%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP127-1.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:32:45 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.53s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 69
% Syntax : Number of formulae : 305 ( 55 unt; 47 def)
% Number of atoms : 689 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 697 ( 313 ~; 337 |; 0 &)
% ( 47 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 51 ( 50 usr; 48 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 81 ( 81 !; 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,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] :
( product(X,Y,e_4)
| product(X,Y,e_3)
| product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
! [Y,X,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f26,plain,
group_element(e_4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f28,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f31,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f32,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f33,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f34,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f35,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f36,plain,
~ equalish(e_4,e_1),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f37,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f38,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f39,plain,
! [X0,X1] :
( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f40,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f47,plain,
! [Y,X,Z2] :
( product(Z2,Y,X)
| ! [Z1] :
( ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f41,f46]) ).
fof(f53,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[f43,f46]) ).
fof(f54,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[f45,f46]) ).
fof(f56,plain,
! [X0] :
( product(e_4,X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f39,f26]) ).
fof(f57,plain,
! [X0] :
( product(e_3,X0,e_4)
| product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f39,f25]) ).
fof(f58,plain,
! [X0] :
( product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f39,f24]) ).
fof(f59,plain,
! [X0] :
( product(e_1,X0,e_4)
| product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f39,f23]) ).
fof(f61,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolution,[status(thm)],[f56,f25]) ).
fof(f62,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[f56,f24]) ).
fof(f63,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(resolution,[status(thm)],[f56,f23]) ).
fof(f77,definition,
( sQ4_spl
<=> product(e_4,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ4_spl
| product(e_4,e_3,e_1) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,definition,
( sQ5_spl
<=> product(e_4,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ5_spl
| product(e_4,e_3,e_2) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,definition,
( sQ6_spl
<=> product(e_4,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ6_spl
| product(e_4,e_3,e_3) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,definition,
( sQ7_spl
<=> product(e_4,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f87,plain,
( ~ sQ7_spl
| product(e_4,e_3,e_4) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,plain,
( sQ7_spl
| sQ6_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f61,f77,f80,f83,f86]) ).
fof(f90,definition,
( sQ8_spl
<=> product(e_4,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ8_spl
| product(e_4,e_2,e_1) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,definition,
( sQ9_spl
<=> product(e_4,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ9_spl
| product(e_4,e_2,e_2) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,definition,
( sQ10_spl
<=> product(e_4,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( ~ sQ10_spl
| product(e_4,e_2,e_3) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,definition,
( sQ11_spl
<=> product(e_4,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ11_spl
| product(e_4,e_2,e_4) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ11_spl
| sQ10_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f62,f90,f93,f96,f99]) ).
fof(f103,definition,
( sQ12_spl
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ12_spl
| product(e_4,e_1,e_1) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,definition,
( sQ13_spl
<=> product(e_4,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ13_spl
| product(e_4,e_1,e_2) ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,definition,
( sQ14_spl
<=> product(e_4,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ14_spl
| product(e_4,e_1,e_3) ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,definition,
( sQ15_spl
<=> product(e_4,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( ~ sQ15_spl
| product(e_4,e_1,e_4) ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,plain,
( sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f63,f103,f106,f109,f112]) ).
fof(f116,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[f57,f26]) ).
fof(f118,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f57,f24]) ).
fof(f119,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f57,f23]) ).
fof(f120,definition,
( sQ16_spl
<=> product(e_3,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f121,plain,
( ~ sQ16_spl
| product(e_3,e_4,e_1) ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,definition,
( sQ17_spl
<=> product(e_3,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( ~ sQ17_spl
| product(e_3,e_4,e_2) ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,definition,
( sQ18_spl
<=> product(e_3,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( ~ sQ18_spl
| product(e_3,e_4,e_3) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,definition,
( sQ19_spl
<=> product(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ19_spl
| product(e_3,e_4,e_4) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f116,f120,f123,f126,f129]) ).
fof(f142,definition,
( sQ23_spl
<=> product(e_3,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( ~ sQ23_spl
| product(e_3,e_3,e_4) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f146,definition,
( sQ24_spl
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( ~ sQ24_spl
| product(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,definition,
( sQ25_spl
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ25_spl
| product(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,definition,
( sQ26_spl
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ26_spl
| product(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,definition,
( sQ27_spl
<=> product(e_3,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ27_spl
| product(e_3,e_2,e_4) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( sQ27_spl
| sQ26_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f118,f146,f149,f152,f155]) ).
fof(f159,definition,
( sQ28_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ28_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,definition,
( sQ29_spl
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( ~ sQ29_spl
| product(e_3,e_1,e_2) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,definition,
( sQ30_spl
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ30_spl
| product(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,definition,
( sQ31_spl
<=> product(e_3,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( ~ sQ31_spl
| product(e_3,e_1,e_4) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( sQ31_spl
| sQ30_spl
| sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f119,f159,f162,f165,f168]) ).
fof(f172,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[f58,f26]) ).
fof(f173,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f58,f25]) ).
fof(f175,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f58,f23]) ).
fof(f176,definition,
( sQ32_spl
<=> product(e_2,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( ~ sQ32_spl
| product(e_2,e_4,e_1) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,definition,
( sQ33_spl
<=> product(e_2,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ33_spl
| product(e_2,e_4,e_2) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,definition,
( sQ34_spl
<=> product(e_2,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( ~ sQ34_spl
| product(e_2,e_4,e_3) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,definition,
( sQ35_spl
<=> product(e_2,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ35_spl
| product(e_2,e_4,e_4) ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( sQ35_spl
| sQ34_spl
| sQ33_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f172,f176,f179,f182,f185]) ).
fof(f189,definition,
( sQ36_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ36_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,definition,
( sQ37_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ37_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,definition,
( sQ38_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( ~ sQ38_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,definition,
( sQ39_spl
<=> product(e_2,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( ~ sQ39_spl
| product(e_2,e_3,e_4) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,plain,
( sQ39_spl
| sQ38_spl
| sQ37_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f173,f189,f192,f195,f198]) ).
fof(f208,definition,
( sQ42_spl
<=> product(e_2,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( ~ sQ42_spl
| product(e_2,e_2,e_3) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
( sQ43_spl
<=> product(e_2,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( ~ sQ43_spl
| product(e_2,e_2,e_4) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f215,definition,
( sQ44_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( ~ sQ44_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,definition,
( sQ45_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f219,plain,
( ~ sQ45_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,definition,
( sQ46_spl
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( ~ sQ46_spl
| product(e_2,e_1,e_3) ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,definition,
( sQ47_spl
<=> product(e_2,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( ~ sQ47_spl
| product(e_2,e_1,e_4) ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,plain,
( sQ47_spl
| sQ46_spl
| sQ45_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f175,f215,f218,f221,f224]) ).
fof(f230,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f59,f24]) ).
fof(f231,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f59,f23]) ).
fof(f258,definition,
( sQ56_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( ~ sQ56_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,definition,
( sQ57_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( ~ sQ57_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f264,definition,
( sQ58_spl
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( ~ sQ58_spl
| product(e_1,e_2,e_3) ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f267,definition,
( sQ59_spl
<=> product(e_1,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( ~ sQ59_spl
| product(e_1,e_2,e_4) ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,plain,
( sQ59_spl
| sQ58_spl
| sQ57_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f230,f258,f261,f264,f267]) ).
fof(f271,definition,
( sQ60_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f274,definition,
( sQ61_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( ~ sQ61_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,definition,
( sQ62_spl
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( ~ sQ62_spl
| product(e_1,e_1,e_3) ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,definition,
( sQ63_spl
<=> product(e_1,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( ~ sQ63_spl
| product(e_1,e_1,e_4) ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f283,plain,
( sQ63_spl
| sQ62_spl
| sQ61_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f231,f271,f274,f277,f280]) ).
fof(f285,plain,
( ~ sQ15_spl
| equalish(e_1,e_4) ),
inference(resolution,[status(thm)],[f113,f53]) ).
fof(f291,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f285,f29]) ).
fof(f292,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f291]) ).
fof(f293,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_4)
| ~ product(X0,e_1,e_3) ),
inference(resolution,[status(thm)],[f110,f45]) ).
fof(f295,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_3)
| ~ product(e_4,e_1,X0) ),
inference(resolution,[status(thm)],[f110,f41]) ).
fof(f296,plain,
! [X0] :
( ~ sQ14_spl
| product(e_3,e_1,X0)
| ~ product(e_1,X0,e_4) ),
inference(resolution,[status(thm)],[f110,f48]) ).
fof(f300,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f107,f295]) ).
fof(f301,plain,
! [X0] :
( ~ sQ13_spl
| equalish(X0,e_4)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f107,f45]) ).
fof(f302,plain,
! [X0] :
( ~ sQ13_spl
| equalish(X0,e_1)
| ~ product(e_4,X0,e_2) ),
inference(resolution,[status(thm)],[f107,f43]) ).
fof(f305,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f300,f31]) ).
fof(f306,plain,
( ~ sQ14_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f305]) ).
fof(f307,plain,
( ~ sQ12_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f104,f54]) ).
fof(f312,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f307,f36]) ).
fof(f313,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f312]) ).
fof(f314,plain,
( ~ sQ11_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f100,f53]) ).
fof(f320,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f314,f32]) ).
fof(f321,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f320]) ).
fof(f325,plain,
! [X0] :
( ~ sQ10_spl
| product(e_3,e_2,X0)
| ~ product(e_2,X0,e_4) ),
inference(resolution,[status(thm)],[f97,f48]) ).
fof(f331,plain,
( ~ sQ9_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f94,f54]) ).
fof(f339,plain,
! [X0] :
( ~ sQ8_spl
| equalish(X0,e_2)
| ~ product(e_4,X0,e_1) ),
inference(resolution,[status(thm)],[f91,f43]) ).
fof(f345,plain,
( ~ sQ7_spl
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[f87,f53]) ).
fof(f351,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f345,f35]) ).
fof(f352,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f351]) ).
fof(f353,plain,
( ~ sQ6_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f84,f54]) ).
fof(f358,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f353,f38]) ).
fof(f359,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f358]) ).
fof(f360,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f81,f302]) ).
fof(f361,plain,
! [X0] :
( ~ sQ5_spl
| equalish(X0,e_4)
| ~ product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f81,f45]) ).
fof(f365,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f360,f33]) ).
fof(f366,plain,
( ~ sQ13_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f365]) ).
fof(f367,plain,
( ~ sQ8_spl
| ~ sQ4_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f78,f339]) ).
fof(f368,plain,
! [X0] :
( ~ sQ4_spl
| equalish(X0,e_4)
| ~ product(X0,e_3,e_1) ),
inference(resolution,[status(thm)],[f78,f45]) ).
fof(f371,plain,
! [X0] :
( ~ sQ4_spl
| product(e_1,e_3,X0)
| ~ product(e_3,X0,e_4) ),
inference(resolution,[status(thm)],[f78,f48]) ).
fof(f372,plain,
( ~ sQ8_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f367,f34]) ).
fof(f373,plain,
( ~ sQ8_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f372]) ).
fof(f379,plain,
( ~ sQ4_spl
| ~ sQ31_spl
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f169,f371]) ).
fof(f383,plain,
! [X0] :
( ~ sQ31_spl
| product(e_4,e_1,X0)
| ~ product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f169,f48]) ).
fof(f384,plain,
( ~ sQ4_spl
| ~ sQ31_spl
| equalish(e_1,e_4) ),
inference(resolution,[status(thm)],[f379,f368]) ).
fof(f391,plain,
( ~ sQ4_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f384,f29]) ).
fof(f392,plain,
( ~ sQ4_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f391]) ).
fof(f393,plain,
( ~ sQ30_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f166,f53]) ).
fof(f399,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f393,f28]) ).
fof(f400,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f399]) ).
fof(f401,plain,
( ~ sQ13_spl
| ~ sQ29_spl
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[f163,f301]) ).
fof(f403,plain,
! [X0] :
( ~ sQ29_spl
| equalish(X0,e_1)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f163,f43]) ).
fof(f406,plain,
( ~ sQ13_spl
| ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f401,f35]) ).
fof(f407,plain,
( ~ sQ13_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f406]) ).
fof(f408,plain,
( ~ sQ28_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f160,f54]) ).
fof(f413,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f408,f33]) ).
fof(f414,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f415,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f331,f37]) ).
fof(f416,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f415]) ).
fof(f421,plain,
! [X0] :
( ~ sQ27_spl
| product(e_4,e_2,X0)
| ~ product(e_2,X0,e_3) ),
inference(resolution,[status(thm)],[f156,f48]) ).
fof(f434,plain,
( ~ sQ26_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f153,f53]) ).
fof(f442,plain,
( ~ sQ29_spl
| ~ sQ25_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f150,f403]) ).
fof(f448,plain,
( ~ sQ29_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f30]) ).
fof(f449,plain,
( ~ sQ29_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f448]) ).
fof(f451,plain,
! [X0] :
( ~ sQ24_spl
| equalish(X0,e_2)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f147,f43]) ).
fof(f459,plain,
( ~ sQ23_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f143,f51]) ).
fof(f462,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f459,f38]) ).
fof(f463,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f462]) ).
fof(f482,plain,
( ~ sQ19_spl
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[f130,f54]) ).
fof(f487,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f35]) ).
fof(f488,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f487]) ).
fof(f489,plain,
( ~ sQ18_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f127,f53]) ).
fof(f495,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f489,f38]) ).
fof(f496,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f495]) ).
fof(f497,plain,
( ~ sQ29_spl
| ~ sQ17_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f124,f403]) ).
fof(f502,plain,
( ~ sQ29_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f497,f36]) ).
fof(f503,plain,
( ~ sQ29_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f504,plain,
( ~ sQ24_spl
| ~ sQ16_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f121,f451]) ).
fof(f509,plain,
( ~ sQ24_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f37]) ).
fof(f510,plain,
( ~ sQ24_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f513,plain,
( ~ sQ10_spl
| ~ sQ47_spl
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f225,f325]) ).
fof(f514,plain,
! [X0] :
( ~ sQ47_spl
| equalish(X0,e_2)
| ~ product(X0,e_1,e_4) ),
inference(resolution,[status(thm)],[f225,f45]) ).
fof(f515,plain,
! [X0] :
( ~ sQ47_spl
| equalish(X0,e_1)
| ~ product(e_2,X0,e_4) ),
inference(resolution,[status(thm)],[f225,f43]) ).
fof(f518,plain,
( ~ sQ10_spl
| ~ sQ47_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f513,f146,f224,f96]) ).
fof(f519,plain,
( ~ sQ14_spl
| ~ sQ46_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f222,f293]) ).
fof(f524,plain,
( ~ sQ14_spl
| ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f32]) ).
fof(f525,plain,
( ~ sQ14_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f524]) ).
fof(f540,plain,
( ~ sQ45_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f219,f53]) ).
fof(f546,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f540,f27]) ).
fof(f547,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f548,plain,
( ~ sQ44_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f216,f54]) ).
fof(f553,plain,
( ~ sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f548,f30]) ).
fof(f554,plain,
~ sQ44_spl,
inference(contradiction_clause,[status(thm)],[f553]) ).
fof(f555,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f434,f31]) ).
fof(f556,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f555]) ).
fof(f557,plain,
( ~ sQ47_spl
| ~ sQ43_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f212,f515]) ).
fof(f565,plain,
( ~ sQ47_spl
| ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f557,f30]) ).
fof(f566,plain,
( ~ sQ47_spl
| ~ sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f565]) ).
fof(f570,plain,
( ~ sQ42_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f209,f51]) ).
fof(f574,plain,
( ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f570,f34]) ).
fof(f575,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f574]) ).
fof(f584,plain,
( ~ sQ47_spl
| ~ sQ39_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f199,f515]) ).
fof(f590,plain,
( ~ sQ47_spl
| ~ sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f584,f33]) ).
fof(f591,plain,
( ~ sQ47_spl
| ~ sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f590]) ).
fof(f593,plain,
( ~ sQ38_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f196,f54]) ).
fof(f599,plain,
( ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f593,f31]) ).
fof(f600,plain,
~ sQ38_spl,
inference(contradiction_clause,[status(thm)],[f599]) ).
fof(f601,plain,
( ~ sQ5_spl
| ~ sQ37_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f193,f361]) ).
fof(f608,plain,
( ~ sQ5_spl
| ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f601,f32]) ).
fof(f609,plain,
( ~ sQ5_spl
| ~ sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f608]) ).
fof(f611,plain,
! [X0] :
( ~ sQ36_spl
| equalish(X0,e_3)
| ~ product(e_2,X0,e_1) ),
inference(resolution,[status(thm)],[f190,f43]) ).
fof(f617,plain,
( ~ sQ47_spl
| ~ sQ35_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f186,f515]) ).
fof(f624,plain,
( ~ sQ47_spl
| ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f617,f36]) ).
fof(f625,plain,
( ~ sQ47_spl
| ~ sQ35_spl ),
inference(contradiction_clause,[status(thm)],[f624]) ).
fof(f626,plain,
( ~ sQ27_spl
| ~ sQ34_spl
| product(e_4,e_2,e_4) ),
inference(resolution,[status(thm)],[f183,f421]) ).
fof(f631,plain,
( ~ sQ27_spl
| ~ sQ34_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f626,f99,f182,f155]) ).
fof(f632,plain,
( ~ sQ33_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f180,f53]) ).
fof(f638,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f632,f37]) ).
fof(f639,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f638]) ).
fof(f640,plain,
( ~ sQ36_spl
| ~ sQ32_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f177,f611]) ).
fof(f646,plain,
( ~ sQ36_spl
| ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f640,f38]) ).
fof(f647,plain,
( ~ sQ36_spl
| ~ sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f646]) ).
fof(f649,plain,
( ~ sQ47_spl
| ~ sQ63_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f281,f514]) ).
fof(f656,plain,
( ~ sQ47_spl
| ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f649,f27]) ).
fof(f657,plain,
( ~ sQ47_spl
| ~ sQ63_spl ),
inference(contradiction_clause,[status(thm)],[f656]) ).
fof(f659,plain,
( ~ sQ14_spl
| ~ sQ62_spl
| equalish(e_1,e_4) ),
inference(resolution,[status(thm)],[f278,f293]) ).
fof(f666,plain,
( ~ sQ14_spl
| ~ sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f659,f29]) ).
fof(f667,plain,
( ~ sQ14_spl
| ~ sQ62_spl ),
inference(contradiction_clause,[status(thm)],[f666]) ).
fof(f671,plain,
( ~ sQ61_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f275,f51]) ).
fof(f675,plain,
( ~ sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f671,f30]) ).
fof(f676,plain,
~ sQ61_spl,
inference(contradiction_clause,[status(thm)],[f675]) ).
fof(f677,plain,
( ~ sQ14_spl
| ~ sQ59_spl
| product(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[f268,f296]) ).
fof(f682,plain,
( ~ sQ14_spl
| ~ sQ59_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f677,f162,f267,f109]) ).
fof(f683,plain,
( ~ sQ31_spl
| ~ sQ58_spl
| product(e_4,e_1,e_2) ),
inference(resolution,[status(thm)],[f265,f383]) ).
fof(f689,plain,
( ~ sQ31_spl
| ~ sQ58_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f683,f106,f264,f168]) ).
fof(f693,plain,
( ~ sQ57_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f262,f54]) ).
fof(f699,plain,
( ~ sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f693,f27]) ).
fof(f700,plain,
~ sQ57_spl,
inference(contradiction_clause,[status(thm)],[f699]) ).
fof(f702,plain,
( ~ sQ56_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f259,f53]) ).
fof(f710,plain,
( ~ sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f702,f30]) ).
fof(f711,plain,
~ sQ56_spl,
inference(contradiction_clause,[status(thm)],[f710]) ).
fof(f712,plain,
$false,
inference(sat_refutation,[status(thm)],[f89,f102,f115,f132,f158,f171,f188,f201,f227,f270,f283,f292,f306,f313,f321,f352,f359,f366,f373,f392,f400,f407,f414,f416,f449,f463,f488,f496,f503,f510,f518,f525,f547,f554,f556,f566,f575,f591,f600,f609,f625,f631,f639,f647,f657,f667,f676,f682,f689,f700,f711]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP127-1.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 19:55:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.53 % Refutation found
% 0.10/0.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.92/0.55 % Elapsed time: 0.180036 seconds
% 0.92/0.55 % CPU time: 1.151464 seconds
% 0.92/0.55 % Total memory used: 22.824 MB
% 0.92/0.55 % Net memory used: 21.877 MB
%------------------------------------------------------------------------------