TSTP Solution File: GRP129-1.003 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP129-1.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 12:10:37 EDT 2023
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 39
% Syntax : Number of formulae : 222 ( 19 unt; 0 def)
% Number of atoms : 570 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 660 ( 312 ~; 323 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 26 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 85 (; 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,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(f11,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
! [Y,X,Z1,Z2] :
( ~ product(Y,X,Z1)
| ~ product(X,Z1,Z2)
| product(Z1,Y,Z2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f16,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f17,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f18,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f19,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f20,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f21,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f22,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f23,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f24,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)],[f10]) ).
fof(f25,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f29,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f31,plain,
! [Y,Z1,Z2] :
( ! [X] :
( ~ product(Y,X,Z1)
| ~ product(X,Z1,Z2) )
| product(Z1,Y,Z2) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X1,X2,X3)
| product(X2,X0,X3) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,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)],[f15,f24]) ).
fof(f34,plain,
( spl0_0
<=> product(e_1,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f35,plain,
( product(e_1,e_1,e_1)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,plain,
( spl0_1
<=> product(e_1,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f40,plain,
( spl0_2
<=> product(e_1,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f41,plain,
( product(e_1,e_1,e_3)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f40]) ).
fof(f43,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)],[f33,f15]) ).
fof(f44,plain,
( spl0_0
| spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f43,f34,f37,f40]) ).
fof(f45,plain,
( spl0_3
<=> product(e_1,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f46,plain,
( product(e_1,e_2,e_1)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( spl0_4
<=> product(e_1,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f49,plain,
( product(e_1,e_2,e_2)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,plain,
( spl0_5
<=> product(e_1,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f52,plain,
( product(e_1,e_2,e_3)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,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)],[f16,f33]) ).
fof(f55,plain,
( spl0_3
| spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f54,f45,f48,f51]) ).
fof(f56,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)],[f16,f24]) ).
fof(f57,plain,
( spl0_6
<=> product(e_2,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f58,plain,
( product(e_2,e_2,e_1)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( spl0_7
<=> product(e_2,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f61,plain,
( product(e_2,e_2,e_2)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( spl0_8
<=> product(e_2,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f64,plain,
( product(e_2,e_2,e_3)
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,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)],[f56,f16]) ).
fof(f67,plain,
( spl0_6
| spl0_7
| spl0_8 ),
inference(split_clause,[status(thm)],[f66,f57,f60,f63]) ).
fof(f68,plain,
( spl0_9
<=> product(e_2,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f69,plain,
( product(e_2,e_1,e_1)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( spl0_10
<=> product(e_2,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f72,plain,
( product(e_2,e_1,e_2)
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( spl0_11
<=> product(e_2,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f75,plain,
( product(e_2,e_1,e_3)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,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)],[f56,f15]) ).
fof(f78,plain,
( spl0_9
| spl0_10
| spl0_11 ),
inference(split_clause,[status(thm)],[f77,f68,f71,f74]) ).
fof(f79,plain,
( spl0_12
<=> product(e_2,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f80,plain,
( product(e_2,e_3,e_1)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( spl0_13
<=> product(e_2,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f83,plain,
( product(e_2,e_3,e_2)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,plain,
( spl0_14
<=> product(e_2,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f86,plain,
( product(e_2,e_3,e_3)
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,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)],[f17,f56]) ).
fof(f89,plain,
( spl0_12
| spl0_13
| spl0_14 ),
inference(split_clause,[status(thm)],[f88,f79,f82,f85]) ).
fof(f90,plain,
( spl0_15
<=> product(e_1,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f91,plain,
( product(e_1,e_3,e_1)
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( spl0_16
<=> product(e_1,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f94,plain,
( product(e_1,e_3,e_2)
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( spl0_17
<=> product(e_1,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f97,plain,
( product(e_1,e_3,e_3)
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f17,f33]) ).
fof(f100,plain,
( spl0_15
| spl0_16
| spl0_17 ),
inference(split_clause,[status(thm)],[f99,f90,f93,f96]) ).
fof(f101,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)],[f17,f24]) ).
fof(f102,plain,
( spl0_18
<=> product(e_3,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f103,plain,
( product(e_3,e_3,e_1)
| ~ spl0_18 ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f113,plain,
( spl0_21
<=> product(e_3,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f114,plain,
( product(e_3,e_2,e_1)
| ~ spl0_21 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( spl0_22
<=> product(e_3,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f117,plain,
( product(e_3,e_2,e_2)
| ~ spl0_22 ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( spl0_23
<=> product(e_3,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f120,plain,
( product(e_3,e_2,e_3)
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,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)],[f101,f16]) ).
fof(f123,plain,
( spl0_21
| spl0_22
| spl0_23 ),
inference(split_clause,[status(thm)],[f122,f113,f116,f119]) ).
fof(f124,plain,
( spl0_24
<=> product(e_3,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f125,plain,
( product(e_3,e_1,e_1)
| ~ spl0_24 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( spl0_25
<=> product(e_3,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f128,plain,
( product(e_3,e_1,e_2)
| ~ spl0_25 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( spl0_26
<=> product(e_3,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f131,plain,
( product(e_3,e_1,e_3)
| ~ spl0_26 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,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)],[f101,f15]) ).
fof(f134,plain,
( spl0_24
| spl0_25
| spl0_26 ),
inference(split_clause,[status(thm)],[f133,f124,f127,f130]) ).
fof(f136,plain,
! [X0] :
( ~ product(e_1,X0,e_3)
| equalish(e_1,X0)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f41,f28]) ).
fof(f142,plain,
( equalish(e_1,e_2)
| ~ spl0_5
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f52,f136]) ).
fof(f143,plain,
( $false
| ~ spl0_5
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f18]) ).
fof(f144,plain,
( ~ spl0_5
| ~ spl0_2 ),
inference(contradiction_clause,[status(thm)],[f143]) ).
fof(f145,plain,
! [X0] :
( ~ product(X0,e_2,e_2)
| equalish(e_1,X0)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f49,f30]) ).
fof(f148,plain,
! [X0] :
( ~ product(e_2,e_2,X0)
| product(e_2,e_1,X0)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f49,f32]) ).
fof(f156,plain,
! [X0] :
( ~ product(e_2,X0,e_3)
| equalish(e_1,X0)
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f75,f28]) ).
fof(f157,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| equalish(e_3,X0)
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f75,f26]) ).
fof(f158,plain,
! [X0] :
( ~ product(e_1,e_3,X0)
| product(e_3,e_2,X0)
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f75,f32]) ).
fof(f159,plain,
! [X0] :
( ~ product(X0,e_1,e_2)
| equalish(e_2,X0)
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f72,f30]) ).
fof(f162,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| product(e_2,e_2,X0)
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f72,f32]) ).
fof(f163,plain,
( equalish(e_3,e_2)
| ~ spl0_11
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f157,f72]) ).
fof(f164,plain,
( $false
| ~ spl0_11
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f23]) ).
fof(f165,plain,
( ~ spl0_11
| ~ spl0_10 ),
inference(contradiction_clause,[status(thm)],[f164]) ).
fof(f166,plain,
! [X0] :
( ~ product(X0,e_1,e_1)
| equalish(e_2,X0)
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f69,f30]) ).
fof(f169,plain,
! [X0] :
( ~ product(e_1,e_1,X0)
| product(e_1,e_2,X0)
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f69,f32]) ).
fof(f170,plain,
( product(e_2,e_1,e_3)
| ~ spl0_8
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f64,f148]) ).
fof(f171,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f170,f74,f63,f48]) ).
fof(f173,plain,
! [X0] :
( ~ product(e_2,X0,e_3)
| equalish(e_2,X0)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f64,f28]) ).
fof(f175,plain,
! [X0] :
( ~ product(e_2,e_3,X0)
| product(e_3,e_2,X0)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f64,f32]) ).
fof(f180,plain,
! [X0] :
( ~ product(e_1,X0,e_1)
| equalish(e_2,X0)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f46,f28]) ).
fof(f182,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| product(e_1,e_1,X0)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f46,f32]) ).
fof(f183,plain,
( product(e_1,e_1,e_1)
| ~ spl0_3
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f182,f69]) ).
fof(f185,plain,
( equalish(e_2,e_1)
| ~ spl0_3
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f183,f166]) ).
fof(f186,plain,
( $false
| ~ spl0_3
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f20]) ).
fof(f187,plain,
( ~ spl0_3
| ~ spl0_9 ),
inference(contradiction_clause,[status(thm)],[f186]) ).
fof(f191,plain,
( equalish(e_1,e_2)
| ~ spl0_7
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f61,f145]) ).
fof(f192,plain,
( $false
| ~ spl0_7
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f18]) ).
fof(f193,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f192]) ).
fof(f194,plain,
( product(e_2,e_1,e_1)
| ~ spl0_6
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f58,f148]) ).
fof(f196,plain,
! [X0] :
( ~ product(e_2,X0,e_1)
| equalish(e_2,X0)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f58,f28]) ).
fof(f198,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| product(e_1,e_2,X0)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f58,f32]) ).
fof(f206,plain,
! [X0] :
( ~ product(X0,e_3,e_1)
| equalish(e_1,X0)
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f91,f30]) ).
fof(f209,plain,
! [X0] :
( ~ product(e_3,e_1,X0)
| product(e_1,e_1,X0)
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f91,f32]) ).
fof(f210,plain,
( equalish(e_1,e_3)
| ~ spl0_14
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f86,f156]) ).
fof(f211,plain,
( $false
| ~ spl0_14
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f19]) ).
fof(f212,plain,
( ~ spl0_14
| ~ spl0_11 ),
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f213,plain,
( product(e_1,e_2,e_1)
| ~ spl0_4
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f194,f198]) ).
fof(f214,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f213,f45,f48,f57]) ).
fof(f215,plain,
( equalish(e_3,e_1)
| ~ spl0_6
| ~ spl0_4
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f194,f157]) ).
fof(f216,plain,
( $false
| ~ spl0_6
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f215,f22]) ).
fof(f217,plain,
( ~ spl0_6
| ~ spl0_4
| ~ spl0_11 ),
inference(contradiction_clause,[status(thm)],[f216]) ).
fof(f219,plain,
! [X0] :
( ~ product(e_2,X0,e_2)
| equalish(e_2,X0)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f61,f28]) ).
fof(f222,plain,
! [X0] :
( ~ product(X0,e_3,e_2)
| equalish(e_2,X0)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f83,f30]) ).
fof(f225,plain,
! [X0] :
( ~ product(e_3,e_2,X0)
| product(e_2,e_2,X0)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f83,f32]) ).
fof(f228,plain,
( equalish(e_2,e_3)
| ~ spl0_7
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f219,f83]) ).
fof(f229,plain,
( $false
| ~ spl0_7
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f21]) ).
fof(f230,plain,
( ~ spl0_7
| ~ spl0_13 ),
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f233,plain,
( equalish(e_2,e_3)
| ~ spl0_3
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f180,f91]) ).
fof(f234,plain,
( $false
| ~ spl0_3
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f233,f21]) ).
fof(f235,plain,
( ~ spl0_3
| ~ spl0_15 ),
inference(contradiction_clause,[status(thm)],[f234]) ).
fof(f237,plain,
( equalish(e_1,e_2)
| ~ spl0_12
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f80,f206]) ).
fof(f238,plain,
( $false
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f237,f18]) ).
fof(f239,plain,
( ~ spl0_12
| ~ spl0_15 ),
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f240,plain,
! [X0] :
( ~ product(X0,e_3,e_1)
| equalish(e_2,X0)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f80,f30]) ).
fof(f247,plain,
! [X0] :
( ~ product(X0,e_2,e_3)
| equalish(e_1,X0)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f52,f30]) ).
fof(f250,plain,
! [X0] :
( ~ product(e_2,e_3,X0)
| product(e_3,e_1,X0)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f52,f32]) ).
fof(f251,plain,
( product(e_1,e_1,e_3)
| ~ spl0_26
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f131,f209]) ).
fof(f252,plain,
( spl0_2
| ~ spl0_26
| ~ spl0_15 ),
inference(split_clause,[status(thm)],[f251,f40,f130,f90]) ).
fof(f257,plain,
( product(e_1,e_1,e_2)
| ~ spl0_25
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f128,f209]) ).
fof(f262,plain,
! [X0] :
( ~ product(e_3,X0,e_1)
| equalish(e_1,X0)
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f125,f28]) ).
fof(f265,plain,
( equalish(e_2,e_3)
| ~ spl0_9
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f166,f125]) ).
fof(f266,plain,
( $false
| ~ spl0_9
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[status(thm)],[f265,f21]) ).
fof(f267,plain,
( ~ spl0_9
| ~ spl0_24 ),
inference(contradiction_clause,[status(thm)],[f266]) ).
fof(f272,plain,
! [X0] :
( ~ product(e_3,e_2,X0)
| product(e_2,e_1,X0)
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f94,f32]) ).
fof(f276,plain,
! [X0] :
( ~ product(e_2,e_3,X0)
| product(e_3,e_3,X0)
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f120,f32]) ).
fof(f284,plain,
( equalish(e_1,e_2)
| ~ spl0_21
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f114,f262]) ).
fof(f285,plain,
( $false
| ~ spl0_21
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[status(thm)],[f284,f18]) ).
fof(f286,plain,
( ~ spl0_21
| ~ spl0_24 ),
inference(contradiction_clause,[status(thm)],[f285]) ).
fof(f287,plain,
( product(e_3,e_2,e_1)
| ~ spl0_11
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f158,f91]) ).
fof(f288,plain,
( spl0_21
| ~ spl0_11
| ~ spl0_15 ),
inference(split_clause,[status(thm)],[f287,f113,f74,f90]) ).
fof(f291,plain,
! [X0] :
( ~ product(X0,e_1,e_2)
| equalish(e_3,X0)
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f128,f30]) ).
fof(f298,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| product(e_1,e_3,X0)
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f114,f32]) ).
fof(f312,plain,
( product(e_3,e_2,e_3)
| ~ spl0_17
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f97,f158]) ).
fof(f313,plain,
( spl0_23
| ~ spl0_17
| ~ spl0_11 ),
inference(split_clause,[status(thm)],[f312,f119,f96,f74]) ).
fof(f314,plain,
! [X0] :
( ~ product(X0,e_3,e_3)
| equalish(e_2,X0)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f86,f30]) ).
fof(f330,plain,
( product(e_1,e_3,e_1)
| ~ spl0_9
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f69,f298]) ).
fof(f331,plain,
( spl0_15
| ~ spl0_9
| ~ spl0_21 ),
inference(split_clause,[status(thm)],[f330,f90,f68,f113]) ).
fof(f332,plain,
( equalish(e_2,e_1)
| ~ spl0_9
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f69,f196]) ).
fof(f333,plain,
( $false
| ~ spl0_9
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f20]) ).
fof(f334,plain,
( ~ spl0_9
| ~ spl0_6 ),
inference(contradiction_clause,[status(thm)],[f333]) ).
fof(f339,plain,
( product(e_3,e_2,e_2)
| ~ spl0_16
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f94,f158]) ).
fof(f340,plain,
( spl0_22
| ~ spl0_16
| ~ spl0_11 ),
inference(split_clause,[status(thm)],[f339,f116,f93,f74]) ).
fof(f345,plain,
( product(e_2,e_1,e_2)
| ~ spl0_22
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f117,f272]) ).
fof(f346,plain,
( spl0_10
| ~ spl0_22
| ~ spl0_16 ),
inference(split_clause,[status(thm)],[f345,f71,f116,f93]) ).
fof(f366,plain,
( product(e_1,e_2,e_1)
| ~ spl0_0
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f35,f169]) ).
fof(f367,plain,
( spl0_3
| ~ spl0_0
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f366,f45,f34,f68]) ).
fof(f383,plain,
( equalish(e_2,e_1)
| ~ spl0_14
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f314,f97]) ).
fof(f384,plain,
( $false
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f383,f20]) ).
fof(f385,plain,
( ~ spl0_14
| ~ spl0_17 ),
inference(contradiction_clause,[status(thm)],[f384]) ).
fof(f409,plain,
( equalish(e_3,e_1)
| ~ spl0_25
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f291,f257]) ).
fof(f410,plain,
( $false
| ~ spl0_25
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f409,f22]) ).
fof(f411,plain,
( ~ spl0_25
| ~ spl0_15 ),
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f421,plain,
( equalish(e_2,e_3)
| ~ spl0_18
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f103,f240]) ).
fof(f422,plain,
( $false
| ~ spl0_18
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f421,f21]) ).
fof(f423,plain,
( ~ spl0_18
| ~ spl0_12 ),
inference(contradiction_clause,[status(thm)],[f422]) ).
fof(f434,plain,
( product(e_3,e_1,e_1)
| ~ spl0_12
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f80,f250]) ).
fof(f435,plain,
( spl0_24
| ~ spl0_12
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f434,f124,f79,f51]) ).
fof(f436,plain,
( product(e_3,e_3,e_1)
| ~ spl0_12
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f80,f276]) ).
fof(f437,plain,
( spl0_18
| ~ spl0_12
| ~ spl0_23 ),
inference(split_clause,[status(thm)],[f436,f102,f79,f119]) ).
fof(f442,plain,
( product(e_2,e_2,e_3)
| ~ spl0_23
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f120,f225]) ).
fof(f443,plain,
( spl0_8
| ~ spl0_23
| ~ spl0_13 ),
inference(split_clause,[status(thm)],[f442,f63,f119,f82]) ).
fof(f460,plain,
( product(e_2,e_1,e_3)
| ~ spl0_23
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f120,f272]) ).
fof(f461,plain,
( spl0_11
| ~ spl0_23
| ~ spl0_16 ),
inference(split_clause,[status(thm)],[f460,f74,f119,f93]) ).
fof(f465,plain,
( equalish(e_2,e_3)
| ~ spl0_14
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f86,f173]) ).
fof(f466,plain,
( $false
| ~ spl0_14
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f21]) ).
fof(f467,plain,
( ~ spl0_14
| ~ spl0_8 ),
inference(contradiction_clause,[status(thm)],[f466]) ).
fof(f475,plain,
( product(e_2,e_2,e_3)
| ~ spl0_5
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f52,f162]) ).
fof(f482,plain,
( equalish(e_2,e_1)
| ~ spl0_16
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f94,f222]) ).
fof(f483,plain,
( $false
| ~ spl0_16
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f20]) ).
fof(f484,plain,
( ~ spl0_16
| ~ spl0_13 ),
inference(contradiction_clause,[status(thm)],[f483]) ).
fof(f491,plain,
( equalish(e_1,e_2)
| ~ spl0_10
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f475,f247]) ).
fof(f492,plain,
( $false
| ~ spl0_10
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f18]) ).
fof(f493,plain,
( ~ spl0_10
| ~ spl0_5 ),
inference(contradiction_clause,[status(thm)],[f492]) ).
fof(f495,plain,
( product(e_3,e_2,e_2)
| ~ spl0_13
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f83,f175]) ).
fof(f500,plain,
( product(e_2,e_2,e_2)
| ~ spl0_8
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f495,f225]) ).
fof(f501,plain,
( spl0_7
| ~ spl0_8
| ~ spl0_13 ),
inference(split_clause,[status(thm)],[f500,f60,f63,f82]) ).
fof(f519,plain,
( product(e_1,e_1,e_2)
| ~ spl0_3
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f182,f72]) ).
fof(f530,plain,
( equalish(e_2,e_1)
| ~ spl0_3
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f519,f159]) ).
fof(f531,plain,
( $false
| ~ spl0_3
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f530,f20]) ).
fof(f532,plain,
( ~ spl0_3
| ~ spl0_10 ),
inference(contradiction_clause,[status(thm)],[f531]) ).
fof(f533,plain,
$false,
inference(sat_refutation,[status(thm)],[f44,f55,f67,f78,f89,f100,f123,f134,f144,f165,f171,f187,f193,f212,f214,f217,f230,f235,f239,f252,f267,f286,f288,f313,f331,f334,f340,f346,f367,f385,f411,f423,f435,f437,f443,f461,f467,f484,f493,f501,f532]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP129-1.003 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 11:00:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.39 % Elapsed time: 0.050813 seconds
% 0.12/0.39 % CPU time: 0.301097 seconds
% 0.12/0.39 % Memory used: 4.976 MB
%------------------------------------------------------------------------------