TSTP Solution File: GRP130-2.003 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP130-2.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 20:19:27 EDT 2024
% Result : Unsatisfiable 0.17s 0.43s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 43
% Syntax : Number of formulae : 227 ( 22 unt; 0 def)
% Number of atoms : 581 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 664 ( 310 ~; 327 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 33 ( 32 usr; 28 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 95 ( 95 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,X1] :
( ~ product(X,e_1,Y)
| ~ next(X,X1)
| ~ greater(Y,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_1,e_2),
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_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(X,Z1,Z2)
| product(Z2,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,plain,
next(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f25,plain,
greater(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f26,plain,
! [Y,X1] :
( ! [X] :
( ~ product(X,e_1,Y)
| ~ next(X,X1) )
| ~ greater(Y,X1) ),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ product(X0,e_1,X1)
| ~ next(X0,X2)
| ~ greater(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f29,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f30,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f31,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f33,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f34,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f35,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f36,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f37,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f38,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f18]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f42,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X,Y,Z2] :
( ! [Z1] :
( ~ product(X,Y,Z1)
| ~ product(X,Z1,Z2) )
| product(Z2,Y,X) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X2,X3)
| product(X3,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f46,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f37,f30]) ).
fof(f47,plain,
! [X0] :
( ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| product(e_2,X0,e_3) ),
inference(resolution,[status(thm)],[f37,f29]) ).
fof(f48,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2)
| product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f37,f28]) ).
fof(f49,plain,
( spl0_0
<=> product(e_3,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f50,plain,
( product(e_3,e_3,e_1)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( spl0_1
<=> product(e_3,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f53,plain,
( product(e_3,e_3,e_2)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( spl0_2
<=> product(e_3,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f56,plain,
( product(e_3,e_3,e_3)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f46,f30]) ).
fof(f59,plain,
( spl0_0
| spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f58,f49,f52,f55]) ).
fof(f60,plain,
( spl0_3
<=> product(e_3,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f61,plain,
( product(e_3,e_2,e_1)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( spl0_4
<=> product(e_3,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f64,plain,
( product(e_3,e_2,e_2)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f65,plain,
( ~ product(e_3,e_2,e_2)
| spl0_4 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( spl0_5
<=> product(e_3,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f67,plain,
( product(e_3,e_2,e_3)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(resolution,[status(thm)],[f46,f29]) ).
fof(f70,plain,
( spl0_3
| spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f69,f60,f63,f66]) ).
fof(f71,plain,
( spl0_6
<=> product(e_3,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f72,plain,
( product(e_3,e_1,e_1)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( spl0_7
<=> product(e_3,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f75,plain,
( product(e_3,e_1,e_2)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( spl0_8
<=> product(e_3,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f78,plain,
( product(e_3,e_1,e_3)
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[f46,f28]) ).
fof(f81,plain,
( spl0_6
| spl0_7
| spl0_8 ),
inference(split_clause,[status(thm)],[f80,f71,f74,f77]) ).
fof(f82,plain,
( spl0_9
<=> product(e_2,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f83,plain,
( product(e_2,e_3,e_1)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,plain,
( spl0_10
<=> product(e_2,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f86,plain,
( product(e_2,e_3,e_2)
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( spl0_11
<=> product(e_2,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f89,plain,
( product(e_2,e_3,e_3)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f47,f30]) ).
fof(f92,plain,
( spl0_9
| spl0_10
| spl0_11 ),
inference(split_clause,[status(thm)],[f91,f82,f85,f88]) ).
fof(f93,plain,
( spl0_12
<=> product(e_2,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f94,plain,
( product(e_2,e_2,e_1)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( spl0_13
<=> product(e_2,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f97,plain,
( product(e_2,e_2,e_2)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f98,plain,
( ~ product(e_2,e_2,e_2)
| spl0_13 ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,plain,
( spl0_14
<=> product(e_2,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f100,plain,
( product(e_2,e_2,e_3)
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f47,f29]) ).
fof(f103,plain,
( spl0_12
| spl0_13
| spl0_14 ),
inference(split_clause,[status(thm)],[f102,f93,f96,f99]) ).
fof(f104,plain,
( spl0_15
<=> product(e_2,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f105,plain,
( product(e_2,e_1,e_1)
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,plain,
( spl0_16
<=> product(e_2,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f108,plain,
( product(e_2,e_1,e_2)
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( spl0_17
<=> product(e_2,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f111,plain,
( product(e_2,e_1,e_3)
| ~ spl0_17 ),
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) ),
inference(resolution,[status(thm)],[f47,f28]) ).
fof(f114,plain,
( spl0_15
| spl0_16
| spl0_17 ),
inference(split_clause,[status(thm)],[f113,f104,f107,f110]) ).
fof(f115,plain,
( spl0_18
<=> product(e_1,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f116,plain,
( product(e_1,e_3,e_1)
| ~ spl0_18 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( spl0_19
<=> product(e_1,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f119,plain,
( product(e_1,e_3,e_2)
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( spl0_20
<=> product(e_1,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f122,plain,
( product(e_1,e_3,e_3)
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f126,plain,
( spl0_21
<=> product(e_1,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f127,plain,
( product(e_1,e_2,e_1)
| ~ spl0_21 ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,plain,
( spl0_22
<=> product(e_1,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f130,plain,
( product(e_1,e_2,e_2)
| ~ spl0_22 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( spl0_23
<=> product(e_1,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f133,plain,
( product(e_1,e_2,e_3)
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f135,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f48,f29]) ).
fof(f136,plain,
( spl0_21
| spl0_22
| spl0_23 ),
inference(split_clause,[status(thm)],[f135,f126,f129,f132]) ).
fof(f137,plain,
( spl0_24
<=> product(e_1,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f140,plain,
( spl0_25
<=> product(e_1,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f141,plain,
( product(e_1,e_1,e_2)
| ~ spl0_25 ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,plain,
( spl0_26
<=> product(e_1,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f144,plain,
( product(e_1,e_1,e_3)
| ~ spl0_26 ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f48,f28]) ).
fof(f147,plain,
( spl0_24
| spl0_25
| spl0_26 ),
inference(split_clause,[status(thm)],[f146,f137,f140,f143]) ).
fof(f149,plain,
! [X0] :
( ~ product(X0,e_1,e_3)
| equalish(e_3,X0)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f78,f43]) ).
fof(f152,plain,
! [X0] :
( ~ product(e_3,e_3,X0)
| product(X0,e_1,e_3)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f78,f45]) ).
fof(f157,plain,
! [X0] :
( ~ product(e_3,e_2,X0)
| product(X0,e_1,e_3)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f75,f45]) ).
fof(f162,plain,
! [X0] :
( ~ product(e_3,e_1,X0)
| product(X0,e_1,e_3)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f72,f45]) ).
fof(f167,plain,
! [X0] :
( ~ product(e_3,e_3,X0)
| product(X0,e_2,e_3)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f67,f45]) ).
fof(f171,plain,
! [X0] :
( ~ product(e_3,e_2,X0)
| product(X0,e_2,e_3)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f64,f45]) ).
fof(f176,plain,
! [X0] :
( ~ product(e_3,e_1,X0)
| product(X0,e_2,e_3)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f61,f45]) ).
fof(f180,plain,
! [X0] :
( ~ product(e_3,X0,e_3)
| equalish(e_3,X0)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f56,f41]) ).
fof(f188,plain,
! [X0] :
( ~ product(e_2,e_3,X0)
| product(X0,e_1,e_2)
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f111,f45]) ).
fof(f193,plain,
! [X0] :
( ~ product(e_2,e_2,X0)
| product(X0,e_1,e_2)
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f108,f45]) ).
fof(f198,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| product(X0,e_1,e_2)
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f105,f45]) ).
fof(f203,plain,
! [X0] :
( ~ product(e_2,e_3,X0)
| product(X0,e_2,e_2)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f100,f45]) ).
fof(f208,plain,
! [X0] :
( ~ product(e_2,e_2,X0)
| product(X0,e_2,e_2)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f97,f45]) ).
fof(f213,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| product(X0,e_2,e_2)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f94,f45]) ).
fof(f217,plain,
! [X0] :
( ~ product(e_2,e_3,X0)
| product(X0,e_3,e_2)
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f89,f45]) ).
fof(f218,plain,
( product(e_3,e_3,e_2)
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f217,f89]) ).
fof(f221,plain,
! [X0] :
( ~ product(e_3,X0,e_2)
| equalish(e_3,X0)
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f218,f41]) ).
fof(f233,plain,
! [X0] :
( ~ product(e_2,e_2,X0)
| product(X0,e_3,e_2)
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f86,f45]) ).
fof(f237,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| product(X0,e_3,e_2)
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f83,f45]) ).
fof(f247,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| product(X0,e_1,e_1)
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f141,f45]) ).
fof(f256,plain,
! [X0] :
( ~ product(e_1,e_3,X0)
| product(X0,e_2,e_1)
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f133,f45]) ).
fof(f260,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| product(X0,e_2,e_1)
| ~ spl0_22 ),
inference(resolution,[status(thm)],[f130,f45]) ).
fof(f268,plain,
! [X0] :
( ~ product(e_1,e_3,X0)
| product(X0,e_3,e_1)
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f122,f45]) ).
fof(f272,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| product(X0,e_3,e_1)
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f119,f45]) ).
fof(f284,plain,
( equalish(e_3,e_1)
| ~ spl0_8
| ~ spl0_26 ),
inference(resolution,[status(thm)],[f149,f144]) ).
fof(f285,plain,
( $false
| ~ spl0_8
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f284,f35]) ).
fof(f286,plain,
( ~ spl0_8
| ~ spl0_26 ),
inference(contradiction_clause,[status(thm)],[f285]) ).
fof(f287,plain,
( product(e_3,e_1,e_3)
| ~ spl0_5
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f67,f157]) ).
fof(f288,plain,
( spl0_8
| ~ spl0_5
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f287,f77,f66,f74]) ).
fof(f290,plain,
( product(e_1,e_1,e_3)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f162,f72]) ).
fof(f291,plain,
( product(e_3,e_1,e_2)
| ~ spl0_14
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f100,f193]) ).
fof(f292,plain,
! [X0] :
( ~ next(e_1,X0)
| ~ greater(e_3,X0)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f290,f27]) ).
fof(f303,plain,
( ~ next(e_1,e_2)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f292,f25]) ).
fof(f304,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f21]) ).
fof(f305,plain,
~ spl0_6,
inference(contradiction_clause,[status(thm)],[f304]) ).
fof(f306,plain,
( equalish(e_3,e_2)
| ~ spl0_8
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f149,f111]) ).
fof(f307,plain,
( $false
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f36]) ).
fof(f308,plain,
( ~ spl0_8
| ~ spl0_17 ),
inference(contradiction_clause,[status(thm)],[f307]) ).
fof(f310,plain,
( product(e_3,e_2,e_3)
| ~ spl0_3
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f176,f78]) ).
fof(f312,plain,
( product(e_3,e_2,e_2)
| ~ spl0_13
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f208,f100]) ).
fof(f313,plain,
( product(e_2,e_1,e_3)
| ~ spl0_4
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f64,f157]) ).
fof(f314,plain,
( spl0_17
| ~ spl0_4
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f313,f110,f63,f74]) ).
fof(f315,plain,
( $false
| ~ spl0_13
| ~ spl0_14
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f312]) ).
fof(f316,plain,
( ~ spl0_13
| ~ spl0_14
| spl0_4 ),
inference(contradiction_clause,[status(thm)],[f315]) ).
fof(f317,plain,
( product(e_2,e_2,e_2)
| ~ spl0_12
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f213,f108]) ).
fof(f318,plain,
( spl0_13
| ~ spl0_12
| ~ spl0_16 ),
inference(split_clause,[status(thm)],[f317,f96,f93,f107]) ).
fof(f319,plain,
( product(e_3,e_1,e_1)
| ~ spl0_25
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f247,f133]) ).
fof(f320,plain,
( spl0_6
| ~ spl0_25
| ~ spl0_23 ),
inference(split_clause,[status(thm)],[f319,f71,f140,f132]) ).
fof(f321,plain,
( product(e_1,e_1,e_2)
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f198,f105]) ).
fof(f322,plain,
( spl0_25
| ~ spl0_15 ),
inference(split_clause,[status(thm)],[f321,f140,f104]) ).
fof(f327,plain,
( product(e_3,e_3,e_1)
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f268,f122]) ).
fof(f329,plain,
! [X0] :
( ~ product(X0,e_3,e_1)
| equalish(e_3,X0)
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f327,f43]) ).
fof(f333,plain,
( equalish(e_3,e_1)
| ~ spl0_20
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f329,f116]) ).
fof(f334,plain,
( $false
| ~ spl0_20
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f333,f35]) ).
fof(f335,plain,
( ~ spl0_20
| ~ spl0_18 ),
inference(contradiction_clause,[status(thm)],[f334]) ).
fof(f336,plain,
( product(e_1,e_3,e_1)
| ~ spl0_19
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f272,f127]) ).
fof(f336_001,plain,
( product(e_1,e_3,e_1)
| ~ spl0_19
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f272,f127]) ).
fof(f337,plain,
! [X0] :
( ~ product(X0,e_3,e_1)
| equalish(e_1,X0)
| ~ spl0_19
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f336,f43]) ).
fof(f342,plain,
( equalish(e_1,e_2)
| ~ spl0_19
| ~ spl0_21
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f337,f83]) ).
fof(f343,plain,
( $false
| ~ spl0_19
| ~ spl0_21
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f342,f31]) ).
fof(f344,plain,
( ~ spl0_19
| ~ spl0_21
| ~ spl0_9 ),
inference(contradiction_clause,[status(thm)],[f343]) ).
fof(f347,plain,
( product(e_1,e_3,e_2)
| ~ spl0_10
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f233,f94]) ).
fof(f348,plain,
( spl0_19
| ~ spl0_10
| ~ spl0_12 ),
inference(split_clause,[status(thm)],[f347,f118,f85,f93]) ).
fof(f349,plain,
( product(e_2,e_3,e_1)
| ~ spl0_19
| ~ spl0_22 ),
inference(resolution,[status(thm)],[f272,f130]) ).
fof(f350,plain,
( spl0_9
| ~ spl0_19
| ~ spl0_22 ),
inference(split_clause,[status(thm)],[f349,f82,f118,f129]) ).
fof(f351,plain,
( equalish(e_3,e_1)
| ~ spl0_11
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f221,f75]) ).
fof(f352,plain,
( $false
| ~ spl0_11
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f351,f35]) ).
fof(f353,plain,
( ~ spl0_11
| ~ spl0_7 ),
inference(contradiction_clause,[status(thm)],[f352]) ).
fof(f354,plain,
( product(e_1,e_1,e_2)
| ~ spl0_9
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f83,f188]) ).
fof(f355,plain,
( spl0_25
| ~ spl0_9
| ~ spl0_17 ),
inference(split_clause,[status(thm)],[f354,f140,f82,f110]) ).
fof(f356,plain,
( product(e_2,e_2,e_3)
| ~ spl0_3
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f176,f75]) ).
fof(f357,plain,
( spl0_14
| ~ spl0_3
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f356,f99,f60,f74]) ).
fof(f359,plain,
( product(e_2,e_2,e_3)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f171,f64]) ).
fof(f360,plain,
( spl0_14
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f359,f99,f63]) ).
fof(f379,plain,
( product(e_1,e_2,e_1)
| ~ spl0_18
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f116,f256]) ).
fof(f385,plain,
! [X0] :
( ~ product(e_1,X0,e_1)
| equalish(e_2,X0)
| ~ spl0_18
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f379,f41]) ).
fof(f390,plain,
( equalish(e_2,e_3)
| ~ spl0_23
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f385,f116]) ).
fof(f391,plain,
( $false
| ~ spl0_23
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f390,f34]) ).
fof(f392,plain,
( ~ spl0_23
| ~ spl0_18 ),
inference(contradiction_clause,[status(thm)],[f391]) ).
fof(f398,plain,
( product(e_2,e_3,e_2)
| ~ spl0_16
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f108,f237]) ).
fof(f405,plain,
! [X0] :
( ~ product(e_2,X0,e_2)
| equalish(e_3,X0)
| ~ spl0_16
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f398,f41]) ).
fof(f409,plain,
( equalish(e_3,e_1)
| ~ spl0_9
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f405,f108]) ).
fof(f410,plain,
( $false
| ~ spl0_9
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f409,f35]) ).
fof(f411,plain,
( ~ spl0_9
| ~ spl0_16 ),
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f413,plain,
( product(e_2,e_1,e_1)
| ~ spl0_25
| ~ spl0_22 ),
inference(resolution,[status(thm)],[f247,f130]) ).
fof(f436,plain,
( equalish(e_3,e_2)
| ~ spl0_2
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f180,f67]) ).
fof(f437,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f436,f36]) ).
fof(f438,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(contradiction_clause,[status(thm)],[f437]) ).
fof(f440,plain,
( product(e_2,e_2,e_1)
| ~ spl0_22 ),
inference(resolution,[status(thm)],[f260,f130]) ).
fof(f450,plain,
( product(e_1,e_1,e_3)
| ~ spl0_0
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f50,f152]) ).
fof(f451,plain,
( spl0_26
| ~ spl0_0
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f450,f143,f49,f77]) ).
fof(f458,plain,
( product(e_2,e_1,e_3)
| ~ spl0_11
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f218,f152]) ).
fof(f459,plain,
( spl0_17
| ~ spl0_11
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f458,f110,f88,f77]) ).
fof(f462,plain,
( spl0_5
| ~ spl0_3
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f310,f66,f60,f77]) ).
fof(f463,plain,
( spl0_7
| ~ spl0_14
| ~ spl0_16 ),
inference(split_clause,[status(thm)],[f291,f74,f99,f107]) ).
fof(f468,plain,
! [X0] :
( ~ product(e_2,X0,e_1)
| equalish(e_2,X0)
| ~ spl0_22 ),
inference(resolution,[status(thm)],[f440,f41]) ).
fof(f512,plain,
( equalish(e_2,e_1)
| ~ spl0_25
| ~ spl0_22 ),
inference(resolution,[status(thm)],[f468,f413]) ).
fof(f513,plain,
( $false
| ~ spl0_25
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f33]) ).
fof(f514,plain,
( ~ spl0_25
| ~ spl0_22 ),
inference(contradiction_clause,[status(thm)],[f513]) ).
fof(f515,plain,
( product(e_2,e_2,e_2)
| ~ spl0_10
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f86,f203]) ).
fof(f516,plain,
( product(e_2,e_1,e_2)
| ~ spl0_10
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f86,f188]) ).
fof(f518,plain,
! [X0] :
( ~ product(e_2,X0,e_2)
| equalish(e_2,X0)
| ~ spl0_10
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f515,f41]) ).
fof(f528,plain,
( equalish(e_2,e_1)
| ~ spl0_14
| ~ spl0_10
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f518,f516]) ).
fof(f529,plain,
( $false
| ~ spl0_14
| ~ spl0_10
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f33]) ).
fof(f530,plain,
( ~ spl0_14
| ~ spl0_10
| ~ spl0_17 ),
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f534,plain,
( product(e_1,e_1,e_1)
| ~ spl0_25
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f247,f127]) ).
fof(f535,plain,
( $false
| ~ spl0_10
| ~ spl0_14
| spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f98,f515]) ).
fof(f536,plain,
( ~ spl0_10
| ~ spl0_14
| spl0_13 ),
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f547,plain,
( product(e_2,e_2,e_3)
| ~ spl0_1
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f53,f167]) ).
fof(f548,plain,
( spl0_14
| ~ spl0_1
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f547,f99,f52,f66]) ).
fof(f553,plain,
( spl0_18
| ~ spl0_19
| ~ spl0_21 ),
inference(split_clause,[status(thm)],[f336,f115,f118,f126]) ).
fof(f575,plain,
! [X0] :
( ~ product(e_1,e_1,X0)
| equalish(e_1,X0)
| ~ spl0_25
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f534,f39]) ).
fof(f581,plain,
( equalish(e_1,e_2)
| ~ spl0_21
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f575,f141]) ).
fof(f582,plain,
( $false
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[status(thm)],[f581,f31]) ).
fof(f583,plain,
( ~ spl0_21
| ~ spl0_25 ),
inference(contradiction_clause,[status(thm)],[f582]) ).
fof(f584,plain,
$false,
inference(sat_refutation,[status(thm)],[f59,f70,f81,f92,f103,f114,f136,f147,f286,f288,f305,f308,f314,f316,f318,f320,f322,f335,f344,f348,f350,f353,f355,f357,f360,f392,f411,f438,f451,f459,f462,f463,f514,f530,f536,f548,f553,f583]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.14 % Problem : GRP130-2.003 : TPTP v8.1.2. Released v1.2.0.
% 0.06/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.35 % Computer : n015.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8042.1875MB
% 0.11/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Tue Apr 30 00:37:17 EDT 2024
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Drodi V3.6.0
% 0.17/0.43 % Refutation found
% 0.17/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.44 % Elapsed time: 0.078938 seconds
% 0.17/0.44 % CPU time: 0.527229 seconds
% 0.17/0.44 % Total memory used: 12.763 MB
% 0.17/0.44 % Net memory used: 11.945 MB
%------------------------------------------------------------------------------