%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP126-1.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 12:32:44 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.62s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 66
% Syntax : Number of formulae : 290 ( 61 unt; 44 def)
% Number of atoms : 634 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 637 ( 293 ~; 300 |; 0 &)
% ( 44 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 48 ( 47 usr; 45 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 76 ( 76 !; 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,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,Y)
| ~ product(Y,X,Z2)
| ~ product(X,Y,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,Z1,Z2] :
( product(Z1,Z2,Y)
| ! [X] :
( ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X1)
| ~ product(X1,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(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(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(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(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(f136,definition,
( sQ21_spl
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ21_spl
| product(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f136]) ).
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(f174,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f58,f24]) ).
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(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(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(f202,definition,
( sQ40_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( ~ sQ40_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
( sQ41_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
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(f214,plain,
( sQ43_spl
| sQ42_spl
| sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f174,f202,f205,f208,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(f228,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(resolution,[status(thm)],[f59,f26]) ).
fof(f229,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f59,f25]) ).
fof(f232,definition,
( sQ48_spl
<=> product(e_1,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( ~ sQ48_spl
| product(e_1,e_4,e_1) ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,definition,
( sQ49_spl
<=> product(e_1,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f236,plain,
( ~ sQ49_spl
| product(e_1,e_4,e_2) ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,definition,
( sQ50_spl
<=> product(e_1,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( ~ sQ50_spl
| product(e_1,e_4,e_3) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,definition,
( sQ51_spl
<=> product(e_1,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f242,plain,
( ~ sQ51_spl
| product(e_1,e_4,e_4) ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,plain,
( sQ51_spl
| sQ50_spl
| sQ49_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f228,f232,f235,f238,f241]) ).
fof(f245,definition,
( sQ52_spl
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( ~ sQ52_spl
| product(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,definition,
( sQ53_spl
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f249,plain,
( ~ sQ53_spl
| product(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,definition,
( sQ54_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f252,plain,
( ~ sQ54_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,definition,
( sQ55_spl
<=> product(e_1,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( ~ sQ55_spl
| product(e_1,e_3,e_4) ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,plain,
( sQ55_spl
| sQ54_spl
| sQ53_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f229,f245,f248,f251,f254]) ).
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(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(f285,plain,
( ~ sQ15_spl
| equalish(e_1,e_4) ),
inference(resolution,[status(thm)],[f113,f53]) ).
fof(f290,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f285,f29]) ).
fof(f291,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f290]) ).
fof(f295,plain,
! [X0] :
( ~ sQ14_spl
| product(X0,e_3,e_4)
| ~ product(e_1,e_4,X0) ),
inference(resolution,[status(thm)],[f110,f48]) ).
fof(f301,plain,
! [X0] :
( ~ sQ13_spl
| equalish(X0,e_1)
| ~ product(e_4,X0,e_2) ),
inference(resolution,[status(thm)],[f107,f43]) ).
fof(f306,plain,
( ~ sQ12_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f104,f54]) ).
fof(f311,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f36]) ).
fof(f312,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f311]) ).
fof(f313,plain,
( ~ sQ11_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f100,f53]) ).
fof(f318,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f313,f32]) ).
fof(f319,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f318]) ).
fof(f329,plain,
( ~ sQ9_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f94,f54]) ).
fof(f343,plain,
( ~ sQ7_spl
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[f87,f53]) ).
fof(f348,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f343,f35]) ).
fof(f349,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f348]) ).
fof(f350,plain,
( ~ sQ6_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f84,f54]) ).
fof(f355,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f350,f38]) ).
fof(f356,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f355]) ).
fof(f357,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f81,f301]) ).
fof(f362,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f357,f33]) ).
fof(f363,plain,
( ~ sQ13_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f362]) ).
fof(f368,plain,
! [X0] :
( ~ sQ4_spl
| product(X0,e_1,e_4)
| ~ product(e_3,e_4,X0) ),
inference(resolution,[status(thm)],[f78,f48]) ).
fof(f376,plain,
! [X0] :
( ~ sQ31_spl
| equalish(X0,e_3)
| ~ product(X0,e_1,e_4) ),
inference(resolution,[status(thm)],[f169,f45]) ).
fof(f377,plain,
! [X0] :
( ~ sQ31_spl
| equalish(X0,e_1)
| ~ product(e_3,X0,e_4) ),
inference(resolution,[status(thm)],[f169,f43]) ).
fof(f384,plain,
( ~ sQ30_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f166,f53]) ).
fof(f393,plain,
! [X0] :
( ~ sQ29_spl
| equalish(X0,e_1)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f163,f43]) ).
fof(f395,plain,
! [X0] :
( ~ sQ29_spl
| product(X0,e_2,e_3)
| ~ product(e_1,e_3,X0) ),
inference(resolution,[status(thm)],[f163,f48]) ).
fof(f398,plain,
( ~ sQ28_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f160,f54]) ).
fof(f403,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f398,f33]) ).
fof(f404,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f403]) ).
fof(f405,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f384,f28]) ).
fof(f406,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f405]) ).
fof(f407,plain,
( ~ sQ31_spl
| ~ sQ27_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f156,f377]) ).
fof(f412,plain,
( ~ sQ31_spl
| ~ sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f407,f30]) ).
fof(f413,plain,
( ~ sQ31_spl
| ~ sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f412]) ).
fof(f415,plain,
( ~ sQ26_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f153,f53]) ).
fof(f422,plain,
( ~ sQ25_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f150,f54]) ).
fof(f427,plain,
( ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f422,f34]) ).
fof(f428,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f427]) ).
fof(f430,plain,
! [X0] :
( ~ sQ24_spl
| equalish(X0,e_2)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f147,f43]) ).
fof(f439,plain,
( ~ sQ23_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f143,f51]) ).
fof(f447,plain,
( ~ sQ21_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f137,f51]) ).
fof(f451,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f447,f31]) ).
fof(f452,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f451]) ).
fof(f463,plain,
( ~ sQ4_spl
| ~ sQ19_spl
| product(e_4,e_1,e_4) ),
inference(resolution,[status(thm)],[f130,f368]) ).
fof(f464,plain,
( ~ sQ31_spl
| ~ sQ19_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f130,f377]) ).
fof(f470,plain,
( ~ sQ4_spl
| ~ sQ19_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f463,f112,f129,f77]) ).
fof(f471,plain,
( ~ sQ31_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f464,f36]) ).
fof(f472,plain,
( ~ sQ31_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f471]) ).
fof(f474,plain,
( ~ sQ18_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f127,f53]) ).
fof(f479,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f474,f38]) ).
fof(f480,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f479]) ).
fof(f481,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| product(e_2,e_1,e_4) ),
inference(resolution,[status(thm)],[f124,f368]) ).
fof(f482,plain,
! [X0] :
( ~ sQ17_spl
| equalish(X0,e_3)
| ~ product(X0,e_4,e_2) ),
inference(resolution,[status(thm)],[f124,f45]) ).
fof(f485,plain,
! [X0] :
( ~ sQ17_spl
| product(X0,e_2,e_3)
| ~ product(e_4,e_3,X0) ),
inference(resolution,[status(thm)],[f124,f48]) ).
fof(f486,plain,
( ~ sQ31_spl
| ~ sQ4_spl
| ~ sQ17_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f481,f376]) ).
fof(f490,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ17_spl
| product(X0,e_4,e_2)
| ~ product(e_1,e_2,X0) ),
inference(resolution,[status(thm)],[f481,f48]) ).
fof(f491,plain,
( ~ sQ31_spl
| ~ sQ4_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f31]) ).
fof(f492,plain,
( ~ sQ31_spl
| ~ sQ4_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f491]) ).
fof(f493,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| product(e_1,e_1,e_4) ),
inference(resolution,[status(thm)],[f121,f368]) ).
fof(f494,plain,
( ~ sQ24_spl
| ~ sQ16_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f121,f430]) ).
fof(f499,plain,
( ~ sQ24_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f494,f37]) ).
fof(f500,plain,
( ~ sQ24_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f499]) ).
fof(f501,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f329,f37]) ).
fof(f502,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f501]) ).
fof(f505,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f493,f51]) ).
fof(f509,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f505,f36]) ).
fof(f510,plain,
( ~ sQ4_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f522,plain,
( ~ sQ45_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f219,f53]) ).
fof(f527,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f27]) ).
fof(f528,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f529,plain,
( ~ sQ44_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f216,f54]) ).
fof(f534,plain,
( ~ sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f529,f30]) ).
fof(f535,plain,
~ sQ44_spl,
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f538,plain,
( ~ sQ43_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f212,f51]) ).
fof(f542,plain,
( ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f538,f37]) ).
fof(f543,plain,
~ sQ43_spl,
inference(contradiction_clause,[status(thm)],[f542]) ).
fof(f546,plain,
( ~ sQ42_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f209,f51]) ).
fof(f550,plain,
( ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f34]) ).
fof(f551,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f550]) ).
fof(f554,plain,
( ~ sQ40_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f203,f51]) ).
fof(f558,plain,
( ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f554,f27]) ).
fof(f559,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f558]) ).
fof(f560,plain,
! [X0] :
( ~ sQ39_spl
| equalish(X0,e_2)
| ~ product(X0,e_3,e_4) ),
inference(resolution,[status(thm)],[f199,f45]) ).
fof(f564,plain,
( ~ sQ38_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f196,f54]) ).
fof(f569,plain,
( ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f564,f31]) ).
fof(f570,plain,
~ sQ38_spl,
inference(contradiction_clause,[status(thm)],[f569]) ).
fof(f577,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f485,f78]) ).
fof(f582,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| product(e_3,e_4,e_2) ),
inference(resolution,[status(thm)],[f490,f577]) ).
fof(f595,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| ~ sQ29_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f393,f582]) ).
fof(f596,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f595,f36]) ).
fof(f597,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f596]) ).
fof(f608,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f415,f31]) ).
fof(f609,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f608]) ).
fof(f631,plain,
( ~ sQ35_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f186,f54]) ).
fof(f655,plain,
( ~ sQ33_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f180,f53]) ).
fof(f660,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f655,f37]) ).
fof(f661,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f660]) ).
fof(f689,plain,
( ~ sQ63_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f281,f51]) ).
fof(f693,plain,
( ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f689,f36]) ).
fof(f694,plain,
~ sQ63_spl,
inference(contradiction_clause,[status(thm)],[f693]) ).
fof(f724,plain,
( ~ sQ57_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f262,f54]) ).
fof(f729,plain,
( ~ sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f724,f27]) ).
fof(f730,plain,
~ sQ57_spl,
inference(contradiction_clause,[status(thm)],[f729]) ).
fof(f740,plain,
( ~ sQ39_spl
| ~ sQ55_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f255,f560]) ).
fof(f746,plain,
( ~ sQ39_spl
| ~ sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f740,f27]) ).
fof(f747,plain,
( ~ sQ39_spl
| ~ sQ55_spl ),
inference(contradiction_clause,[status(thm)],[f746]) ).
fof(f749,plain,
( ~ sQ54_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f252,f54]) ).
fof(f755,plain,
( ~ sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f749,f28]) ).
fof(f756,plain,
~ sQ54_spl,
inference(contradiction_clause,[status(thm)],[f755]) ).
fof(f757,plain,
( ~ sQ29_spl
| ~ sQ53_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f249,f395]) ).
fof(f763,plain,
( ~ sQ29_spl
| ~ sQ53_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f757,f208,f248,f162]) ).
fof(f770,plain,
( ~ sQ52_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f246,f53]) ).
fof(f775,plain,
( ~ sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f770,f33]) ).
fof(f776,plain,
~ sQ52_spl,
inference(contradiction_clause,[status(thm)],[f775]) ).
fof(f777,plain,
( ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f631,f32]) ).
fof(f778,plain,
~ sQ35_spl,
inference(contradiction_clause,[status(thm)],[f777]) ).
fof(f795,plain,
( ~ sQ14_spl
| ~ sQ51_spl
| product(e_4,e_3,e_4) ),
inference(resolution,[status(thm)],[f242,f295]) ).
fof(f802,plain,
( ~ sQ14_spl
| ~ sQ51_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f795,f86,f241,f109]) ).
fof(f805,plain,
( ~ sQ14_spl
| ~ sQ50_spl
| product(e_3,e_3,e_4) ),
inference(resolution,[status(thm)],[f239,f295]) ).
fof(f812,plain,
( ~ sQ14_spl
| ~ sQ50_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f805,f142,f238,f109]) ).
fof(f815,plain,
( ~ sQ14_spl
| ~ sQ49_spl
| product(e_2,e_3,e_4) ),
inference(resolution,[status(thm)],[f236,f295]) ).
fof(f816,plain,
( ~ sQ17_spl
| ~ sQ49_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f236,f482]) ).
fof(f821,plain,
( ~ sQ14_spl
| ~ sQ49_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f815,f198,f235,f109]) ).
fof(f822,plain,
( ~ sQ17_spl
| ~ sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f816,f28]) ).
fof(f823,plain,
( ~ sQ17_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f822]) ).
fof(f825,plain,
( ~ sQ48_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f233,f53]) ).
fof(f830,plain,
( ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f825,f36]) ).
fof(f831,plain,
~ sQ48_spl,
inference(contradiction_clause,[status(thm)],[f830]) ).
fof(f832,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f439,f38]) ).
fof(f833,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f832]) ).
fof(f834,plain,
$false,
inference(sat_refutation,[status(thm)],[f89,f115,f132,f158,f171,f214,f244,f257,f291,f312,f319,f349,f356,f363,f404,f406,f413,f428,f452,f470,f472,f480,f492,f500,f502,f510,f528,f535,f543,f551,f559,f570,f597,f609,f661,f694,f730,f747,f756,f763,f776,f778,f802,f812,f821,f823,f831,f833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP126-1.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n014.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sun Sep 20 19:59:35 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.17/0.62 % Refutation found
% 0.17/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.66 % Elapsed time: 0.193875 seconds
% 0.17/0.66 % CPU time: 1.207154 seconds
% 0.17/0.66 % Total memory used: 21.237 MB
% 0.17/0.66 % Net memory used: 20.654 MB
%------------------------------------------------------------------------------