%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP130-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 0.13s 0.50s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 37
% Syntax : Number of formulae : 220 ( 15 unt; 25 def)
% Number of atoms : 598 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 693 ( 315 ~; 353 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 26 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 89 ( 89 !; 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,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,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/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
! [X,Y,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,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)],[f10]) ).
fof(f25,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X,Y,Z2] :
( product(Z2,Y,X)
| ! [Z1] :
( ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( product(X3,X1,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,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)],[f24,f17]) ).
fof(f34,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)],[f24,f16]) ).
fof(f35,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)],[f24,f15]) ).
fof(f37,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)],[f33,f16]) ).
fof(f38,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)],[f33,f15]) ).
fof(f39,definition,
( sQ0_spl
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( ~ sQ0_spl
| product(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f45,definition,
( sQ2_spl
<=> product(e_3,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( ~ sQ2_spl
| product(e_3,e_3,e_3) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f49,definition,
( sQ3_spl
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ3_spl
| product(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,definition,
( sQ4_spl
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( ~ sQ4_spl
| product(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,definition,
( sQ5_spl
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ5_spl
| product(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( sQ5_spl
| sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f37,f49,f52,f55]) ).
fof(f59,definition,
( sQ6_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( ~ sQ6_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,definition,
( sQ7_spl
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( ~ sQ7_spl
| product(e_3,e_1,e_2) ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,definition,
( sQ8_spl
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ8_spl
| product(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( sQ8_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f38,f59,f62,f65]) ).
fof(f72,plain,
! [X0] :
( ~ sQ8_spl
| product(e_3,X0,e_3)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f66,f32]) ).
fof(f76,plain,
! [X0] :
( ~ sQ7_spl
| product(e_2,X0,e_3)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f63,f32]) ).
fof(f80,plain,
! [X0] :
( ~ sQ6_spl
| product(e_1,X0,e_3)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f60,f32]) ).
fof(f81,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)],[f34,f17]) ).
fof(f82,plain,
( 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)],[f34,f16]) ).
fof(f83,plain,
( 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)],[f34,f15]) ).
fof(f84,definition,
( sQ9_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( ~ sQ9_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,definition,
( sQ10_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ10_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,definition,
( sQ11_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ11_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( sQ11_spl
| sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f81,f84,f87,f90]) ).
fof(f94,definition,
( sQ12_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ12_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
( sQ13_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ13_spl
| product(e_2,e_2,e_2) ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,definition,
( sQ14_spl
<=> product(e_2,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( ~ sQ14_spl
| product(e_2,e_2,e_3) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f82,f94,f97,f100]) ).
fof(f104,definition,
( sQ15_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( ~ sQ15_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,definition,
( sQ16_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ16_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,definition,
( sQ17_spl
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ17_spl
| product(e_2,e_1,e_3) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( sQ17_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f83,f104,f107,f110]) ).
fof(f114,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)],[f35,f17]) ).
fof(f115,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f35,f16]) ).
fof(f117,definition,
( sQ18_spl
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ18_spl
| product(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,definition,
( sQ19_spl
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f123,definition,
( sQ20_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( ~ sQ20_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,plain,
( sQ20_spl
| sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f114,f117,f120,f123]) ).
fof(f127,definition,
( sQ21_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ21_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,definition,
( sQ22_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ22_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ23_spl
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ23_spl
| product(e_1,e_2,e_3) ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ23_spl
| sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f115,f127,f130,f133]) ).
fof(f137,definition,
( sQ24_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ24_spl
| product(e_1,e_1,e_1) ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f143,definition,
( sQ26_spl
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ26_spl
| product(e_1,e_1,e_3) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f147,plain,
! [X0] :
( ~ sQ8_spl
| product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| ~ group_element(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f33,f72]) ).
fof(f150,plain,
( ~ sQ8_spl
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f147,f16]) ).
fof(f153,plain,
( ~ sQ8_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f150,f52,f55,f65]) ).
fof(f164,plain,
! [X0] :
( ~ sQ5_spl
| product(e_3,X0,e_3)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f56,f32]) ).
fof(f165,plain,
! [X0] :
( ~ sQ5_spl
| product(e_3,X0,e_3)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f33,f164]) ).
fof(f167,plain,
( ~ sQ5_spl
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f165,f17]) ).
fof(f169,plain,
( ~ sQ5_spl
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f165,f15]) ).
fof(f170,plain,
( ~ sQ5_spl
| sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f167,f39,f45,f55]) ).
fof(f172,plain,
( ~ sQ5_spl
| sQ8_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f169,f59,f65,f55]) ).
fof(f182,plain,
! [X0] :
( ~ sQ4_spl
| product(e_2,X0,e_3)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f53,f32]) ).
fof(f183,plain,
( ~ sQ4_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f182,f53]) ).
fof(f184,plain,
! [X0] :
( ~ sQ4_spl
| equalish(X0,e_2)
| ~ product(X0,e_2,e_3) ),
inference(resolution,[status(thm)],[f183,f30]) ).
fof(f185,plain,
! [X0] :
( ~ sQ4_spl
| equalish(X0,e_2)
| ~ product(e_2,X0,e_3) ),
inference(resolution,[status(thm)],[f183,f28]) ).
fof(f187,plain,
! [X0] :
( ~ sQ4_spl
| product(e_3,X0,e_2)
| ~ product(e_2,X0,e_2) ),
inference(resolution,[status(thm)],[f183,f32]) ).
fof(f195,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f111,f185]) ).
fof(f199,plain,
! [X0] :
( ~ sQ17_spl
| product(e_3,X0,e_2)
| ~ product(e_2,X0,e_1) ),
inference(resolution,[status(thm)],[f111,f32]) ).
fof(f200,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f18]) ).
fof(f201,plain,
( ~ sQ4_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f200]) ).
fof(f211,plain,
! [X0] :
( ~ sQ16_spl
| product(e_2,X0,e_2)
| ~ product(e_2,X0,e_1) ),
inference(resolution,[status(thm)],[f108,f32]) ).
fof(f212,plain,
! [X0] :
( ~ sQ16_spl
| product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| ~ group_element(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f34,f211]) ).
fof(f213,plain,
( ~ sQ16_spl
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[f212,f17]) ).
fof(f216,plain,
( ~ sQ16_spl
| sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f213,f87,f90,f107]) ).
fof(f228,plain,
! [X0] :
( ~ sQ15_spl
| product(e_1,X0,e_2)
| ~ product(e_2,X0,e_1) ),
inference(resolution,[status(thm)],[f105,f32]) ).
fof(f229,plain,
( ~ sQ15_spl
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f228,f105]) ).
fof(f231,plain,
! [X0] :
( ~ sQ15_spl
| equalish(X0,e_1)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f229,f28]) ).
fof(f232,plain,
! [X0] :
( ~ sQ15_spl
| equalish(X0,e_2)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f229,f26]) ).
fof(f240,plain,
! [X0] :
( ~ sQ14_spl
| product(e_3,X0,e_2)
| ~ product(e_2,X0,e_2) ),
inference(resolution,[status(thm)],[f101,f32]) ).
fof(f241,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f98,f240]) ).
fof(f246,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f241,f52,f97,f100]) ).
fof(f250,plain,
! [X0] :
( ~ sQ11_spl
| product(e_3,X0,e_2)
| ~ product(e_2,X0,e_3) ),
inference(resolution,[status(thm)],[f91,f32]) ).
fof(f251,plain,
( ~ sQ11_spl
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f250,f91]) ).
fof(f252,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f250,f101]) ).
fof(f253,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f252,f52,f90,f100]) ).
fof(f254,plain,
( ~ sQ15_spl
| ~ sQ26_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f144,f232]) ).
fof(f258,plain,
! [X0] :
( ~ sQ26_spl
| product(e_3,X0,e_1)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[f144,f32]) ).
fof(f259,plain,
( ~ sQ15_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f254,f23]) ).
fof(f260,plain,
( ~ sQ15_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f261,plain,
( ~ sQ15_spl
| ~ sQ24_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f138,f232]) ).
fof(f267,plain,
( ~ sQ15_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f261,f18]) ).
fof(f268,plain,
( ~ sQ15_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f267]) ).
fof(f288,plain,
( ~ sQ4_spl
| ~ sQ23_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f134,f184]) ).
fof(f292,plain,
! [X0] :
( ~ sQ23_spl
| product(e_3,X0,e_1)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f134,f32]) ).
fof(f293,plain,
( ~ sQ4_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f288,f18]) ).
fof(f294,plain,
( ~ sQ4_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f293]) ).
fof(f314,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f131,f231]) ).
fof(f319,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f314,f20]) ).
fof(f320,plain,
( ~ sQ15_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f319]) ).
fof(f324,plain,
! [X0] :
( ~ sQ21_spl
| product(e_1,X0,e_1)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f128,f32]) ).
fof(f328,plain,
! [X0] :
( ~ sQ20_spl
| product(e_3,X0,e_1)
| ~ product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f124,f32]) ).
fof(f333,plain,
( ~ sQ6_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f60,f80]) ).
fof(f338,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f40,f80]) ).
fof(f347,plain,
! [X0] :
( ~ sQ3_spl
| product(e_1,X0,e_3)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f50,f32]) ).
fof(f352,plain,
! [X0] :
( ~ sQ10_spl
| product(e_2,X0,e_2)
| ~ product(e_2,X0,e_3) ),
inference(resolution,[status(thm)],[f88,f32]) ).
fof(f373,plain,
! [X0] :
( ~ sQ21_spl
| product(e_1,X0,e_3)
| product(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f35,f324]) ).
fof(f374,plain,
( ~ sQ21_spl
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f373,f17]) ).
fof(f376,plain,
( ~ sQ21_spl
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f373,f15]) ).
fof(f377,plain,
( ~ sQ21_spl
| sQ20_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f374,f117,f123,f127]) ).
fof(f379,plain,
( ~ sQ21_spl
| sQ26_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f376,f137,f143,f127]) ).
fof(f380,plain,
( ~ sQ10_spl
| ~ sQ4_spl
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f187,f88]) ).
fof(f381,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f380,f182]) ).
fof(f386,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f381,f185]) ).
fof(f391,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f386,f23]) ).
fof(f392,plain,
( ~ sQ4_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f391]) ).
fof(f393,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f251,f182]) ).
fof(f396,plain,
! [X0] :
( ~ sQ11_spl
| equalish(X0,e_2)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f251,f26]) ).
fof(f398,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f393,f185]) ).
fof(f403,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f398,f23]) ).
fof(f404,plain,
( ~ sQ4_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f403]) ).
fof(f405,plain,
( ~ sQ6_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f333,f143,f59]) ).
fof(f438,plain,
( ~ sQ15_spl
| ~ sQ23_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f292,f229]) ).
fof(f439,plain,
( ~ sQ15_spl
| ~ sQ23_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f438,f59,f133,f104]) ).
fof(f446,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ5_spl
| product(e_3,X0,e_3)
| ~ group_element(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f147,f164]) ).
fof(f447,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f446,f17]) ).
fof(f448,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| product(e_3,e_2,e_3) ),
inference(resolution,[status(thm)],[f446,f16]) ).
fof(f451,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ5_spl
| equalish(X0,e_2)
| ~ product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f448,f28]) ).
fof(f467,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ10_spl
| product(e_2,X0,e_2)
| ~ group_element(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f212,f352]) ).
fof(f468,plain,
( ~ sQ16_spl
| ~ sQ10_spl
| product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[f467,f17]) ).
fof(f470,plain,
( ~ sQ16_spl
| ~ sQ10_spl
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f467,f15]) ).
fof(f473,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ10_spl
| equalish(X0,e_3)
| ~ product(e_2,X0,e_2) ),
inference(resolution,[status(thm)],[f468,f28]) ).
fof(f481,plain,
( ~ sQ16_spl
| ~ sQ10_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f473,f470]) ).
fof(f483,plain,
( ~ sQ16_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f481,f19]) ).
fof(f484,plain,
( ~ sQ16_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f483]) ).
fof(f491,plain,
( ~ sQ26_spl
| ~ sQ18_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f118,f258]) ).
fof(f497,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ18_spl
| equalish(X0,e_3)
| ~ product(X0,e_3,e_1) ),
inference(resolution,[status(thm)],[f491,f30]) ).
fof(f505,plain,
( ~ sQ18_spl
| ~ sQ26_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f497,f118]) ).
fof(f507,plain,
( ~ sQ18_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f505,f19]) ).
fof(f508,plain,
( ~ sQ18_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f523,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f396,f46]) ).
fof(f524,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f523,f23]) ).
fof(f525,plain,
( ~ sQ2_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f524]) ).
fof(f535,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ0_spl
| equalish(X0,e_3)
| ~ product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f338,f28]) ).
fof(f558,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ26_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f144,f535]) ).
fof(f564,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f558,f19]) ).
fof(f565,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f564]) ).
fof(f592,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f347,f251]) ).
fof(f646,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f451,f447]) ).
fof(f649,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f646,f23]) ).
fof(f650,plain,
( ~ sQ8_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f649]) ).
fof(f668,plain,
( ~ sQ17_spl
| ~ sQ9_spl
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f85,f199]) ).
fof(f673,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ9_spl
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f668,f347]) ).
fof(f676,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ9_spl
| equalish(X0,e_2)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f668,f26]) ).
fof(f678,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ9_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f673,f123,f84,f110,f49]) ).
fof(f679,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f592,f123,f49,f90]) ).
fof(f680,plain,
! [X0] :
( ~ sQ10_spl
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f34,f352]) ).
fof(f682,plain,
( ~ sQ10_spl
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f680,f16]) ).
fof(f683,plain,
( ~ sQ10_spl
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f680,f15]) ).
fof(f685,plain,
( ~ sQ10_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f682,f94,f97,f87]) ).
fof(f686,plain,
( ~ sQ10_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f683,f104,f107,f87]) ).
fof(f722,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ9_spl
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f668,f347]) ).
fof(f729,plain,
( ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ9_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f722,f328]) ).
fof(f735,plain,
( ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ9_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f729,f76]) ).
fof(f743,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f50,f76]) ).
fof(f748,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f743,f100,f49,f62]) ).
fof(f749,plain,
( ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f735,f90,f84,f110,f49,f123,f62]) ).
fof(f750,plain,
( ~ sQ20_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f124,f328]) ).
fof(f755,plain,
( ~ sQ20_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f750,f39,f123]) ).
fof(f783,plain,
( ~ sQ12_spl
| ~ sQ17_spl
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f199,f95]) ).
fof(f784,plain,
( ~ sQ12_spl
| ~ sQ17_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f783,f52,f110,f94]) ).
fof(f785,plain,
( ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ5_spl
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f164,f668]) ).
fof(f786,plain,
( ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ5_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f785,f676]) ).
fof(f791,plain,
( ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f786,f23]) ).
fof(f792,plain,
( ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f791]) ).
fof(f793,plain,
$false,
inference(sat_refutation,[status(thm)],[f58,f68,f93,f103,f113,f126,f136,f153,f170,f172,f201,f216,f246,f253,f260,f268,f294,f320,f377,f379,f392,f404,f405,f439,f484,f508,f525,f565,f650,f678,f679,f685,f686,f748,f749,f755,f784,f792]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP130-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n002.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 20:03:31 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.13/0.50 % Refutation found
% 0.13/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.52 % Elapsed time: 0.167744 seconds
% 0.13/0.52 % CPU time: 1.130369 seconds
% 0.13/0.52 % Total memory used: 21.322 MB
% 0.13/0.52 % Net memory used: 20.577 MB
%------------------------------------------------------------------------------