TSTP Solution File: GRP129-1.003 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% 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 : 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 : Tue Apr 30 20:19:26 EDT 2024
% Result : Unsatisfiable 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 41
% Syntax : Number of formulae : 243 ( 19 unt; 0 def)
% Number of atoms : 656 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 774 ( 361 ~; 386 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 31 ( 30 usr; 28 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 87 ( 87 !; 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,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/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/sandbox2/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_3,X0,e_1)
| product(e_3,X0,e_2)
| product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f24,f17]) ).
fof(f34,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)],[f24,f16]) ).
fof(f35,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)],[f24,f15]) ).
fof(f36,plain,
( spl0_0
<=> product(e_3,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f37,plain,
( product(e_3,e_3,e_1)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,plain,
( spl0_1
<=> product(e_3,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f40,plain,
( product(e_3,e_3,e_2)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,plain,
( spl0_2
<=> product(e_3,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f43,plain,
( product(e_3,e_3,e_3)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,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)],[f33,f17]) ).
fof(f46,plain,
( spl0_0
| spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f45,f36,f39,f42]) ).
fof(f47,plain,
( spl0_3
<=> product(e_3,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f48,plain,
( product(e_3,e_2,e_1)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( spl0_4
<=> product(e_3,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f51,plain,
( product(e_3,e_2,e_2)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( spl0_5
<=> product(e_3,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f54,plain,
( product(e_3,e_2,e_3)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,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)],[f33,f16]) ).
fof(f57,plain,
( spl0_3
| spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f56,f47,f50,f53]) ).
fof(f58,plain,
( spl0_6
<=> product(e_3,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f59,plain,
( product(e_3,e_1,e_1)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,plain,
( spl0_7
<=> product(e_3,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f62,plain,
( product(e_3,e_1,e_2)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( spl0_8
<=> product(e_3,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f65,plain,
( product(e_3,e_1,e_3)
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,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)],[f33,f15]) ).
fof(f68,plain,
( spl0_6
| spl0_7
| spl0_8 ),
inference(split_clause,[status(thm)],[f67,f58,f61,f64]) ).
fof(f69,plain,
( spl0_9
<=> product(e_2,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f70,plain,
( product(e_2,e_3,e_1)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( spl0_10
<=> product(e_2,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f73,plain,
( product(e_2,e_3,e_2)
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,plain,
( spl0_11
<=> product(e_2,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f76,plain,
( product(e_2,e_3,e_3)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,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)],[f34,f17]) ).
fof(f79,plain,
( spl0_9
| spl0_10
| spl0_11 ),
inference(split_clause,[status(thm)],[f78,f69,f72,f75]) ).
fof(f80,plain,
( spl0_12
<=> product(e_2,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f81,plain,
( product(e_2,e_2,e_1)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,plain,
( spl0_13
<=> product(e_2,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f84,plain,
( product(e_2,e_2,e_2)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( spl0_14
<=> product(e_2,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f87,plain,
( product(e_2,e_2,e_3)
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,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)],[f34,f16]) ).
fof(f90,plain,
( spl0_12
| spl0_13
| spl0_14 ),
inference(split_clause,[status(thm)],[f89,f80,f83,f86]) ).
fof(f91,plain,
( spl0_15
<=> product(e_2,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f92,plain,
( product(e_2,e_1,e_1)
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( spl0_16
<=> product(e_2,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f95,plain,
( product(e_2,e_1,e_2)
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f96,plain,
( ~ product(e_2,e_1,e_2)
| spl0_16 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,plain,
( spl0_17
<=> product(e_2,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f98,plain,
( product(e_2,e_1,e_3)
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,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)],[f34,f15]) ).
fof(f101,plain,
( spl0_15
| spl0_16
| spl0_17 ),
inference(split_clause,[status(thm)],[f100,f91,f94,f97]) ).
fof(f102,plain,
( spl0_18
<=> product(e_1,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f103,plain,
( product(e_1,e_3,e_1)
| ~ spl0_18 ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,plain,
( spl0_19
<=> product(e_1,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f106,plain,
( product(e_1,e_3,e_2)
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( spl0_20
<=> product(e_1,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f109,plain,
( product(e_1,e_3,e_3)
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,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)],[f35,f17]) ).
fof(f112,plain,
( spl0_18
| spl0_19
| spl0_20 ),
inference(split_clause,[status(thm)],[f111,f102,f105,f108]) ).
fof(f113,plain,
( spl0_21
<=> product(e_1,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f114,plain,
( product(e_1,e_2,e_1)
| ~ spl0_21 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( spl0_22
<=> product(e_1,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f117,plain,
( product(e_1,e_2,e_2)
| ~ spl0_22 ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( spl0_23
<=> product(e_1,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f120,plain,
( product(e_1,e_2,e_3)
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,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)],[f35,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_1,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f125,plain,
( product(e_1,e_1,e_1)
| ~ spl0_24 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( spl0_25
<=> product(e_1,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f128,plain,
( product(e_1,e_1,e_2)
| ~ spl0_25 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( spl0_26
<=> product(e_1,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f131,plain,
( product(e_1,e_1,e_3)
| ~ spl0_26 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,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)],[f35,f15]) ).
fof(f134,plain,
( spl0_24
| spl0_25
| spl0_26 ),
inference(split_clause,[status(thm)],[f133,f124,f127,f130]) ).
fof(f138,plain,
! [X0] :
( ~ product(e_1,e_3,X0)
| product(e_3,e_3,X0)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f65,f32]) ).
fof(f142,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| product(e_2,e_3,X0)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f62,f32]) ).
fof(f146,plain,
! [X0] :
( ~ product(e_1,e_1,X0)
| product(e_1,e_3,X0)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f59,f32]) ).
fof(f150,plain,
! [X0] :
( ~ product(e_2,e_3,X0)
| product(e_3,e_3,X0)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f54,f32]) ).
fof(f154,plain,
! [X0] :
( ~ product(e_2,e_2,X0)
| product(e_2,e_3,X0)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f51,f32]) ).
fof(f158,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| product(e_1,e_3,X0)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f48,f32]) ).
fof(f165,plain,
! [X0] :
( ~ product(e_1,e_3,X0)
| product(e_3,e_2,X0)
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f98,f32]) ).
fof(f169,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| product(e_2,e_2,X0)
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f95,f32]) ).
fof(f173,plain,
! [X0] :
( ~ product(e_1,e_1,X0)
| product(e_1,e_2,X0)
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f92,f32]) ).
fof(f177,plain,
! [X0] :
( ~ product(e_2,e_3,X0)
| product(e_3,e_2,X0)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f87,f32]) ).
fof(f184,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| product(e_1,e_2,X0)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f81,f32]) ).
fof(f188,plain,
! [X0] :
( ~ product(e_3,e_3,X0)
| product(e_3,e_2,X0)
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f76,f32]) ).
fof(f189,plain,
( product(e_3,e_3,e_2)
| ~ spl0_10
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f73,f150]) ).
fof(f193,plain,
! [X0] :
( ~ product(e_3,e_2,X0)
| product(e_2,e_2,X0)
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f73,f32]) ).
fof(f194,plain,
! [X0] :
( ~ product(X0,e_3,e_2)
| equalish(e_3,X0)
| ~ spl0_10
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f189,f30]) ).
fof(f198,plain,
( equalish(e_3,e_2)
| ~ spl0_5
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f194,f73]) ).
fof(f199,plain,
( $false
| ~ spl0_5
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f23]) ).
fof(f200,plain,
( ~ spl0_5
| ~ spl0_10 ),
inference(contradiction_clause,[status(thm)],[f199]) ).
fof(f201,plain,
( product(e_3,e_2,e_3)
| ~ spl0_11
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f188,f43]) ).
fof(f202,plain,
( spl0_5
| ~ spl0_11
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f201,f53,f75,f42]) ).
fof(f203,plain,
( product(e_3,e_2,e_3)
| ~ spl0_11
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f76,f177]) ).
fof(f204,plain,
( spl0_5
| ~ spl0_11
| ~ spl0_14 ),
inference(split_clause,[status(thm)],[f203,f53,f75,f86]) ).
fof(f205,plain,
( product(e_2,e_3,e_2)
| ~ spl0_13
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f84,f154]) ).
fof(f207,plain,
! [X0] :
( ~ product(e_2,X0,e_2)
| equalish(e_3,X0)
| ~ spl0_13
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f205,f28]) ).
fof(f212,plain,
( equalish(e_3,e_2)
| ~ spl0_4
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f207,f84]) ).
fof(f213,plain,
( $false
| ~ spl0_4
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f212,f23]) ).
fof(f214,plain,
( ~ spl0_4
| ~ spl0_13 ),
inference(contradiction_clause,[status(thm)],[f213]) ).
fof(f215,plain,
( product(e_3,e_3,e_3)
| ~ spl0_11
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f76,f150]) ).
fof(f217,plain,
! [X0] :
( ~ product(e_3,X0,e_3)
| equalish(e_3,X0)
| ~ spl0_11
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f215,f28]) ).
fof(f221,plain,
( product(e_3,e_3,e_1)
| ~ spl0_9
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f70,f150]) ).
fof(f221_001,plain,
( product(e_3,e_3,e_1)
| ~ spl0_9
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f70,f150]) ).
fof(f225,plain,
! [X0] :
( ~ product(e_3,e_1,X0)
| product(e_1,e_2,X0)
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f70,f32]) ).
fof(f229,plain,
! [X0] :
( ~ product(e_1,e_3,X0)
| product(e_3,e_1,X0)
| ~ spl0_26 ),
inference(resolution,[status(thm)],[f131,f32]) ).
fof(f233,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| product(e_2,e_1,X0)
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f128,f32]) ).
fof(f241,plain,
! [X0] :
( ~ product(e_2,e_3,X0)
| product(e_3,e_1,X0)
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f120,f32]) ).
fof(f242,plain,
( product(e_2,e_2,e_2)
| ~ spl0_22
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f117,f169]) ).
fof(f242_002,plain,
( product(e_2,e_2,e_2)
| ~ spl0_22
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f117,f169]) ).
fof(f243,plain,
( product(e_2,e_3,e_2)
| ~ spl0_22
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f117,f142]) ).
fof(f244,plain,
( spl0_10
| ~ spl0_22
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f243,f72,f116,f61]) ).
fof(f249,plain,
( product(e_1,e_2,e_2)
| ~ spl0_25
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f128,f173]) ).
fof(f250,plain,
( spl0_22
| ~ spl0_25
| ~ spl0_15 ),
inference(split_clause,[status(thm)],[f249,f116,f127,f91]) ).
fof(f251,plain,
( product(e_1,e_2,e_2)
| ~ spl0_12
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f184,f95]) ).
fof(f252,plain,
( spl0_22
| ~ spl0_12
| ~ spl0_16 ),
inference(split_clause,[status(thm)],[f251,f116,f80,f94]) ).
fof(f264,plain,
( product(e_3,e_3,e_3)
| ~ spl0_20
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f109,f138]) ).
fof(f265,plain,
( product(e_3,e_2,e_3)
| ~ spl0_20
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f109,f165]) ).
fof(f266,plain,
( spl0_5
| ~ spl0_20
| ~ spl0_17 ),
inference(split_clause,[status(thm)],[f265,f53,f108,f97]) ).
fof(f267,plain,
( product(e_1,e_3,e_3)
| ~ spl0_26
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f131,f146]) ).
fof(f268,plain,
( spl0_20
| ~ spl0_26
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f267,f108,f130,f58]) ).
fof(f269,plain,
( product(e_1,e_3,e_3)
| ~ spl0_17
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f98,f158]) ).
fof(f270,plain,
( spl0_20
| ~ spl0_17
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f269,f108,f97,f47]) ).
fof(f274,plain,
! [X0] :
( ~ product(e_3,e_2,X0)
| product(e_2,e_1,X0)
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f106,f32]) ).
fof(f278,plain,
! [X0] :
( ~ product(e_3,e_1,X0)
| product(e_1,e_1,X0)
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f103,f32]) ).
fof(f282,plain,
! [X0] :
( ~ product(e_3,e_2,X0)
| product(e_2,e_3,X0)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f40,f32]) ).
fof(f286,plain,
! [X0] :
( ~ product(e_3,e_1,X0)
| product(e_1,e_3,X0)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f37,f32]) ).
fof(f299,plain,
( equalish(e_3,e_2)
| ~ spl0_11
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f217,f54]) ).
fof(f300,plain,
( $false
| ~ spl0_11
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f299,f23]) ).
fof(f301,plain,
( ~ spl0_11
| ~ spl0_5 ),
inference(contradiction_clause,[status(thm)],[f300]) ).
fof(f303,plain,
! [X0] :
( ~ product(e_3,X0,e_3)
| equalish(e_3,X0)
| ~ spl0_20
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f264,f28]) ).
fof(f310,plain,
( equalish(e_3,e_1)
| ~ spl0_20
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f303,f65]) ).
fof(f311,plain,
( $false
| ~ spl0_20
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f22]) ).
fof(f312,plain,
( ~ spl0_20
| ~ spl0_8 ),
inference(contradiction_clause,[status(thm)],[f311]) ).
fof(f313,plain,
( product(e_2,e_1,e_3)
| ~ spl0_25
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f233,f120]) ).
fof(f314,plain,
( spl0_17
| ~ spl0_25
| ~ spl0_23 ),
inference(split_clause,[status(thm)],[f313,f97,f127,f119]) ).
fof(f319,plain,
( product(e_2,e_1,e_2)
| ~ spl0_22
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f117,f233]) ).
fof(f327,plain,
! [X0] :
( ~ product(e_2,X0,e_2)
| equalish(e_1,X0)
| ~ spl0_22
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f319,f28]) ).
fof(f336,plain,
( product(e_2,e_1,e_1)
| ~ spl0_25
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f233,f114]) ).
fof(f337,plain,
( spl0_15
| ~ spl0_25
| ~ spl0_21 ),
inference(split_clause,[status(thm)],[f336,f91,f127,f113]) ).
fof(f338,plain,
( equalish(e_1,e_2)
| ~ spl0_16
| ~ spl0_22
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f242,f327]) ).
fof(f339,plain,
( $false
| ~ spl0_16
| ~ spl0_22
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[status(thm)],[f338,f18]) ).
fof(f340,plain,
( ~ spl0_16
| ~ spl0_22
| ~ spl0_25 ),
inference(contradiction_clause,[status(thm)],[f339]) ).
fof(f341,plain,
( $false
| ~ spl0_22
| ~ spl0_25
| spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f96,f319]) ).
fof(f342,plain,
( ~ spl0_22
| ~ spl0_25
| spl0_16 ),
inference(contradiction_clause,[status(thm)],[f341]) ).
fof(f345,plain,
( product(e_3,e_2,e_1)
| ~ spl0_17
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f165,f103]) ).
fof(f346,plain,
( spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(split_clause,[status(thm)],[f345,f47,f97,f102]) ).
fof(f347,plain,
( product(e_1,e_3,e_1)
| ~ spl0_6
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f146,f125]) ).
fof(f348,plain,
( spl0_18
| ~ spl0_6
| ~ spl0_24 ),
inference(split_clause,[status(thm)],[f347,f102,f58,f124]) ).
fof(f351,plain,
( product(e_3,e_1,e_1)
| ~ spl0_23
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f241,f70]) ).
fof(f352,plain,
( spl0_6
| ~ spl0_23
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f351,f58,f119,f69]) ).
fof(f353,plain,
( product(e_1,e_2,e_1)
| ~ spl0_15
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f173,f125]) ).
fof(f368,plain,
( product(e_2,e_2,e_1)
| ~ spl0_3
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f48,f193]) ).
fof(f373,plain,
! [X0] :
( ~ product(X0,e_2,e_1)
| equalish(e_2,X0)
| ~ spl0_3
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f368,f30]) ).
fof(f383,plain,
! [X0] :
( ~ product(e_1,X0,e_1)
| equalish(e_2,X0)
| ~ spl0_15
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f353,f28]) ).
fof(f393,plain,
( product(e_2,e_2,e_2)
| ~ spl0_4
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f51,f193]) ).
fof(f394,plain,
( spl0_13
| ~ spl0_4
| ~ spl0_10 ),
inference(split_clause,[status(thm)],[f393,f83,f50,f72]) ).
fof(f395,plain,
( product(e_2,e_1,e_2)
| ~ spl0_4
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f51,f274]) ).
fof(f403,plain,
( product(e_1,e_3,e_3)
| ~ spl0_8
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f65,f286]) ).
fof(f404,plain,
( spl0_20
| ~ spl0_8
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f403,f108,f64,f36]) ).
fof(f442,plain,
! [X0] :
( ~ product(X0,e_3,e_1)
| equalish(e_3,X0)
| ~ spl0_9
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f221,f30]) ).
fof(f449,plain,
( equalish(e_3,e_1)
| ~ spl0_9
| ~ spl0_5
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f442,f103]) ).
fof(f450,plain,
( $false
| ~ spl0_9
| ~ spl0_5
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f449,f22]) ).
fof(f451,plain,
( ~ spl0_9
| ~ spl0_5
| ~ spl0_18 ),
inference(contradiction_clause,[status(thm)],[f450]) ).
fof(f452,plain,
( product(e_2,e_1,e_1)
| ~ spl0_3
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f48,f274]) ).
fof(f453,plain,
( spl0_15
| ~ spl0_3
| ~ spl0_19 ),
inference(split_clause,[status(thm)],[f452,f91,f47,f105]) ).
fof(f455,plain,
( equalish(e_2,e_3)
| ~ spl0_10
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f373,f48]) ).
fof(f456,plain,
( $false
| ~ spl0_10
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f455,f21]) ).
fof(f457,plain,
( ~ spl0_10
| ~ spl0_3 ),
inference(contradiction_clause,[status(thm)],[f456]) ).
fof(f458,plain,
( product(e_1,e_2,e_3)
| ~ spl0_9
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f225,f65]) ).
fof(f459,plain,
( spl0_23
| ~ spl0_9
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f458,f119,f69,f64]) ).
fof(f460,plain,
( product(e_2,e_3,e_2)
| ~ spl0_4
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f51,f282]) ).
fof(f461,plain,
( spl0_10
| ~ spl0_4
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f460,f72,f50,f39]) ).
fof(f466,plain,
( product(e_1,e_2,e_1)
| ~ spl0_15
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f92,f184]) ).
fof(f469,plain,
( product(e_1,e_3,e_1)
| ~ spl0_6
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f59,f286]) ).
fof(f469_003,plain,
( product(e_1,e_3,e_1)
| ~ spl0_6
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f59,f286]) ).
fof(f472,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| equalish(e_1,X0)
| ~ spl0_15
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f466,f26]) ).
fof(f474,plain,
! [X0] :
( ~ product(X0,e_3,e_1)
| equalish(e_1,X0)
| ~ spl0_6
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f469,f30]) ).
fof(f482,plain,
( product(e_2,e_3,e_3)
| ~ spl0_14
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f87,f154]) ).
fof(f483,plain,
( spl0_11
| ~ spl0_14
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f482,f75,f86,f50]) ).
fof(f492,plain,
( equalish(e_1,e_2)
| ~ spl0_9
| ~ spl0_6
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f70,f474]) ).
fof(f493,plain,
( $false
| ~ spl0_9
| ~ spl0_6
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f492,f18]) ).
fof(f494,plain,
( ~ spl0_9
| ~ spl0_6
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f493]) ).
fof(f496,plain,
( product(e_1,e_3,e_1)
| ~ spl0_15
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f92,f158]) ).
fof(f497,plain,
( spl0_18
| ~ spl0_15
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f496,f102,f91,f47]) ).
fof(f500,plain,
( spl0_18
| ~ spl0_6
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f469,f102,f58,f36]) ).
fof(f503,plain,
( spl0_16
| ~ spl0_4
| ~ spl0_19 ),
inference(split_clause,[status(thm)],[f395,f94,f50,f105]) ).
fof(f510,plain,
( product(e_1,e_3,e_2)
| ~ spl0_16
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f95,f158]) ).
fof(f511,plain,
( spl0_19
| ~ spl0_16
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f510,f105,f94,f47]) ).
fof(f512,plain,
! [X0] :
( ~ product(e_3,e_1,X0)
| product(e_1,e_2,X0)
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f70,f32]) ).
fof(f516,plain,
( product(e_1,e_1,e_1)
| ~ spl0_6
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f59,f278]) ).
fof(f517,plain,
( spl0_24
| ~ spl0_6
| ~ spl0_18 ),
inference(split_clause,[status(thm)],[f516,f124,f58,f102]) ).
fof(f537,plain,
( product(e_3,e_1,e_1)
| ~ spl0_18
| ~ spl0_26 ),
inference(resolution,[status(thm)],[f103,f229]) ).
fof(f538,plain,
( spl0_6
| ~ spl0_18
| ~ spl0_26 ),
inference(split_clause,[status(thm)],[f537,f58,f102,f130]) ).
fof(f543,plain,
( equalish(e_2,e_1)
| ~ spl0_15
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f383,f125]) ).
fof(f544,plain,
( $false
| ~ spl0_15
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[status(thm)],[f543,f20]) ).
fof(f545,plain,
( ~ spl0_15
| ~ spl0_24 ),
inference(contradiction_clause,[status(thm)],[f544]) ).
fof(f548,plain,
( product(e_3,e_2,e_1)
| ~ spl0_9
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f70,f177]) ).
fof(f549,plain,
( spl0_3
| ~ spl0_9
| ~ spl0_14 ),
inference(split_clause,[status(thm)],[f548,f47,f69,f86]) ).
fof(f562,plain,
( product(e_1,e_2,e_2)
| ~ spl0_9
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f512,f62]) ).
fof(f563,plain,
( spl0_22
| ~ spl0_9
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f562,f116,f69,f61]) ).
fof(f564,plain,
( spl0_0
| ~ spl0_9
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f221,f36,f69,f53]) ).
fof(f569,plain,
( product(e_1,e_2,e_3)
| ~ spl0_26
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f131,f173]) ).
fof(f574,plain,
( equalish(e_1,e_3)
| ~ spl0_12
| ~ spl0_26
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f472,f569]) ).
fof(f575,plain,
( $false
| ~ spl0_12
| ~ spl0_26
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f574,f19]) ).
fof(f576,plain,
( ~ spl0_12
| ~ spl0_26
| ~ spl0_15 ),
inference(contradiction_clause,[status(thm)],[f575]) ).
fof(f577,plain,
( spl0_13
| ~ spl0_22
| ~ spl0_16 ),
inference(split_clause,[status(thm)],[f242,f83,f116,f94]) ).
fof(f578,plain,
$false,
inference(sat_refutation,[status(thm)],[f46,f57,f68,f79,f90,f101,f112,f123,f134,f200,f202,f204,f214,f244,f250,f252,f266,f268,f270,f301,f312,f314,f337,f340,f342,f346,f348,f352,f394,f404,f451,f453,f457,f459,f461,f483,f494,f497,f500,f503,f511,f517,f538,f545,f549,f563,f564,f576,f577]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP129-1.003 : TPTP v8.1.2. Released v1.2.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 Apr 30 00:22:32 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 0.19/0.47 % Refutation found
% 0.19/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.48 % Elapsed time: 0.132913 seconds
% 0.19/0.48 % CPU time: 0.991788 seconds
% 0.19/0.48 % Total memory used: 14.146 MB
% 0.19/0.48 % Net memory used: 12.848 MB
%------------------------------------------------------------------------------