TSTP Solution File: GRP134-1.003 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP134-1.003 : 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 20:19:29 EDT 2024
% Result : Unsatisfiable 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 41
% Syntax : Number of formulae : 306 ( 19 unt; 0 def)
% Number of atoms : 851 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1053 ( 508 ~; 518 |; 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 : 99 ( 99 !; 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,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2)
| product(Z1,Z2,Y) ),
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(X,Y,Z1)
| ~ product(Y,X,Z2) )
| product(Z1,Z2,Y) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X1,X0,X3)
| product(X2,X3,X1) ),
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(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(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(f132,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(f135,plain,
! [X0] :
( ~ product(X0,e_1,e_3)
| equalish(e_3,X0)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f65,f30]) ).
fof(f138,plain,
! [X0] :
( ~ product(e_1,e_3,X0)
| product(e_3,X0,e_1)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f65,f32]) ).
fof(f142,plain,
! [X0] :
( ~ product(e_1,e_3,X0)
| product(e_2,X0,e_1)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f62,f32]) ).
fof(f146,plain,
! [X0] :
( ~ product(e_1,e_3,X0)
| product(e_1,X0,e_1)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f59,f32]) ).
fof(f150,plain,
! [X0] :
( ~ product(e_2,e_3,X0)
| product(e_3,X0,e_2)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f54,f32]) ).
fof(f154,plain,
! [X0] :
( ~ product(e_2,e_3,X0)
| product(e_2,X0,e_2)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f51,f32]) ).
fof(f158,plain,
! [X0] :
( ~ product(e_2,e_3,X0)
| product(e_1,X0,e_2)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f48,f32]) ).
fof(f167,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| product(e_3,X0,e_1)
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f98,f32]) ).
fof(f171,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| product(e_2,X0,e_1)
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f95,f32]) ).
fof(f175,plain,
! [X0] :
( ~ product(e_1,e_2,X0)
| product(e_1,X0,e_1)
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f92,f32]) ).
fof(f179,plain,
! [X0] :
( ~ product(e_2,e_2,X0)
| product(e_3,X0,e_2)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f87,f32]) ).
fof(f180,plain,
( product(e_3,e_3,e_2)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f179,f87]) ).
fof(f180_001,plain,
( product(e_3,e_3,e_2)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f179,f87]) ).
fof(f182,plain,
! [X0] :
( ~ product(e_3,X0,e_2)
| equalish(e_3,X0)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f180,f28]) ).
fof(f187,plain,
( equalish(e_3,e_2)
| ~ spl0_14
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f182,f51]) ).
fof(f188,plain,
( $false
| ~ spl0_14
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f187,f23]) ).
fof(f189,plain,
( ~ spl0_14
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f188]) ).
fof(f191,plain,
! [X0] :
( ~ product(e_2,X0,e_2)
| equalish(e_2,X0)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f84,f28]) ).
fof(f192,plain,
! [X0] :
( ~ product(e_2,e_2,X0)
| equalish(e_2,X0)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f84,f26]) ).
fof(f193,plain,
! [X0] :
( ~ product(e_2,e_2,X0)
| product(e_2,X0,e_2)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f84,f32]) ).
fof(f198,plain,
! [X0] :
( ~ product(e_2,e_2,X0)
| product(e_1,X0,e_2)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f81,f32]) ).
fof(f199,plain,
( product(e_3,e_3,e_2)
| ~ spl0_11
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f76,f150]) ).
fof(f205,plain,
! [X0] :
( ~ product(X0,e_3,e_2)
| equalish(e_3,X0)
| ~ spl0_11
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f199,f30]) ).
fof(f206,plain,
! [X0] :
( ~ product(e_3,X0,e_2)
| equalish(e_3,X0)
| ~ spl0_11
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f199,f28]) ).
fof(f211,plain,
( equalish(e_3,e_1)
| ~ spl0_11
| ~ spl0_5
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f206,f62]) ).
fof(f212,plain,
( $false
| ~ spl0_11
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f211,f22]) ).
fof(f213,plain,
( ~ spl0_11
| ~ spl0_5
| ~ spl0_7 ),
inference(contradiction_clause,[status(thm)],[f212]) ).
fof(f217,plain,
! [X0] :
( ~ product(e_3,e_2,X0)
| product(e_2,X0,e_3)
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f73,f32]) ).
fof(f221,plain,
! [X0] :
( ~ product(e_3,e_2,X0)
| product(e_1,X0,e_3)
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f70,f32]) ).
fof(f225,plain,
! [X0] :
( ~ product(e_1,e_1,X0)
| product(e_3,X0,e_1)
| ~ spl0_26 ),
inference(resolution,[status(thm)],[f131,f32]) ).
fof(f233,plain,
! [X0] :
( ~ product(e_1,e_1,X0)
| product(e_1,X0,e_1)
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f125,f32]) ).
fof(f237,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| product(e_3,X0,e_2)
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f120,f32]) ).
fof(f245,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| product(e_1,X0,e_2)
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f114,f32]) ).
fof(f249,plain,
! [X0] :
( ~ product(e_3,e_1,X0)
| product(e_3,X0,e_3)
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f109,f32]) ).
fof(f253,plain,
! [X0] :
( ~ product(e_3,e_1,X0)
| product(e_2,X0,e_3)
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f106,f32]) ).
fof(f254,plain,
! [X0] :
( ~ product(X0,e_3,e_1)
| equalish(e_1,X0)
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f103,f30]) ).
fof(f257,plain,
! [X0] :
( ~ product(e_3,e_1,X0)
| product(e_1,X0,e_3)
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f103,f32]) ).
fof(f262,plain,
! [X0] :
( ~ product(e_3,e_3,X0)
| product(e_2,X0,e_3)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f40,f32]) ).
fof(f266,plain,
! [X0] :
( ~ product(e_3,e_3,X0)
| product(e_1,X0,e_3)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f37,f32]) ).
fof(f277,plain,
( equalish(e_3,e_1)
| ~ spl0_8
| ~ spl0_26 ),
inference(resolution,[status(thm)],[f135,f131]) ).
fof(f278,plain,
( $false
| ~ spl0_8
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f277,f22]) ).
fof(f279,plain,
( ~ spl0_8
| ~ spl0_26 ),
inference(contradiction_clause,[status(thm)],[f278]) ).
fof(f280,plain,
( product(e_1,e_1,e_3)
| ~ spl0_9
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f221,f48]) ).
fof(f280_002,plain,
( product(e_1,e_1,e_3)
| ~ spl0_9
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f221,f48]) ).
fof(f281,plain,
! [X0] :
( ~ product(X0,e_1,e_3)
| equalish(e_1,X0)
| ~ spl0_9
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f280,f30]) ).
fof(f286,plain,
( equalish(e_1,e_2)
| ~ spl0_9
| ~ spl0_3
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f281,f98]) ).
fof(f287,plain,
( $false
| ~ spl0_9
| ~ spl0_3
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f286,f18]) ).
fof(f288,plain,
( ~ spl0_9
| ~ spl0_3
| ~ spl0_17 ),
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f289,plain,
( product(e_2,e_3,e_1)
| ~ spl0_23
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f120,f171]) ).
fof(f290,plain,
( spl0_9
| ~ spl0_23
| ~ spl0_16 ),
inference(split_clause,[status(thm)],[f289,f69,f119,f94]) ).
fof(f291,plain,
( product(e_2,e_1,e_2)
| ~ spl0_12
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f81,f193]) ).
fof(f292,plain,
! [X0] :
( ~ product(X0,e_1,e_2)
| equalish(e_2,X0)
| ~ spl0_12
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f291,f30]) ).
fof(f296,plain,
( equalish(e_2,e_1)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f292,f128]) ).
fof(f297,plain,
( $false
| ~ spl0_12
| ~ spl0_13
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[status(thm)],[f296,f20]) ).
fof(f298,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_25 ),
inference(contradiction_clause,[status(thm)],[f297]) ).
fof(f299,plain,
( product(e_1,e_1,e_2)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f198,f81]) ).
fof(f302,plain,
! [X0] :
( ~ product(e_1,X0,e_2)
| equalish(e_1,X0)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f299,f28]) ).
fof(f303,plain,
! [X0] :
( ~ product(e_1,e_1,X0)
| equalish(e_2,X0)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f299,f26]) ).
fof(f306,plain,
( equalish(e_1,e_3)
| ~ spl0_12
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f302,f106]) ).
fof(f307,plain,
( $false
| ~ spl0_12
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f19]) ).
fof(f308,plain,
( ~ spl0_12
| ~ spl0_19 ),
inference(contradiction_clause,[status(thm)],[f307]) ).
fof(f317,plain,
( product(e_1,e_1,e_2)
| ~ spl0_21
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f245,f92]) ).
fof(f318,plain,
( product(e_3,e_1,e_3)
| ~ spl0_20
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f249,f59]) ).
fof(f319,plain,
( spl0_8
| ~ spl0_20
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f318,f64,f108,f58]) ).
fof(f324,plain,
( product(e_1,e_2,e_1)
| ~ spl0_22
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f117,f175]) ).
fof(f325,plain,
( spl0_21
| ~ spl0_22
| ~ spl0_15 ),
inference(split_clause,[status(thm)],[f324,f113,f116,f91]) ).
fof(f326,plain,
( product(e_2,e_1,e_1)
| ~ spl0_21
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f114,f171]) ).
fof(f327,plain,
( spl0_15
| ~ spl0_21
| ~ spl0_16 ),
inference(split_clause,[status(thm)],[f326,f91,f113,f94]) ).
fof(f330,plain,
! [X0] :
( ~ product(e_1,e_1,X0)
| equalish(e_2,X0)
| ~ spl0_21
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f317,f26]) ).
fof(f340,plain,
( equalish(e_2,e_1)
| ~ spl0_21
| ~ spl0_15
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f330,f125]) ).
fof(f341,plain,
( $false
| ~ spl0_21
| ~ spl0_15
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[status(thm)],[f340,f20]) ).
fof(f342,plain,
( ~ spl0_21
| ~ spl0_15
| ~ spl0_24 ),
inference(contradiction_clause,[status(thm)],[f341]) ).
fof(f343,plain,
( product(e_2,e_2,e_1)
| ~ spl0_22
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f117,f171]) ).
fof(f344,plain,
( spl0_12
| ~ spl0_22
| ~ spl0_16 ),
inference(split_clause,[status(thm)],[f343,f80,f116,f94]) ).
fof(f345,plain,
( product(e_1,e_1,e_1)
| ~ spl0_18
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f103,f146]) ).
fof(f346,plain,
( spl0_24
| ~ spl0_18
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f345,f124,f102,f58]) ).
fof(f347,plain,
( product(e_1,e_1,e_1)
| ~ spl0_21
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f114,f175]) ).
fof(f348,plain,
( spl0_24
| ~ spl0_21
| ~ spl0_15 ),
inference(split_clause,[status(thm)],[f347,f124,f113,f91]) ).
fof(f349,plain,
( product(e_1,e_3,e_2)
| ~ spl0_11
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f76,f158]) ).
fof(f353,plain,
! [X0] :
( ~ product(e_1,e_3,X0)
| equalish(e_2,X0)
| ~ spl0_11
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f349,f26]) ).
fof(f358,plain,
( equalish(e_2,e_1)
| ~ spl0_11
| ~ spl0_3
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f353,f103]) ).
fof(f359,plain,
( $false
| ~ spl0_11
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f358,f20]) ).
fof(f360,plain,
( ~ spl0_11
| ~ spl0_3
| ~ spl0_18 ),
inference(contradiction_clause,[status(thm)],[f359]) ).
fof(f361,plain,
( product(e_1,e_1,e_3)
| ~ spl0_18
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f257,f59]) ).
fof(f364,plain,
! [X0] :
( ~ product(e_1,e_1,X0)
| equalish(e_3,X0)
| ~ spl0_18
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f361,f26]) ).
fof(f370,plain,
( product(e_2,e_3,e_2)
| ~ spl0_4
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f154,f76]) ).
fof(f373,plain,
! [X0] :
( ~ product(e_2,e_3,X0)
| equalish(e_2,X0)
| ~ spl0_4
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f370,f26]) ).
fof(f377,plain,
( equalish(e_2,e_3)
| ~ spl0_4
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f373,f76]) ).
fof(f378,plain,
( $false
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f377,f21]) ).
fof(f379,plain,
( ~ spl0_4
| ~ spl0_11 ),
inference(contradiction_clause,[status(thm)],[f378]) ).
fof(f380,plain,
( product(e_1,e_1,e_3)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f266,f37]) ).
fof(f410,plain,
( equalish(e_1,e_2)
| ~ spl0_12
| ~ spl0_22 ),
inference(resolution,[status(thm)],[f302,f117]) ).
fof(f411,plain,
( $false
| ~ spl0_12
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[status(thm)],[f410,f18]) ).
fof(f412,plain,
( ~ spl0_12
| ~ spl0_22 ),
inference(contradiction_clause,[status(thm)],[f411]) ).
fof(f413,plain,
( $false
| ~ spl0_0
| spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f380]) ).
fof(f414,plain,
( ~ spl0_0
| spl0_26 ),
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f415,plain,
( product(e_1,e_2,e_1)
| ~ spl0_19
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f106,f146]) ).
fof(f416,plain,
( spl0_21
| ~ spl0_19
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f415,f113,f105,f58]) ).
fof(f417,plain,
( product(e_3,e_2,e_1)
| ~ spl0_22
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f117,f167]) ).
fof(f418,plain,
( spl0_3
| ~ spl0_22
| ~ spl0_17 ),
inference(split_clause,[status(thm)],[f417,f47,f116,f97]) ).
fof(f422,plain,
( equalish(e_3,e_1)
| ~ spl0_18
| ~ spl0_6
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f364,f125]) ).
fof(f423,plain,
( $false
| ~ spl0_18
| ~ spl0_6
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[status(thm)],[f422,f22]) ).
fof(f424,plain,
( ~ spl0_18
| ~ spl0_6
| ~ spl0_24 ),
inference(contradiction_clause,[status(thm)],[f423]) ).
fof(f427,plain,
! [X0] :
( ~ product(e_1,X0,e_3)
| equalish(e_1,X0)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f380,f28]) ).
fof(f428,plain,
! [X0] :
( ~ product(X0,e_1,e_3)
| equalish(e_1,X0)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f380,f30]) ).
fof(f452,plain,
( product(e_1,e_2,e_3)
| ~ spl0_4
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f51,f221]) ).
fof(f457,plain,
( product(e_3,e_3,e_1)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f452,f167]) ).
fof(f458,plain,
( spl0_0
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17 ),
inference(split_clause,[status(thm)],[f457,f36,f50,f69,f97]) ).
fof(f469,plain,
( product(e_3,e_3,e_1)
| ~ spl0_26 ),
inference(resolution,[status(thm)],[f131,f225]) ).
fof(f470,plain,
( spl0_0
| ~ spl0_26 ),
inference(split_clause,[status(thm)],[f469,f36,f130]) ).
fof(f486,plain,
( equalish(e_3,e_1)
| ~ spl0_11
| ~ spl0_5
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f205,f106]) ).
fof(f487,plain,
( $false
| ~ spl0_11
| ~ spl0_5
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f22]) ).
fof(f488,plain,
( ~ spl0_11
| ~ spl0_5
| ~ spl0_19 ),
inference(contradiction_clause,[status(thm)],[f487]) ).
fof(f489,plain,
( equalish(e_3,e_2)
| ~ spl0_8
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f135,f98]) ).
fof(f490,plain,
( $false
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f489,f23]) ).
fof(f491,plain,
( ~ spl0_8
| ~ spl0_17 ),
inference(contradiction_clause,[status(thm)],[f490]) ).
fof(f492,plain,
( product(e_3,e_1,e_1)
| ~ spl0_18
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f103,f138]) ).
fof(f493,plain,
( spl0_6
| ~ spl0_18
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f492,f58,f102,f64]) ).
fof(f495,plain,
( spl0_26
| ~ spl0_9
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f280,f130,f69,f47]) ).
fof(f502,plain,
( product(e_2,e_2,e_3)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f40,f262]) ).
fof(f527,plain,
( product(e_1,e_3,e_3)
| ~ spl0_5
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f54,f221]) ).
fof(f533,plain,
! [X0] :
( ~ product(X0,e_2,e_3)
| equalish(e_2,X0)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f502,f30]) ).
fof(f539,plain,
( equalish(e_2,e_3)
| ~ spl0_13
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f192,f502]) ).
fof(f540,plain,
( $false
| ~ spl0_13
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f21]) ).
fof(f541,plain,
( ~ spl0_13
| ~ spl0_1 ),
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f543,plain,
( product(e_3,e_1,e_1)
| ~ spl0_21
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f114,f167]) ).
fof(f544,plain,
( spl0_6
| ~ spl0_21
| ~ spl0_17 ),
inference(split_clause,[status(thm)],[f543,f58,f113,f97]) ).
fof(f545,plain,
( product(e_1,e_3,e_2)
| ~ spl0_17
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f98,f245]) ).
fof(f546,plain,
( spl0_19
| ~ spl0_17
| ~ spl0_21 ),
inference(split_clause,[status(thm)],[f545,f105,f97,f113]) ).
fof(f553,plain,
( product(e_2,e_1,e_1)
| ~ spl0_18
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f103,f142]) ).
fof(f554,plain,
( spl0_15
| ~ spl0_18
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f553,f91,f102,f61]) ).
fof(f557,plain,
( product(e_1,e_2,e_2)
| ~ spl0_10
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f73,f158]) ).
fof(f558,plain,
( spl0_22
| ~ spl0_10
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f557,f116,f72,f47]) ).
fof(f560,plain,
( product(e_1,e_2,e_3)
| ~ spl0_7
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f62,f257]) ).
fof(f561,plain,
( product(e_3,e_1,e_2)
| ~ spl0_15
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f92,f237]) ).
fof(f562,plain,
( spl0_7
| ~ spl0_15
| ~ spl0_23 ),
inference(split_clause,[status(thm)],[f561,f61,f91,f119]) ).
fof(f563,plain,
( product(e_3,e_1,e_2)
| ~ spl0_9
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f70,f150]) ).
fof(f564,plain,
( spl0_7
| ~ spl0_9
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f563,f61,f69,f53]) ).
fof(f565,plain,
( product(e_1,e_3,e_1)
| ~ spl0_20
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f109,f146]) ).
fof(f566,plain,
( spl0_18
| ~ spl0_20
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f565,f102,f108,f58]) ).
fof(f567,plain,
( product(e_1,e_3,e_1)
| ~ spl0_23
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f120,f175]) ).
fof(f568,plain,
( spl0_18
| ~ spl0_23
| ~ spl0_15 ),
inference(split_clause,[status(thm)],[f567,f102,f119,f91]) ).
fof(f571,plain,
( product(e_3,e_3,e_1)
| ~ spl0_20
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f109,f138]) ).
fof(f572,plain,
( spl0_0
| ~ spl0_20
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f571,f36,f108,f64]) ).
fof(f573,plain,
( product(e_1,e_2,e_1)
| ~ spl0_12
| ~ spl0_24 ),
inference(resolution,[status(thm)],[f299,f233]) ).
fof(f574,plain,
( spl0_21
| ~ spl0_12
| ~ spl0_24 ),
inference(split_clause,[status(thm)],[f573,f113,f80,f124]) ).
fof(f583,plain,
( equalish(e_2,e_3)
| ~ spl0_12
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f303,f380]) ).
fof(f584,plain,
( $false
| ~ spl0_12
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f583,f21]) ).
fof(f585,plain,
( ~ spl0_12
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f584]) ).
fof(f587,plain,
( product(e_1,e_2,e_1)
| ~ spl0_19
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f106,f146]) ).
fof(f588,plain,
( product(e_2,e_1,e_3)
| ~ spl0_6
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f59,f253]) ).
fof(f589,plain,
( equalish(e_1,e_2)
| ~ spl0_0
| ~ spl0_6
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f428,f588]) ).
fof(f590,plain,
( $false
| ~ spl0_0
| ~ spl0_6
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f589,f18]) ).
fof(f591,plain,
( ~ spl0_0
| ~ spl0_6
| ~ spl0_19 ),
inference(contradiction_clause,[status(thm)],[f590]) ).
fof(f597,plain,
( equalish(e_1,e_3)
| ~ spl0_0
| ~ spl0_5
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f427,f527]) ).
fof(f598,plain,
( $false
| ~ spl0_0
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f597,f19]) ).
fof(f599,plain,
( ~ spl0_0
| ~ spl0_5
| ~ spl0_9 ),
inference(contradiction_clause,[status(thm)],[f598]) ).
fof(f600,plain,
( equalish(e_1,e_2)
| ~ spl0_0
| ~ spl0_7
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f427,f560]) ).
fof(f601,plain,
( $false
| ~ spl0_0
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f600,f18]) ).
fof(f602,plain,
( ~ spl0_0
| ~ spl0_7
| ~ spl0_18 ),
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f631,plain,
( product(e_2,e_2,e_3)
| ~ spl0_4
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f51,f217]) ).
fof(f632,plain,
( spl0_14
| ~ spl0_4
| ~ spl0_10 ),
inference(split_clause,[status(thm)],[f631,f86,f50,f72]) ).
fof(f637,plain,
( product(e_3,e_2,e_2)
| ~ spl0_5
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f150,f73]) ).
fof(f638,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_10 ),
inference(split_clause,[status(thm)],[f637,f50,f53,f72]) ).
fof(f648,plain,
( product(e_2,e_1,e_2)
| ~ spl0_9
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f70,f154]) ).
fof(f654,plain,
! [X0] :
( ~ product(X0,e_1,e_2)
| equalish(e_2,X0)
| ~ spl0_9
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f648,f30]) ).
fof(f658,plain,
( equalish(e_2,e_3)
| ~ spl0_9
| ~ spl0_4
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f654,f62]) ).
fof(f659,plain,
( $false
| ~ spl0_9
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f658,f21]) ).
fof(f660,plain,
( ~ spl0_9
| ~ spl0_4
| ~ spl0_7 ),
inference(contradiction_clause,[status(thm)],[f659]) ).
fof(f674,plain,
( equalish(e_1,e_2)
| ~ spl0_18
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f254,f70]) ).
fof(f675,plain,
( $false
| ~ spl0_18
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f674,f18]) ).
fof(f676,plain,
( ~ spl0_18
| ~ spl0_9 ),
inference(contradiction_clause,[status(thm)],[f675]) ).
fof(f677,plain,
( product(e_2,e_2,e_1)
| ~ spl0_19
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f106,f142]) ).
fof(f678,plain,
( spl0_12
| ~ spl0_19
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f677,f80,f105,f61]) ).
fof(f680,plain,
( product(e_2,e_3,e_1)
| ~ spl0_20
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f109,f142]) ).
fof(f681,plain,
( spl0_9
| ~ spl0_20
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f680,f69,f108,f61]) ).
fof(f688,plain,
( equalish(e_2,e_1)
| ~ spl0_16
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f95,f191]) ).
fof(f689,plain,
( $false
| ~ spl0_16
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f688,f20]) ).
fof(f690,plain,
( ~ spl0_16
| ~ spl0_13 ),
inference(contradiction_clause,[status(thm)],[f689]) ).
fof(f708,plain,
( equalish(e_2,e_1)
| ~ spl0_1
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f533,f120]) ).
fof(f709,plain,
( $false
| ~ spl0_1
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[status(thm)],[f708,f20]) ).
fof(f710,plain,
( ~ spl0_1
| ~ spl0_23 ),
inference(contradiction_clause,[status(thm)],[f709]) ).
fof(f711,plain,
( spl0_1
| ~ spl0_14 ),
inference(split_clause,[status(thm)],[f180,f39,f86]) ).
fof(f712,plain,
( equalish(e_3,e_1)
| ~ spl0_14
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f182,f62]) ).
fof(f713,plain,
( $false
| ~ spl0_14
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f712,f22]) ).
fof(f714,plain,
( ~ spl0_14
| ~ spl0_7 ),
inference(contradiction_clause,[status(thm)],[f713]) ).
fof(f715,plain,
( product(e_3,e_2,e_2)
| ~ spl0_23
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f237,f95]) ).
fof(f716,plain,
( spl0_4
| ~ spl0_23
| ~ spl0_16 ),
inference(split_clause,[status(thm)],[f715,f50,f119,f94]) ).
fof(f717,plain,
( product(e_3,e_3,e_1)
| ~ spl0_23
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f120,f167]) ).
fof(f718,plain,
( spl0_0
| ~ spl0_23
| ~ spl0_17 ),
inference(split_clause,[status(thm)],[f717,f36,f119,f97]) ).
fof(f721,plain,
! [X0] :
( ~ product(e_1,X0,e_1)
| equalish(e_2,X0)
| ~ spl0_19
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f587,f28]) ).
fof(f722,plain,
! [X0] :
( ~ product(X0,e_2,e_1)
| equalish(e_1,X0)
| ~ spl0_19
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f587,f30]) ).
fof(f741,plain,
( equalish(e_2,e_1)
| ~ spl0_24
| ~ spl0_19
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f125,f721]) ).
fof(f742,plain,
( $false
| ~ spl0_24
| ~ spl0_19
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f741,f20]) ).
fof(f743,plain,
( ~ spl0_24
| ~ spl0_19
| ~ spl0_6 ),
inference(contradiction_clause,[status(thm)],[f742]) ).
fof(f749,plain,
( equalish(e_1,e_3)
| ~ spl0_3
| ~ spl0_19
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f48,f722]) ).
fof(f750,plain,
( $false
| ~ spl0_3
| ~ spl0_19
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f749,f19]) ).
fof(f751,plain,
( ~ spl0_3
| ~ spl0_19
| ~ spl0_6 ),
inference(contradiction_clause,[status(thm)],[f750]) ).
fof(f752,plain,
$false,
inference(sat_refutation,[status(thm)],[f46,f57,f68,f79,f90,f101,f112,f123,f134,f189,f213,f279,f288,f290,f298,f308,f319,f325,f327,f342,f344,f346,f348,f360,f379,f412,f414,f416,f418,f424,f458,f470,f488,f491,f493,f495,f541,f544,f546,f554,f558,f562,f564,f566,f568,f572,f574,f585,f591,f599,f602,f632,f638,f660,f676,f678,f681,f690,f710,f711,f714,f716,f718,f743,f751]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP134-1.003 : TPTP v8.1.2. Released v1.2.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 30 00:08:17 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % Drodi V3.6.0
% 0.18/0.52 % Refutation found
% 0.18/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.54 % Elapsed time: 0.199491 seconds
% 0.18/0.54 % CPU time: 1.390000 seconds
% 0.18/0.54 % Total memory used: 14.959 MB
% 0.18/0.54 % Net memory used: 13.397 MB
%------------------------------------------------------------------------------