%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP127-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:32:46 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.56s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 71
% Syntax : Number of formulae : 292 ( 59 unt; 45 def)
% Number of atoms : 689 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 666 ( 269 ~; 352 |; 0 &)
% ( 45 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 49 ( 48 usr; 46 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 113 ( 113 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( product(e_4,X,Y)
| product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( product(X,e_4,Y)
| product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [Y,X,Z1,Z2] :
( ~ product(Z1,Y,Z2)
| ~ product(Z2,Y,X)
| product(Y,X,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [Z1,Y,Z2,X] :
( ~ product(Y,X,Z1)
| ~ product(Z2,Y,X)
| product(Z1,Y,Z2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,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(f22,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,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(f27,plain,
! [X0,X1] :
( product(e_4,X0,X1)
| product(e_3,X0,X1)
| product(e_2,X0,X1)
| product(e_1,X0,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f28,plain,
! [X0,X1] :
( product(X0,e_4,X1)
| product(X0,e_3,X1)
| product(X0,e_2,X1)
| product(X0,e_1,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f29,plain,
! [Y,Z1,Z2] :
( ~ product(Z1,Y,Z2)
| ! [X] :
( ~ product(Z2,Y,X)
| product(Y,X,Z1) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( ~ product(X2,X0,X3)
| ~ product(X3,X0,X1)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [Z1,Y,X] :
( ~ product(Y,X,Z1)
| ! [Z2] :
( ~ product(Z2,Y,X)
| product(Z1,Y,Z2) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ~ product(X1,X3,X0)
| ~ product(X2,X1,X3)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f36,plain,
group_element(e_4),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f37,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f39,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f40,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f41,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f42,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f43,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f44,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f45,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f46,plain,
~ equalish(e_4,e_1),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f47,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f48,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f49,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)],[f21]) ).
fof(f50,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f57,plain,
! [Y,X,Z2] :
( product(Z2,Y,X)
| ! [Z1] :
( ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f69,plain,
! [X0] :
( product(e_4,X0,e_1)
| product(e_3,X0,e_1)
| product(e_2,X0,e_1)
| product(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f33,f27]) ).
fof(f70,plain,
! [X0] :
( product(e_4,X0,e_2)
| product(e_3,X0,e_2)
| product(e_2,X0,e_2)
| product(e_1,X0,e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f34,f27]) ).
fof(f72,plain,
! [X0] :
( product(X0,e_4,e_3)
| product(X0,e_3,e_3)
| product(X0,e_2,e_3)
| product(X0,e_1,e_3)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f28,f35]) ).
fof(f73,plain,
! [X0] :
( product(X0,e_4,e_2)
| product(X0,e_3,e_2)
| product(X0,e_2,e_2)
| product(X0,e_1,e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f28,f34]) ).
fof(f74,plain,
! [X0] :
( product(X0,e_4,e_1)
| product(X0,e_3,e_1)
| product(X0,e_2,e_1)
| product(X0,e_1,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f28,f33]) ).
fof(f75,plain,
! [X0] :
( product(X0,e_4,e_4)
| product(X0,e_3,e_4)
| product(X0,e_2,e_4)
| product(X0,e_1,e_4)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f36,f28]) ).
fof(f76,plain,
! [X0] :
( product(e_4,X0,e_4)
| product(e_3,X0,e_4)
| product(e_2,X0,e_4)
| product(e_1,X0,e_4)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f36,f27]) ).
fof(f77,plain,
! [X0] :
( product(X0,e_4,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f49,f36]) ).
fof(f78,plain,
! [X0] :
( product(X0,e_3,e_4)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f49,f35]) ).
fof(f80,plain,
! [X0] :
( product(X0,e_1,e_4)
| product(X0,e_1,e_3)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f49,f33]) ).
fof(f81,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f51,f56]) ).
fof(f83,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[f53,f56]) ).
fof(f84,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[f55,f56]) ).
fof(f86,plain,
( product(e_4,e_3,e_1)
| product(e_3,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f69,f35]) ).
fof(f88,plain,
( product(e_4,e_1,e_1)
| product(e_3,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f69,f33]) ).
fof(f89,definition,
( sQ0_spl
<=> product(e_1,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ0_spl
| product(e_1,e_4,e_1) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,definition,
( sQ1_spl
<=> product(e_2,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f93,plain,
( ~ sQ1_spl
| product(e_2,e_4,e_1) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,definition,
( sQ2_spl
<=> product(e_3,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ2_spl
| product(e_3,e_4,e_1) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f102,definition,
( sQ4_spl
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( ~ sQ4_spl
| product(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,definition,
( sQ5_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ5_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,definition,
( sQ6_spl
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f109,plain,
( ~ sQ6_spl
| product(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,definition,
( sQ7_spl
<=> product(e_4,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ7_spl
| product(e_4,e_3,e_1) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( sQ7_spl
| sQ6_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f86,f102,f105,f108,f111]) ).
fof(f115,definition,
( sQ8_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ8_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
( sQ9_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ9_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
( sQ10_spl
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ10_spl
| product(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f128,definition,
( sQ12_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f131,definition,
( sQ13_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ13_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,definition,
( sQ14_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( ~ sQ14_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,definition,
( sQ15_spl
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ15_spl
| product(e_4,e_1,e_1) ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f88,f128,f131,f134,f137]) ).
fof(f142,plain,
( product(e_4,e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f70,f35]) ).
fof(f144,plain,
( product(e_4,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f70,f33]) ).
fof(f145,definition,
( sQ16_spl
<=> product(e_1,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ16_spl
| product(e_1,e_4,e_2) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,definition,
( sQ17_spl
<=> product(e_2,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( ~ sQ17_spl
| product(e_2,e_4,e_2) ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,definition,
( sQ18_spl
<=> product(e_3,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( ~ sQ18_spl
| product(e_3,e_4,e_2) ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f158,definition,
( sQ20_spl
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( ~ sQ20_spl
| product(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,definition,
( sQ21_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ21_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,definition,
( sQ22_spl
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( ~ sQ22_spl
| product(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,definition,
( sQ23_spl
<=> product(e_4,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( ~ sQ23_spl
| product(e_4,e_3,e_2) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( sQ23_spl
| sQ22_spl
| sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f142,f158,f161,f164,f167]) ).
fof(f171,definition,
( sQ24_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ24_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,definition,
( sQ25_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f177,definition,
( sQ26_spl
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( ~ sQ26_spl
| product(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,definition,
( sQ27_spl
<=> product(e_4,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( ~ sQ27_spl
| product(e_4,e_2,e_2) ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f184,definition,
( sQ28_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ28_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,definition,
( sQ29_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( ~ sQ29_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,definition,
( sQ30_spl
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( ~ sQ30_spl
| product(e_3,e_1,e_2) ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,definition,
( sQ31_spl
<=> product(e_4,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ31_spl
| product(e_4,e_1,e_2) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( sQ31_spl
| sQ30_spl
| sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f144,f184,f187,f190,f193]) ).
fof(f201,definition,
( sQ32_spl
<=> product(e_1,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f202,plain,
( ~ sQ32_spl
| product(e_1,e_4,e_3) ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,definition,
( sQ33_spl
<=> product(e_2,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( ~ sQ33_spl
| product(e_2,e_4,e_3) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,definition,
( sQ34_spl
<=> product(e_3,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( ~ sQ34_spl
| product(e_3,e_4,e_3) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f214,definition,
( sQ36_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f215,plain,
( ~ sQ36_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f227,definition,
( sQ40_spl
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( ~ sQ40_spl
| product(e_1,e_2,e_3) ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f240,definition,
( sQ44_spl
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( ~ sQ44_spl
| product(e_1,e_1,e_3) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,definition,
( sQ45_spl
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( ~ sQ45_spl
| product(e_2,e_1,e_3) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f256,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_3,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f72,f33]) ).
fof(f260,plain,
( sQ32_spl
| sQ36_spl
| sQ40_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f256,f240,f227,f214,f201]) ).
fof(f265,plain,
( product(e_2,e_4,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f73,f34]) ).
fof(f266,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f73,f33]) ).
fof(f269,plain,
( sQ17_spl
| sQ21_spl
| sQ25_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f265,f187,f174,f161,f148]) ).
fof(f270,plain,
( sQ16_spl
| sQ20_spl
| sQ24_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f266,f184,f171,f158,f145]) ).
fof(f271,plain,
( ~ sQ15_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f138,f84]) ).
fof(f280,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f271,f46]) ).
fof(f281,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f280]) ).
fof(f282,plain,
( ~ sQ14_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f135,f84]) ).
fof(f291,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f282,f43]) ).
fof(f292,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f291]) ).
fof(f295,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f74,f34]) ).
fof(f299,plain,
( sQ1_spl
| sQ5_spl
| sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f295,f131,f118,f105,f92]) ).
fof(f304,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_3,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_1,e_4) ),
inference(resolution,[status(thm)],[f75,f33]) ).
fof(f314,definition,
( sQ51_spl
<=> product(e_4,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f327,definition,
( sQ55_spl
<=> product(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f328,plain,
( ~ sQ55_spl
| product(e_3,e_4,e_4) ),
inference(component_clause,[status(thm)],[f327]) ).
fof(f331,definition,
( sQ56_spl
<=> product(e_2,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( ~ sQ56_spl
| product(e_2,e_1,e_4) ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,definition,
( sQ57_spl
<=> product(e_2,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( ~ sQ57_spl
| product(e_2,e_2,e_4) ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f340,definition,
( sQ59_spl
<=> product(e_2,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f341,plain,
( ~ sQ59_spl
| product(e_2,e_4,e_4) ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f344,definition,
( sQ60_spl
<=> product(e_1,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f345,plain,
( ~ sQ60_spl
| product(e_1,e_1,e_4) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,definition,
( sQ61_spl
<=> product(e_1,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( ~ sQ61_spl
| product(e_1,e_2,e_4) ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f350,definition,
( sQ62_spl
<=> product(e_1,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f351,plain,
( ~ sQ62_spl
| product(e_1,e_3,e_4) ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,definition,
( sQ63_spl
<=> product(e_1,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f354,plain,
( ~ sQ63_spl
| product(e_1,e_4,e_4) ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,plain,
( sQ63_spl
| sQ62_spl
| sQ61_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f304,f344,f347,f350,f353]) ).
fof(f357,plain,
( product(e_4,e_4,e_4)
| product(e_3,e_4,e_4)
| product(e_2,e_4,e_4)
| product(e_1,e_4,e_4) ),
inference(resolution,[status(thm)],[f76,f36]) ).
fof(f361,plain,
( sQ51_spl
| sQ55_spl
| sQ59_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f357,f353,f340,f327,f314]) ).
fof(f366,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)],[f77,f35]) ).
fof(f367,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)],[f77,f34]) ).
fof(f370,plain,
( sQ55_spl
| sQ34_spl
| sQ18_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f366,f95,f151,f207,f327]) ).
fof(f371,plain,
( sQ59_spl
| sQ33_spl
| sQ17_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f367,f92,f148,f204,f340]) ).
fof(f373,plain,
( ~ sQ13_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f132,f84]) ).
fof(f382,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f373,f40]) ).
fof(f383,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f382]) ).
fof(f397,plain,
! [X0] :
( ~ sQ10_spl
| ~ product(X0,e_2,e_3)
| product(e_2,e_1,X0) ),
inference(resolution,[status(thm)],[f122,f30]) ).
fof(f401,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)],[f78,f33]) ).
fof(f405,plain,
( sQ62_spl
| sQ36_spl
| sQ20_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f401,f102,f158,f214,f350]) ).
fof(f416,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)],[f80,f34]) ).
fof(f420,plain,
( sQ56_spl
| sQ45_spl
| sQ29_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f416,f131,f187,f243,f331]) ).
fof(f424,plain,
( ~ sQ9_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f119,f81]) ).
fof(f432,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f424,f37]) ).
fof(f433,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f432]) ).
fof(f434,plain,
( ~ sQ8_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f116,f83]) ).
fof(f445,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f434,f40]) ).
fof(f446,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f445]) ).
fof(f451,plain,
! [X0] :
( ~ sQ7_spl
| ~ product(e_3,e_1,X0)
| product(X0,e_3,e_4) ),
inference(resolution,[status(thm)],[f112,f32]) ).
fof(f453,plain,
! [X0] :
( ~ sQ7_spl
| ~ product(X0,e_3,e_4)
| product(e_3,e_1,X0) ),
inference(resolution,[status(thm)],[f112,f30]) ).
fof(f456,plain,
( ~ sQ6_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f109,f81]) ).
fof(f464,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f456,f38]) ).
fof(f465,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f464]) ).
fof(f471,plain,
! [X0] :
( ~ sQ5_spl
| ~ product(e_1,e_3,X0)
| product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f106,f30]) ).
fof(f473,plain,
( ~ sQ4_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f103,f83]) ).
fof(f484,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f473,f43]) ).
fof(f485,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f484]) ).
fof(f489,plain,
! [X0] :
( ~ sQ31_spl
| product(e_2,e_1,X0)
| ~ product(e_1,X0,e_4) ),
inference(resolution,[status(thm)],[f194,f58]) ).
fof(f498,plain,
! [X0] :
( ~ sQ30_spl
| ~ product(e_2,e_1,X0)
| product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f191,f30]) ).
fof(f502,plain,
( ~ sQ29_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f188,f83]) ).
fof(f513,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f37]) ).
fof(f514,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f513]) ).
fof(f517,plain,
( ~ sQ28_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f185,f81]) ).
fof(f525,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f517,f40]) ).
fof(f526,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f527,plain,
( ~ sQ27_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f181,f84]) ).
fof(f536,plain,
( ~ sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f47]) ).
fof(f537,plain,
~ sQ27_spl,
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f538,plain,
( ~ sQ26_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f178,f84]) ).
fof(f547,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f538,f44]) ).
fof(f548,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f549,plain,
( ~ sQ30_spl
| ~ sQ7_spl
| product(e_2,e_3,e_4) ),
inference(resolution,[status(thm)],[f451,f191]) ).
fof(f553,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ7_spl
| equalish(X0,e_3)
| ~ product(e_2,X0,e_4) ),
inference(resolution,[status(thm)],[f549,f53]) ).
fof(f572,plain,
( ~ sQ24_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f172,f84]) ).
fof(f581,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f572,f37]) ).
fof(f582,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f581]) ).
fof(f590,plain,
! [X0] :
( ~ sQ23_spl
| ~ product(X0,e_3,e_4)
| product(e_3,e_2,X0) ),
inference(resolution,[status(thm)],[f168,f30]) ).
fof(f595,plain,
( ~ sQ22_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f165,f81]) ).
fof(f603,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f595,f41]) ).
fof(f604,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f603]) ).
fof(f606,plain,
( ~ sQ21_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f162,f83]) ).
fof(f617,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f606,f44]) ).
fof(f618,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f617]) ).
fof(f619,plain,
( ~ sQ5_spl
| ~ sQ20_spl
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f159,f471]) ).
fof(f628,plain,
( ~ sQ5_spl
| ~ sQ20_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f619,f177,f158,f105]) ).
fof(f636,plain,
! [X0] :
( ~ sQ18_spl
| ~ product(X0,e_4,e_3)
| product(e_4,e_2,X0) ),
inference(resolution,[status(thm)],[f152,f30]) ).
fof(f637,plain,
( ~ sQ17_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f149,f83]) ).
fof(f648,plain,
( ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f637,f47]) ).
fof(f649,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f648]) ).
fof(f655,plain,
! [X0] :
( ~ sQ16_spl
| ~ product(e_2,e_4,X0)
| product(e_4,X0,e_1) ),
inference(resolution,[status(thm)],[f146,f30]) ).
fof(f659,plain,
( ~ sQ44_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f241,f81]) ).
fof(f667,plain,
( ~ sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f659,f43]) ).
fof(f668,plain,
~ sQ44_spl,
inference(contradiction_clause,[status(thm)],[f667]) ).
fof(f672,plain,
( ~ sQ10_spl
| ~ sQ40_spl
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f228,f397]) ).
fof(f680,plain,
( ~ sQ10_spl
| ~ sQ40_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f672,f131,f227,f121]) ).
fof(f681,plain,
( ~ sQ36_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f215,f84]) ).
fof(f690,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f681,f38]) ).
fof(f691,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f690]) ).
fof(f692,plain,
( ~ sQ34_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f208,f83]) ).
fof(f703,plain,
( ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f692,f48]) ).
fof(f704,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f703]) ).
fof(f717,plain,
! [X0] :
( ~ sQ32_spl
| ~ product(e_3,e_4,X0)
| product(e_4,X0,e_1) ),
inference(resolution,[status(thm)],[f202,f30]) ).
fof(f719,plain,
( ~ sQ0_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f90,f83]) ).
fof(f730,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f719,f46]) ).
fof(f731,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f730]) ).
fof(f741,plain,
( ~ sQ33_spl
| ~ sQ18_spl
| product(e_4,e_2,e_2) ),
inference(resolution,[status(thm)],[f636,f205]) ).
fof(f743,plain,
( ~ sQ33_spl
| ~ sQ18_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f741,f180,f151,f204]) ).
fof(f752,plain,
( ~ sQ63_spl
| equalish(e_1,e_4) ),
inference(resolution,[status(thm)],[f354,f84]) ).
fof(f761,plain,
( ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f752,f39]) ).
fof(f762,plain,
~ sQ63_spl,
inference(contradiction_clause,[status(thm)],[f761]) ).
fof(f765,plain,
( ~ sQ7_spl
| ~ sQ62_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f351,f453]) ).
fof(f766,plain,
( ~ sQ23_spl
| ~ sQ62_spl
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f351,f590]) ).
fof(f774,plain,
( ~ sQ7_spl
| ~ sQ62_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f765,f134,f350,f111]) ).
fof(f776,plain,
( ~ sQ31_spl
| ~ sQ61_spl
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f348,f489]) ).
fof(f784,plain,
( ~ sQ31_spl
| ~ sQ61_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f776,f187,f347,f193]) ).
fof(f787,plain,
( ~ sQ60_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f345,f81]) ).
fof(f795,plain,
( ~ sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f787,f46]) ).
fof(f796,plain,
~ sQ60_spl,
inference(contradiction_clause,[status(thm)],[f795]) ).
fof(f797,plain,
( ~ sQ59_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f341,f84]) ).
fof(f806,plain,
( ~ sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f797,f42]) ).
fof(f807,plain,
~ sQ59_spl,
inference(contradiction_clause,[status(thm)],[f806]) ).
fof(f810,plain,
( ~ sQ57_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f335,f81]) ).
fof(f818,plain,
( ~ sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f810,f47]) ).
fof(f819,plain,
~ sQ57_spl,
inference(contradiction_clause,[status(thm)],[f818]) ).
fof(f845,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| product(e_4,e_1,e_1) ),
inference(resolution,[status(thm)],[f655,f93]) ).
fof(f846,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f845,f137,f145,f92]) ).
fof(f855,plain,
( ~ sQ2_spl
| ~ sQ32_spl
| product(e_4,e_1,e_1) ),
inference(resolution,[status(thm)],[f717,f96]) ).
fof(f856,plain,
( ~ sQ2_spl
| ~ sQ32_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f855,f137,f201,f95]) ).
fof(f886,plain,
( ~ sQ56_spl
| ~ sQ30_spl
| ~ sQ7_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f553,f332]) ).
fof(f887,plain,
( ~ sQ56_spl
| ~ sQ30_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f886,f38]) ).
fof(f888,plain,
( ~ sQ56_spl
| ~ sQ30_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f887]) ).
fof(f892,plain,
( ~ sQ23_spl
| ~ sQ62_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f766,f121,f350,f167]) ).
fof(f893,plain,
( ~ sQ45_spl
| ~ sQ30_spl
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f498,f244]) ).
fof(f894,plain,
( ~ sQ45_spl
| ~ sQ30_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f893,f214,f190,f243]) ).
fof(f917,plain,
( ~ sQ55_spl
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[f328,f84]) ).
fof(f926,plain,
( ~ sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f917,f45]) ).
fof(f927,plain,
~ sQ55_spl,
inference(contradiction_clause,[status(thm)],[f926]) ).
fof(f928,plain,
$false,
inference(sat_refutation,[status(thm)],[f114,f140,f170,f196,f260,f269,f270,f281,f292,f299,f356,f361,f370,f371,f383,f405,f420,f433,f446,f465,f485,f514,f526,f537,f548,f582,f604,f618,f628,f649,f668,f680,f691,f704,f731,f743,f762,f774,f784,f796,f807,f819,f846,f856,f888,f892,f894,f927]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP127-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n009.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 20 20:00:12 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 0.19/0.56 % Refutation found
% 0.19/0.56 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.27/0.61 % Elapsed time: 0.144660 seconds
% 0.27/0.61 % CPU time: 0.752299 seconds
% 0.27/0.61 % Total memory used: 23.115 MB
% 0.27/0.61 % Net memory used: 22.706 MB
%------------------------------------------------------------------------------