false
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[status(thm)],[f279,f38]) ).
fof(f281,plain,
~ spl0_30,
inference(contradiction_clause,[status(thm)],[f280]) ).
fof(f295,plain,
( equalish(e_3,e_1)
| ~ spl0_28 ),
inference(resolution,[status(thm)],[f187,f79]) ).
fof(f296,plain,
( $false
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[status(thm)],[f295,f43]) ).
fof(f297,plain,
~ spl0_28,
inference(contradiction_clause,[status(thm)],[f296]) ).
fof(f307,plain,
( equalish(e_2,e_3)
| ~ spl0_26 ),
inference(resolution,[status(thm)],[f179,f81]) ).
fof(f308,plain,
( $false
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f307,f41]) ).
fof(f309,plain,
~ spl0_26,
inference(contradiction_clause,[status(thm)],[f308]) ).
fof(f314,plain,
( equalish(e_3,e_2)
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f176,f79]) ).
fof(f315,plain,
( $false
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[status(thm)],[f314,f44]) ).
fof(f316,plain,
~ spl0_25,
inference(contradiction_clause,[status(thm)],[f315]) ).
fof(f324,plain,
! [X0] :
( product(e_2,X0,e_1)
| ~ product(e_3,e_2,X0)
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f173,f30]) ).
fof(f329,plain,
( product(e_3,e_3,e_4)
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f168,f66]) ).
fof(f330,plain,
( spl0_6
| ~ spl0_23 ),
inference(split_clause,[status(thm)],[f329,f108,f167]) ).
fof(f353,plain,
( equalish(e_3,e_4)
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f154,f79]) ).
fof(f354,plain,
( $false
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f353,f45]) ).
fof(f355,plain,
~ spl0_19,
inference(contradiction_clause,[status(thm)],[f354]) ).
fof(f356,plain,
( equalish(e_1,e_3)
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f83,f159]) ).
fof(f357,plain,
( $false
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f356,f38]) ).
fof(f358,plain,
~ spl0_20,
inference(contradiction_clause,[status(thm)],[f357]) ).
fof(f359,plain,
( equalish(e_2,e_3)
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f83,f162]) ).
fof(f360,plain,
( $false
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[status(thm)],[f359,f41]) ).
fof(f361,plain,
~ spl0_21,
inference(contradiction_clause,[status(thm)],[f360]) ).
fof(f365,plain,
( product(e_2,e_3,e_3)
| ~ spl0_27
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f182,f232]) ).
fof(f366,plain,
( spl0_21
| ~ spl0_27
| ~ spl0_10 ),
inference(split_clause,[status(thm)],[f365,f161,f181,f122]) ).
fof(f384,plain,
( spl0_37
<=> product(e_2,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f385,plain,
( product(e_2,e_3,e_2)
| ~ spl0_37 ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f395,plain,
( spl0_40
<=> product(e_1,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f396,plain,
( product(e_1,e_2,e_2)
| ~ spl0_40 ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f398,plain,
( spl0_41
<=> product(e_2,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f409,plain,
( spl0_44
<=> product(e_1,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f410,plain,
( product(e_1,e_1,e_2)
| ~ spl0_44 ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f423,plain,
( spl0_48
<=> product(e_1,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f424,plain,
( product(e_1,e_4,e_1)
| ~ spl0_48 ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f437,plain,
( spl0_52
<=> product(e_1,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f438,plain,
( product(e_1,e_3,e_1)
| ~ spl0_52 ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f443,plain,
( spl0_54
<=> product(e_3,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f444,plain,
( product(e_3,e_3,e_1)
| ~ spl0_54 ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f451,plain,
( spl0_56
<=> product(e_1,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f452,plain,
( product(e_1,e_2,e_1)
| ~ spl0_56 ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,plain,
( spl0_57
<=> product(e_2,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f455,plain,
( product(e_2,e_2,e_1)
| ~ spl0_57 ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,plain,
( spl0_58
<=> product(e_3,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f458,plain,
( product(e_3,e_2,e_1)
| ~ spl0_58 ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,plain,
( spl0_59
<=> product(e_4,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f461,plain,
( product(e_4,e_2,e_1)
| ~ spl0_59 ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[f74,f34]) ).
fof(f464,plain,
( spl0_56
| spl0_57
| spl0_58
| spl0_59 ),
inference(split_clause,[status(thm)],[f463,f451,f454,f457,f460]) ).
fof(f465,plain,
( spl0_60
<=> product(e_1,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f468,plain,
( spl0_61
<=> product(e_2,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f469,plain,
( product(e_2,e_1,e_1)
| ~ spl0_61 ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f471,plain,
( spl0_62
<=> product(e_3,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f472,plain,
( product(e_3,e_1,e_1)
| ~ spl0_62 ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,plain,
( spl0_63
<=> product(e_4,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f475,plain,
( product(e_4,e_1,e_1)
| ~ spl0_63 ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f479,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_2,e_4)
| product(e_4,e_3,e_4)
| product(e_4,e_4,e_4) ),
inference(resolution,[status(thm)],[f75,f36]) ).
fof(f480,plain,
( spl0_15
| spl0_11
| spl0_7
| spl0_3 ),
inference(split_clause,[status(thm)],[f479,f139,f125,f111,f97]) ).
fof(f481,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| product(e_3,e_4,e_4) ),
inference(resolution,[status(thm)],[f75,f35]) ).
fof(f482,plain,
( spl0_14
| spl0_10
| spl0_6
| spl0_2 ),
inference(split_clause,[status(thm)],[f481,f136,f122,f108,f94]) ).
fof(f485,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_1,e_4,e_4) ),
inference(resolution,[status(thm)],[f75,f33]) ).
fof(f486,plain,
( spl0_12
| spl0_8
| spl0_4
| spl0_0 ),
inference(split_clause,[status(thm)],[f485,f130,f116,f102,f88]) ).
fof(f487,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_4,e_3) ),
inference(resolution,[status(thm)],[f76,f36]) ).
fof(f488,plain,
( spl0_31
| spl0_27
| spl0_23
| spl0_19 ),
inference(split_clause,[status(thm)],[f487,f195,f181,f167,f153]) ).
fof(f493,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_3)
| product(e_1,e_4,e_3) ),
inference(resolution,[status(thm)],[f76,f33]) ).
fof(f494,plain,
( spl0_28
| spl0_24
| spl0_20
| spl0_16 ),
inference(split_clause,[status(thm)],[f493,f186,f172,f158,f144]) ).
fof(f531,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(resolution,[status(thm)],[f86,f34]) ).
fof(f532,plain,
( spl0_57
| spl0_41
| spl0_25
| spl0_9 ),
inference(split_clause,[status(thm)],[f531,f454,f398,f175,f119]) ).
fof(f541,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)],[f87,f33]) ).
fof(f542,plain,
( spl0_60
| spl0_44
| spl0_28
| spl0_12 ),
inference(split_clause,[status(thm)],[f541,f465,f409,f186,f130]) ).
fof(f543,plain,
( product(e_3,e_1,e_3)
| ~ spl0_31
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f274,f103]) ).
fof(f544,plain,
( spl0_30
| ~ spl0_31
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f543,f192,f195,f102]) ).
fof(f547,plain,
( equalish(e_2,e_1)
| ~ spl0_44 ),
inference(resolution,[status(thm)],[f410,f79]) ).
fof(f548,plain,
( $false
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[status(thm)],[f547,f40]) ).
fof(f549,plain,
~ spl0_44,
inference(contradiction_clause,[status(thm)],[f548]) ).
fof(f550,plain,
( equalish(e_1,e_2)
| ~ spl0_40 ),
inference(resolution,[status(thm)],[f396,f83]) ).
fof(f551,plain,
( $false
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[status(thm)],[f550,f37]) ).
fof(f552,plain,
~ spl0_40,
inference(contradiction_clause,[status(thm)],[f551]) ).
fof(f566,plain,
( equalish(e_4,e_1)
| ~ spl0_63 ),
inference(resolution,[status(thm)],[f475,f83]) ).
fof(f567,plain,
( $false
| ~ spl0_63 ),
inference(forward_subsumption_resolution,[status(thm)],[f566,f46]) ).
fof(f568,plain,
~ spl0_63,
inference(contradiction_clause,[status(thm)],[f567]) ).
fof(f571,plain,
( equalish(e_3,e_1)
| ~ spl0_62 ),
inference(resolution,[status(thm)],[f472,f83]) ).
fof(f572,plain,
( $false
| ~ spl0_62 ),
inference(forward_subsumption_resolution,[status(thm)],[f571,f43]) ).
fof(f573,plain,
~ spl0_62,
inference(contradiction_clause,[status(thm)],[f572]) ).
fof(f574,plain,
( equalish(e_2,e_1)
| ~ spl0_61 ),
inference(resolution,[status(thm)],[f469,f83]) ).
fof(f575,plain,
( $false
| ~ spl0_61 ),
inference(forward_subsumption_resolution,[status(thm)],[f574,f40]) ).
fof(f576,plain,
~ spl0_61,
inference(contradiction_clause,[status(thm)],[f575]) ).
fof(f577,plain,
( product(e_2,e_1,e_1)
| ~ spl0_59
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f461,f244]) ).
fof(f578,plain,
( spl0_61
| ~ spl0_59
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f577,f468,f460,f116]) ).
fof(f587,plain,
( product(e_2,e_1,e_1)
| ~ spl0_58
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f458,f324]) ).
fof(f588,plain,
( spl0_61
| ~ spl0_58
| ~ spl0_24 ),
inference(split_clause,[status(thm)],[f587,f468,f457,f172]) ).
fof(f605,plain,
( equalish(e_1,e_2)
| ~ spl0_57 ),
inference(resolution,[status(thm)],[f455,f79]) ).
fof(f606,plain,
( $false
| ~ spl0_57 ),
inference(forward_subsumption_resolution,[status(thm)],[f605,f37]) ).
fof(f607,plain,
~ spl0_57,
inference(contradiction_clause,[status(thm)],[f606]) ).
fof(f610,plain,
( equalish(e_2,e_1)
| ~ spl0_56 ),
inference(resolution,[status(thm)],[f452,f81]) ).
fof(f611,plain,
( $false
| ~ spl0_56 ),
inference(forward_subsumption_resolution,[status(thm)],[f610,f40]) ).
fof(f612,plain,
~ spl0_56,
inference(contradiction_clause,[status(thm)],[f611]) ).
fof(f622,plain,
( equalish(e_1,e_3)
| ~ spl0_54 ),
inference(resolution,[status(thm)],[f444,f79]) ).
fof(f623,plain,
( $false
| ~ spl0_54 ),
inference(forward_subsumption_resolution,[status(thm)],[f622,f38]) ).
fof(f624,plain,
~ spl0_54,
inference(contradiction_clause,[status(thm)],[f623]) ).
fof(f633,plain,
( equalish(e_3,e_1)
| ~ spl0_52 ),
inference(resolution,[status(thm)],[f438,f81]) ).
fof(f634,plain,
( $false
| ~ spl0_52 ),
inference(forward_subsumption_resolution,[status(thm)],[f633,f43]) ).
fof(f635,plain,
~ spl0_52,
inference(contradiction_clause,[status(thm)],[f634]) ).
fof(f636,plain,
( equalish(e_3,e_4)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f95,f83]) ).
fof(f637,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f636,f45]) ).
fof(f638,plain,
~ spl0_2,
inference(contradiction_clause,[status(thm)],[f637]) ).
fof(f654,plain,
( equalish(e_4,e_1)
| ~ spl0_48 ),
inference(resolution,[status(thm)],[f424,f81]) ).
fof(f655,plain,
( $false
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[status(thm)],[f654,f46]) ).
fof(f656,plain,
~ spl0_48,
inference(contradiction_clause,[status(thm)],[f655]) ).
fof(f664,plain,
( equalish(e_1,e_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f89,f83]) ).
fof(f665,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f664,f39]) ).
fof(f666,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f665]) ).
fof(f681,plain,
( equalish(e_3,e_2)
| ~ spl0_37 ),
inference(resolution,[status(thm)],[f385,f81]) ).
fof(f682,plain,
( $false
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[status(thm)],[f681,f44]) ).
fof(f683,plain,
~ spl0_37,
inference(contradiction_clause,[status(thm)],[f682]) ).
fof(f696,plain,
( product(e_4,e_1,e_4)
| ~ spl0_14
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f207,f145]) ).
fof(f697,plain,
( spl0_15
| ~ spl0_14
| ~ spl0_16 ),
inference(split_clause,[status(thm)],[f696,f139,f136,f144]) ).
fof(f698,plain,
$false,
inference(sat_refutation,[status(thm)],[f129,f171,f185,f203,f222,f226,f238,f249,f254,f281,f297,f309,f316,f330,f355,f358,f361,f366,f464,f480,f482,f486,f488,f494,f532,f542,f544,f549,f552,f568,f573,f576,f578,f588,f607,f612,f624,f635,f638,f656,f666,f683,f697]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP127-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n007.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue May 30 11:21:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.045048 seconds
% 0.13/0.40 % CPU time: 0.238292 seconds
% 0.13/0.40 % Memory used: 5.114 MB
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