%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP130-3.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:32:48 PM UTC 2026
% Result : Unsatisfiable 1.16s 0.69s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 80
% Syntax : Number of formulae : 329 ( 46 unt; 52 def)
% Number of atoms : 924 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1148 ( 553 ~; 543 |; 0 &)
% ( 52 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 59 ( 58 usr; 53 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 194 ( 194 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
next(e_0,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
greater(e_1,e_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
greater(e_2,e_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
greater(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
greater(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] :
( cycle(X,e_2)
| cycle(X,e_1)
| cycle(X,e_0)
| ~ group_element(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
cycle(e_3,e_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,W,Z,Z1] :
( equalish(Y,Z1)
| ~ next(Z,Z1)
| ~ greater(Y,e_0)
| ~ next(X,W)
| ~ cycle(W,Z)
| ~ cycle(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Z1,Y,W,Z2] :
( ~ greater(Z1,Z2)
| ~ greater(Y,X)
| ~ next(Y,W)
| ~ cycle(W,Z2)
| ~ cycle(Y,e_0)
| ~ cycle(X,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] :
( ~ greater(Y,X)
| ~ product(X,e_1,Y)
| ~ cycle(X,e_0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,Z,X1] :
( equalish(Z,X1)
| ~ next(X,X1)
| ~ greater(Y,e_0)
| ~ product(X,e_1,Z)
| ~ cycle(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] :
( product(X,Y,e_3)
| product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
! [X,Y,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,plain,
next(e_0,e_1),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f32,plain,
next(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f33,plain,
next(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f34,plain,
greater(e_1,e_0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f35,plain,
greater(e_2,e_0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f37,plain,
greater(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f38,plain,
greater(e_3,e_1),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f39,plain,
greater(e_3,e_2),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
! [X0] :
( cycle(X0,e_2)
| cycle(X0,e_1)
| cycle(X0,e_0)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f43,plain,
cycle(e_3,e_0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f44,plain,
! [Y,Z1] :
( equalish(Y,Z1)
| ! [Z] :
( ~ next(Z,Z1)
| ~ greater(Y,e_0)
| ! [X,W] :
( ~ next(X,W)
| ~ cycle(W,Z)
| ~ cycle(X,Y) ) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( equalish(X1,X4)
| ~ next(X3,X4)
| ~ greater(X1,e_0)
| ~ next(X0,X2)
| ~ cycle(X2,X3)
| ~ cycle(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [Z1,Z2] :
( ~ greater(Z1,Z2)
| ! [X,Y] :
( ~ greater(Y,X)
| ! [W] :
( ~ next(Y,W)
| ~ cycle(W,Z2)
| ~ cycle(Y,e_0)
| ~ cycle(X,Z1) ) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4] :
( ~ greater(X1,X4)
| ~ greater(X2,X0)
| ~ next(X2,X3)
| ~ cycle(X3,X4)
| ~ cycle(X2,e_0)
| ~ cycle(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| ~ product(X0,e_1,X1)
| ~ cycle(X0,e_0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f49,plain,
! [Z,X1] :
( equalish(Z,X1)
| ! [X] :
( ~ next(X,X1)
| ! [Y] :
( ~ greater(Y,e_0)
| ~ product(X,e_1,Z)
| ~ cycle(X,Y) ) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ next(X0,X3)
| ~ greater(X1,e_0)
| ~ product(X0,e_1,X2)
| ~ cycle(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
! [X0,X1] :
( 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)],[f26]) ).
fof(f61,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X,Y,Z2] :
( product(Z2,Y,X)
| ! [Z1] :
( ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( product(X3,X1,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f70,plain,
! [X0,X1,X2] :
( equalish(X1,X2)
| ~ next(e_0,X2)
| ~ greater(X1,e_0)
| ~ next(X0,e_3)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f45,f43]) ).
fof(f71,plain,
! [X0,X1] :
( ~ greater(X1,e_0)
| ~ greater(e_3,X0)
| ~ next(e_3,e_3)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f47,f43]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( ~ greater(X1,X3)
| ~ greater(e_3,X0)
| ~ next(e_3,X2)
| ~ cycle(X2,X3)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f47,f43]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ greater(X1,e_0)
| ~ greater(X2,X0)
| ~ next(X2,e_3)
| ~ cycle(X2,e_0)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f47,f43]) ).
fof(f74,definition,
! [X0,X1] :
( sQ0_spl
<=> ( ~ greater(X1,e_0)
| ~ greater(e_3,X0)
| ~ cycle(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f75,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ greater(X1,e_0)
| ~ greater(e_3,X0)
| ~ cycle(X0,X1) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,definition,
( sQ1_spl
<=> next(e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f74,f77]) ).
fof(f82,plain,
( cycle(e_2,e_2)
| cycle(e_2,e_1)
| cycle(e_2,e_0) ),
inference(resolution,[status(thm)],[f42,f52]) ).
fof(f83,plain,
( cycle(e_1,e_2)
| cycle(e_1,e_1)
| cycle(e_1,e_0) ),
inference(resolution,[status(thm)],[f42,f51]) ).
fof(f84,definition,
( sQ2_spl
<=> cycle(e_3,e_0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( sQ2_spl
| ~ cycle(e_3,e_0) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,definition,
( sQ3_spl
<=> cycle(e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ3_spl
| cycle(e_3,e_1) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,definition,
( sQ4_spl
<=> cycle(e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ4_spl
| cycle(e_3,e_2) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f94,definition,
( sQ5_spl
<=> cycle(e_2,e_0) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ5_spl
| cycle(e_2,e_0) ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
( sQ6_spl
<=> cycle(e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ6_spl
| cycle(e_2,e_1) ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,definition,
( sQ7_spl
<=> cycle(e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( ~ sQ7_spl
| cycle(e_2,e_2) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( sQ7_spl
| sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f82,f94,f97,f100]) ).
fof(f104,definition,
( sQ8_spl
<=> cycle(e_1,e_0) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( ~ sQ8_spl
| cycle(e_1,e_0) ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,definition,
( sQ9_spl
<=> cycle(e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ9_spl
| cycle(e_1,e_1) ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,definition,
( sQ10_spl
<=> cycle(e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ10_spl
| cycle(e_1,e_2) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( sQ10_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f83,f104,f107,f110]) ).
fof(f114,plain,
! [X0] :
( 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)],[f60,f53]) ).
fof(f115,plain,
! [X0] :
( 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)],[f60,f52]) ).
fof(f116,plain,
! [X0] :
( 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)],[f60,f51]) ).
fof(f118,plain,
( 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)],[f114,f52]) ).
fof(f119,plain,
( 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)],[f114,f51]) ).
fof(f120,definition,
( sQ11_spl
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f121,plain,
( ~ sQ11_spl
| product(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f130,definition,
( sQ14_spl
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ14_spl
| product(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ15_spl
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ15_spl
| product(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
( sQ16_spl
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ16_spl
| product(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( sQ16_spl
| sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f118,f130,f133,f136]) ).
fof(f140,definition,
( sQ17_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( ~ sQ17_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,definition,
( sQ18_spl
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ18_spl
| product(e_3,e_1,e_2) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,definition,
( sQ19_spl
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( ~ sQ19_spl
| product(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f119,f140,f143,f146]) ).
fof(f150,plain,
( 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)],[f115,f53]) ).
fof(f153,definition,
( sQ20_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ20_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,definition,
( sQ21_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( ~ sQ21_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,definition,
( sQ22_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ22_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,plain,
( sQ22_spl
| sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f150,f153,f156,f159]) ).
fof(f173,definition,
( sQ26_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ26_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f175,plain,
( sQ26_spl
| ~ product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f183,plain,
( 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)],[f116,f53]) ).
fof(f185,plain,
( 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)],[f116,f51]) ).
fof(f186,definition,
( sQ29_spl
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ29_spl
| product(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,definition,
( sQ30_spl
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ30_spl
| product(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,definition,
( sQ31_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ31_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( sQ31_spl
| sQ30_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f183,f186,f189,f192]) ).
fof(f199,definition,
( sQ33_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ33_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f206,definition,
( sQ35_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( ~ sQ35_spl
| product(e_1,e_1,e_1) ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,definition,
( sQ36_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( ~ sQ36_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,definition,
( sQ37_spl
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( ~ sQ37_spl
| product(e_1,e_1,e_3) ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,plain,
( sQ37_spl
| sQ36_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f185,f206,f209,f212]) ).
fof(f223,plain,
! [X0,X1,X2,X3] :
( ~ sQ8_spl
| ~ greater(X1,X3)
| ~ greater(e_1,X0)
| ~ next(e_1,X2)
| ~ cycle(X2,X3)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f105,f47]) ).
fof(f228,definition,
! [X0,X1] :
( sQ38_spl
<=> ( ~ greater(X1,e_0)
| ~ greater(e_1,X0)
| ~ cycle(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f229,plain,
! [X0,X1] :
( ~ sQ38_spl
| ~ greater(X1,e_0)
| ~ greater(e_1,X0)
| ~ cycle(X0,X1) ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f246,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| equalish(X1,X2)
| ~ next(e_0,X2)
| ~ greater(X1,e_0)
| ~ next(X0,e_2)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f95,f45]) ).
fof(f248,definition,
! [X0,X1] :
( sQ40_spl
<=> ( ~ greater(X1,e_0)
| ~ greater(e_2,X0)
| ~ cycle(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f249,plain,
! [X0,X1] :
( ~ sQ40_spl
| ~ greater(X1,e_0)
| ~ greater(e_2,X0)
| ~ cycle(X0,X1) ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f261,plain,
! [X0] :
( ~ sQ19_spl
| product(e_3,X0,e_3)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f147,f68]) ).
fof(f274,plain,
( ~ sQ18_spl
| ~ greater(e_2,e_3)
| ~ cycle(e_3,e_0) ),
inference(resolution,[status(thm)],[f144,f48]) ).
fof(f275,plain,
! [X0] :
( ~ sQ18_spl
| product(e_2,X0,e_3)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f144,f68]) ).
fof(f280,definition,
( sQ46_spl
<=> greater(e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( ~ sQ18_spl
| ~ sQ46_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f274,f84,f280,f143]) ).
fof(f286,plain,
! [X0] :
( ~ sQ17_spl
| product(e_1,X0,e_3)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f141,f68]) ).
fof(f291,definition,
( sQ48_spl
<=> greater(e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f86,f43]) ).
fof(f296,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f295]) ).
fof(f299,plain,
! [X0] :
( ~ sQ6_spl
| equalish(e_1,X0)
| ~ next(e_0,X0)
| ~ greater(e_1,e_0)
| ~ next(e_2,e_3) ),
inference(resolution,[status(thm)],[f70,f98]) ).
fof(f300,plain,
! [X0] :
( ~ sQ7_spl
| equalish(e_2,X0)
| ~ next(e_0,X0)
| ~ greater(e_2,e_0)
| ~ next(e_2,e_3) ),
inference(resolution,[status(thm)],[f70,f101]) ).
fof(f302,plain,
! [X0] :
( ~ sQ10_spl
| equalish(e_2,X0)
| ~ next(e_0,X0)
| ~ greater(e_2,e_0)
| ~ next(e_1,e_3) ),
inference(resolution,[status(thm)],[f70,f111]) ).
fof(f303,plain,
! [X0] :
( ~ sQ4_spl
| equalish(e_2,X0)
| ~ next(e_0,X0)
| ~ greater(e_2,e_0)
| ~ next(e_3,e_3) ),
inference(resolution,[status(thm)],[f70,f91]) ).
fof(f305,definition,
( sQ49_spl
<=> next(e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( sQ49_spl
| ~ next(e_2,e_3) ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,definition,
( sQ50_spl
<=> greater(e_1,e_0) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f310,plain,
( sQ50_spl
| ~ greater(e_1,e_0) ),
inference(component_clause,[status(thm)],[f308]) ).
fof(f311,definition,
! [X0] :
( sQ51_spl
<=> ( equalish(e_1,X0)
| ~ next(e_0,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f314,plain,
( ~ sQ6_spl
| sQ51_spl
| ~ sQ50_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f299,f305,f308,f311,f97]) ).
fof(f315,definition,
( sQ52_spl
<=> greater(e_2,e_0) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f317,plain,
( sQ52_spl
| ~ greater(e_2,e_0) ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f318,definition,
! [X0] :
( sQ53_spl
<=> ( equalish(e_2,X0)
| ~ next(e_0,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f319,plain,
! [X0] :
( ~ sQ53_spl
| equalish(e_2,X0)
| ~ next(e_0,X0) ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f321,plain,
( ~ sQ7_spl
| sQ53_spl
| ~ sQ52_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f300,f305,f315,f318,f100]) ).
fof(f322,definition,
( sQ54_spl
<=> next(e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( ~ sQ10_spl
| sQ53_spl
| ~ sQ52_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f302,f322,f315,f318,f110]) ).
fof(f327,plain,
( ~ sQ4_spl
| sQ53_spl
| ~ sQ52_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f303,f77,f315,f318,f90]) ).
fof(f328,definition,
( sQ55_spl
<=> greater(e_0,e_0) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f331,definition,
! [X0] :
( sQ56_spl
<=> ( equalish(e_0,X0)
| ~ next(e_0,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f317,f35]) ).
fof(f336,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f335]) ).
fof(f337,plain,
( sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f34]) ).
fof(f338,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f339,plain,
( sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f307,f33]) ).
fof(f340,plain,
sQ49_spl,
inference(contradiction_clause,[status(thm)],[f339]) ).
fof(f342,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ greater(X1,e_1)
| ~ greater(e_3,X0)
| ~ next(e_3,e_1)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f72,f108]) ).
fof(f343,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ greater(X1,e_2)
| ~ greater(e_3,X0)
| ~ next(e_3,e_1)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f72,f111]) ).
fof(f346,definition,
! [X0,X1] :
( sQ57_spl
<=> ( ~ greater(X1,e_2)
| ~ greater(e_3,X0)
| ~ cycle(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f349,definition,
( sQ58_spl
<=> next(e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f353,definition,
! [X0,X1] :
( sQ59_spl
<=> ( ~ greater(X1,e_1)
| ~ greater(e_3,X0)
| ~ cycle(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f356,definition,
( sQ60_spl
<=> next(e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f359,plain,
( ~ sQ9_spl
| ~ sQ60_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f342,f353,f356,f107]) ).
fof(f360,plain,
( ~ sQ10_spl
| ~ sQ60_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f343,f346,f356,f110]) ).
fof(f365,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ greater(e_1,e_0)
| ~ greater(e_3,e_1) ),
inference(resolution,[status(thm)],[f75,f108]) ).
fof(f367,definition,
( sQ61_spl
<=> greater(e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f369,plain,
( sQ61_spl
| ~ greater(e_3,e_1) ),
inference(component_clause,[status(thm)],[f367]) ).
fof(f370,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f365,f367,f308,f74,f107]) ).
fof(f372,plain,
( sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f369,f38]) ).
fof(f373,plain,
sQ61_spl,
inference(contradiction_clause,[status(thm)],[f372]) ).
fof(f375,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ greater(X1,e_1)
| ~ greater(e_3,X0)
| ~ next(e_3,e_3)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f88,f72]) ).
fof(f376,plain,
! [X0] :
( ~ sQ3_spl
| equalish(e_1,X0)
| ~ next(e_0,X0)
| ~ greater(e_1,e_0)
| ~ next(e_3,e_3) ),
inference(resolution,[status(thm)],[f88,f70]) ).
fof(f380,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f375,f353,f77,f87]) ).
fof(f381,plain,
( ~ sQ3_spl
| sQ51_spl
| ~ sQ50_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f376,f77,f308,f311,f87]) ).
fof(f382,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ greater(X1,e_0)
| ~ greater(e_2,X0)
| ~ next(e_2,e_3)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f95,f73]) ).
fof(f385,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ greater(X1,e_0)
| ~ greater(e_3,X0)
| ~ next(e_3,e_2)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f95,f72]) ).
fof(f386,plain,
! [X0] :
( ~ sQ5_spl
| equalish(e_0,X0)
| ~ next(e_0,X0)
| ~ greater(e_0,e_0)
| ~ next(e_2,e_3) ),
inference(resolution,[status(thm)],[f95,f70]) ).
fof(f391,plain,
( ~ sQ5_spl
| ~ sQ49_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f382,f248,f305,f94]) ).
fof(f393,plain,
( ~ sQ5_spl
| ~ sQ58_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f385,f74,f349,f94]) ).
fof(f394,plain,
( ~ sQ5_spl
| sQ56_spl
| ~ sQ55_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f386,f305,f328,f331,f94]) ).
fof(f413,plain,
! [X0] :
( ~ sQ16_spl
| product(e_3,X0,e_3)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f137,f68]) ).
fof(f414,plain,
! [X0] :
( ~ sQ16_spl
| product(e_3,X0,e_3)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f114,f413]) ).
fof(f417,plain,
( ~ sQ16_spl
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f414,f51]) ).
fof(f420,plain,
( ~ sQ16_spl
| sQ19_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f417,f140,f146,f136]) ).
fof(f430,plain,
! [X0] :
( ~ sQ15_spl
| product(e_2,X0,e_3)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f134,f68]) ).
fof(f431,plain,
( ~ sQ15_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f430,f134]) ).
fof(f433,plain,
! [X0] :
( ~ sQ15_spl
| equalish(X0,e_2)
| ~ product(e_2,X0,e_3) ),
inference(resolution,[status(thm)],[f431,f64]) ).
fof(f434,plain,
! [X0] :
( ~ sQ15_spl
| equalish(X0,e_3)
| ~ product(e_2,e_2,X0) ),
inference(resolution,[status(thm)],[f431,f62]) ).
fof(f443,plain,
! [X0] :
( ~ sQ14_spl
| product(e_1,X0,e_3)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f131,f68]) ).
fof(f474,plain,
( ~ sQ18_spl
| ~ sQ11_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f121,f275]) ).
fof(f510,plain,
! [X0] :
( ~ sQ26_spl
| product(e_1,X0,e_2)
| ~ product(e_2,X0,e_1) ),
inference(resolution,[status(thm)],[f174,f68]) ).
fof(f599,plain,
! [X0] :
( ~ sQ22_spl
| product(e_3,X0,e_2)
| ~ product(e_2,X0,e_3) ),
inference(resolution,[status(thm)],[f160,f68]) ).
fof(f603,plain,
( ~ sQ37_spl
| ~ greater(e_3,e_1)
| ~ cycle(e_1,e_0) ),
inference(resolution,[status(thm)],[f213,f48]) ).
fof(f607,plain,
! [X0] :
( ~ sQ37_spl
| product(e_3,X0,e_1)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[f213,f68]) ).
fof(f608,definition,
! [X0] :
( sQ67_spl
<=> ( ~ greater(X0,e_0)
| ~ cycle(e_1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( ~ sQ37_spl
| ~ sQ61_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f603,f104,f367,f212]) ).
fof(f619,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ greater(X1,e_0)
| ~ greater(e_3,X0)
| ~ next(e_3,e_1)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f105,f72]) ).
fof(f627,plain,
( ~ sQ8_spl
| ~ sQ60_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f619,f74,f356,f104]) ).
fof(f630,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ greater(e_0,e_0)
| ~ greater(e_3,e_1) ),
inference(resolution,[status(thm)],[f75,f105]) ).
fof(f633,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ55_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f630,f367,f328,f74,f104]) ).
fof(f634,definition,
( sQ69_spl
<=> greater(e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( sQ69_spl
| ~ greater(e_3,e_2) ),
inference(component_clause,[status(thm)],[f634]) ).
fof(f639,plain,
( sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f636,f39]) ).
fof(f640,plain,
sQ69_spl,
inference(contradiction_clause,[status(thm)],[f639]) ).
fof(f658,plain,
( ~ sQ36_spl
| ~ greater(e_2,e_1)
| ~ cycle(e_1,e_0) ),
inference(resolution,[status(thm)],[f210,f48]) ).
fof(f665,plain,
! [X0,X1] :
( ~ sQ35_spl
| equalish(e_1,X1)
| ~ next(e_1,X1)
| ~ greater(X0,e_0)
| ~ cycle(e_1,X0) ),
inference(resolution,[status(thm)],[f207,f50]) ).
fof(f666,plain,
( ~ sQ35_spl
| ~ greater(e_1,e_1)
| ~ cycle(e_1,e_0) ),
inference(resolution,[status(thm)],[f207,f48]) ).
fof(f671,definition,
! [X1] :
( sQ70_spl
<=> ( equalish(e_1,X1)
| ~ next(e_1,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f674,plain,
( ~ sQ35_spl
| sQ70_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f665,f608,f671,f206]) ).
fof(f675,definition,
( sQ71_spl
<=> greater(e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f678,plain,
( ~ sQ35_spl
| ~ sQ71_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f666,f104,f675,f206]) ).
fof(f694,plain,
! [X0] :
( ~ sQ33_spl
| product(e_2,X0,e_1)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f200,f68]) ).
fof(f717,plain,
! [X0] :
( ~ sQ31_spl
| product(e_3,X0,e_1)
| ~ product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f193,f68]) ).
fof(f718,plain,
( ~ sQ31_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f717,f193]) ).
fof(f721,plain,
! [X0] :
( ~ sQ31_spl
| equalish(X0,e_3)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f718,f64]) ).
fof(f722,plain,
! [X0] :
( ~ sQ31_spl
| equalish(X0,e_1)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f718,f62]) ).
fof(f728,plain,
( ~ sQ9_spl
| ~ sQ38_spl
| ~ greater(e_1,e_0)
| ~ greater(e_1,e_1) ),
inference(resolution,[status(thm)],[f229,f108]) ).
fof(f729,plain,
( ~ sQ38_spl
| ~ greater(e_0,e_0)
| ~ greater(e_1,e_3) ),
inference(resolution,[status(thm)],[f229,f43]) ).
fof(f731,plain,
( ~ sQ9_spl
| ~ sQ38_spl
| ~ sQ50_spl
| ~ sQ71_spl ),
inference(split_clause,[status(thm)],[f728,f675,f308,f228,f107]) ).
fof(f732,plain,
( ~ sQ38_spl
| ~ sQ55_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f729,f291,f328,f228]) ).
fof(f734,plain,
( ~ sQ9_spl
| ~ sQ40_spl
| ~ greater(e_1,e_0)
| ~ greater(e_2,e_1) ),
inference(resolution,[status(thm)],[f249,f108]) ).
fof(f735,plain,
( ~ sQ40_spl
| ~ greater(e_0,e_0)
| ~ greater(e_2,e_3) ),
inference(resolution,[status(thm)],[f249,f43]) ).
fof(f737,definition,
( sQ72_spl
<=> greater(e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f739,plain,
( sQ72_spl
| ~ greater(e_2,e_1) ),
inference(component_clause,[status(thm)],[f737]) ).
fof(f740,plain,
( ~ sQ9_spl
| ~ sQ40_spl
| ~ sQ50_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f734,f737,f308,f248,f107]) ).
fof(f741,plain,
( ~ sQ40_spl
| ~ sQ55_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f735,f280,f328,f248]) ).
fof(f742,plain,
( sQ72_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f739,f37]) ).
fof(f743,plain,
sQ72_spl,
inference(contradiction_clause,[status(thm)],[f742]) ).
fof(f768,plain,
( ~ sQ22_spl
| ~ sQ18_spl
| ~ sQ11_spl
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f474,f599]) ).
fof(f778,plain,
( ~ sQ31_spl
| ~ sQ22_spl
| ~ sQ18_spl
| ~ sQ11_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f768,f722]) ).
fof(f784,plain,
( ~ sQ31_spl
| ~ sQ22_spl
| ~ sQ18_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f778,f56]) ).
fof(f785,plain,
( ~ sQ31_spl
| ~ sQ22_spl
| ~ sQ18_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f784]) ).
fof(f790,plain,
! [X0] :
( ~ sQ21_spl
| product(e_2,X0,e_2)
| ~ product(e_2,X0,e_3) ),
inference(resolution,[status(thm)],[f157,f68]) ).
fof(f794,plain,
! [X0] :
( ~ sQ30_spl
| product(e_2,X0,e_1)
| ~ product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f190,f68]) ).
fof(f798,plain,
! [X0] :
( ~ sQ29_spl
| product(e_1,X0,e_1)
| ~ product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f187,f68]) ).
fof(f802,plain,
! [X0] :
( ~ sQ20_spl
| product(e_1,X0,e_2)
| ~ product(e_2,X0,e_3) ),
inference(resolution,[status(thm)],[f154,f68]) ).
fof(f807,plain,
( ~ sQ53_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f319,f31]) ).
fof(f808,plain,
( ~ sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f807,f56]) ).
fof(f809,plain,
~ sQ53_spl,
inference(contradiction_clause,[status(thm)],[f808]) ).
fof(f913,plain,
( ~ sQ31_spl
| ~ sQ17_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f141,f721]) ).
fof(f914,plain,
( ~ sQ17_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f141,f286]) ).
fof(f921,plain,
( ~ sQ31_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f913,f55]) ).
fof(f922,plain,
( ~ sQ31_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f921]) ).
fof(f923,plain,
( ~ sQ17_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f914,f212,f140]) ).
fof(f926,plain,
( ~ sQ18_spl
| ~ sQ11_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f474,f159,f120,f143]) ).
fof(f994,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ19_spl
| product(e_3,X0,e_3)
| ~ group_element(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f414,f261]) ).
fof(f996,plain,
( ~ sQ16_spl
| ~ sQ19_spl
| product(e_3,e_2,e_3) ),
inference(resolution,[status(thm)],[f994,f52]) ).
fof(f997,plain,
( ~ sQ16_spl
| ~ sQ19_spl
| product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[f994,f51]) ).
fof(f1000,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ19_spl
| equalish(X0,e_2)
| ~ product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f996,f64]) ).
fof(f1017,plain,
( ~ sQ31_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f718,f120,f192]) ).
fof(f1020,plain,
( ~ sQ16_spl
| ~ sQ19_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f1000,f997]) ).
fof(f1022,plain,
( ~ sQ16_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1020,f54]) ).
fof(f1023,plain,
( ~ sQ16_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f1022]) ).
fof(f1025,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ8_spl
| ~ greater(X1,e_0)
| ~ greater(e_1,X0)
| ~ next(e_1,e_2)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f223,f95]) ).
fof(f1028,definition,
( sQ73_spl
<=> next(e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1030,plain,
( sQ73_spl
| ~ next(e_1,e_2) ),
inference(component_clause,[status(thm)],[f1028]) ).
fof(f1031,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ73_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f1025,f228,f1028,f104,f94]) ).
fof(f1034,plain,
( sQ73_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1030,f32]) ).
fof(f1035,plain,
sQ73_spl,
inference(contradiction_clause,[status(thm)],[f1034]) ).
fof(f1119,plain,
( ~ sQ15_spl
| ~ sQ20_spl
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f802,f431]) ).
fof(f1125,plain,
( ~ sQ15_spl
| ~ sQ20_spl
| ~ sQ33_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f694,f1119]) ).
fof(f1128,plain,
( ~ sQ15_spl
| ~ sQ20_spl
| ~ sQ33_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f1125,f434]) ).
fof(f1134,plain,
( ~ sQ15_spl
| ~ sQ20_spl
| ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1128,f55]) ).
fof(f1135,plain,
( ~ sQ15_spl
| ~ sQ20_spl
| ~ sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f1134]) ).
fof(f1142,plain,
( ~ sQ15_spl
| ~ sQ21_spl
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f790,f431]) ).
fof(f1143,plain,
( ~ sQ15_spl
| ~ sQ21_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f1142,f434]) ).
fof(f1149,plain,
( ~ sQ15_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1143,f57]) ).
fof(f1150,plain,
( ~ sQ15_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f1149]) ).
fof(f1151,plain,
( ~ sQ15_spl
| ~ sQ20_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f1119,f199,f153,f133]) ).
fof(f1189,plain,
( ~ sQ18_spl
| ~ sQ14_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f443,f144]) ).
fof(f1190,plain,
( ~ sQ18_spl
| ~ sQ14_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f1189,f212,f130,f143]) ).
fof(f1197,plain,
! [X0] :
( ~ sQ19_spl
| product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| ~ group_element(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f114,f261]) ).
fof(f1199,plain,
( ~ sQ19_spl
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f1197,f52]) ).
fof(f1202,plain,
( ~ sQ19_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f1199,f133,f136,f146]) ).
fof(f1250,plain,
( ~ sQ19_spl
| ~ sQ11_spl
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f121,f261]) ).
fof(f1256,plain,
( ~ sQ31_spl
| ~ sQ19_spl
| ~ sQ11_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f1250,f722]) ).
fof(f1262,plain,
( ~ sQ31_spl
| ~ sQ19_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1256,f58]) ).
fof(f1263,plain,
( ~ sQ31_spl
| ~ sQ19_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1262]) ).
fof(f1297,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f160,f433]) ).
fof(f1303,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1297,f59]) ).
fof(f1304,plain,
( ~ sQ15_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f1303]) ).
fof(f1342,plain,
( ~ sQ36_spl
| ~ sQ72_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f658,f104,f737,f209]) ).
fof(f1379,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ10_spl
| equalish(e_2,X0)
| ~ next(e_0,X0)
| ~ greater(e_2,e_0)
| ~ next(e_1,e_2) ),
inference(resolution,[status(thm)],[f111,f246]) ).
fof(f1386,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| sQ53_spl
| ~ sQ52_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f1379,f1028,f315,f318,f110,f94]) ).
fof(f1393,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ greater(X1,e_1)
| ~ greater(e_3,X0)
| ~ next(e_3,e_2)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f98,f72]) ).
fof(f1398,plain,
( ~ sQ6_spl
| ~ sQ58_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f1393,f353,f349,f97]) ).
fof(f1488,plain,
( ~ sQ30_spl
| ~ sQ37_spl
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f213,f794]) ).
fof(f1534,plain,
( ~ sQ37_spl
| ~ sQ29_spl
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f798,f213]) ).
fof(f1535,plain,
( ~ sQ37_spl
| ~ sQ29_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f1534,f607]) ).
fof(f1538,plain,
! [X0] :
( ~ sQ37_spl
| ~ sQ29_spl
| equalish(X0,e_1)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f1534,f66]) ).
fof(f1553,plain,
( ~ sQ37_spl
| ~ sQ29_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f1538,f1535]) ).
fof(f1555,plain,
( ~ sQ37_spl
| ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1553,f58]) ).
fof(f1556,plain,
( ~ sQ37_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f1555]) ).
fof(f1563,plain,
( ~ sQ26_spl
| ~ sQ30_spl
| ~ sQ37_spl
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f1488,f510]) ).
fof(f1577,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ30_spl
| ~ sQ37_spl
| equalish(X0,e_2)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f1563,f62]) ).
fof(f1581,plain,
( sQ26_spl
| ~ sQ30_spl
| ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f1488]) ).
fof(f1582,plain,
( sQ26_spl
| ~ sQ30_spl
| ~ sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f1581]) ).
fof(f1606,plain,
( ~ sQ37_spl
| ~ sQ26_spl
| ~ sQ30_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f1577,f213]) ).
fof(f1607,plain,
( ~ sQ37_spl
| ~ sQ26_spl
| ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1606,f59]) ).
fof(f1608,plain,
( ~ sQ37_spl
| ~ sQ26_spl
| ~ sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f1607]) ).
fof(f1609,plain,
$false,
inference(sat_refutation,[status(thm)],[f80,f103,f113,f139,f149,f162,f195,f215,f283,f296,f314,f321,f326,f327,f336,f338,f340,f359,f360,f370,f373,f380,f381,f391,f393,f394,f420,f615,f627,f633,f640,f674,f678,f731,f732,f740,f741,f743,f785,f809,f922,f923,f926,f1017,f1023,f1031,f1035,f1135,f1150,f1151,f1190,f1202,f1263,f1304,f1342,f1386,f1398,f1556,f1582,f1608]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP130-3.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 20:01:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 1.16/0.69 % Refutation found
% 1.16/0.69 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.16/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.25/0.70 % Elapsed time: 0.322565 seconds
% 1.25/0.70 % CPU time: 2.297576 seconds
% 1.25/0.70 % Total memory used: 26.430 MB
% 1.25/0.70 % Net memory used: 25.127 MB
%------------------------------------------------------------------------------