%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP130-2.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 0.14s 0.51s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 39
% Syntax : Number of formulae : 200 ( 20 unt; 24 def)
% Number of atoms : 515 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 573 ( 258 ~; 291 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 30 ( 29 usr; 25 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 92 ( 92 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,X1] :
( ~ greater(Y,X1)
| ~ next(X,X1)
| ~ product(X,e_1,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,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(f17,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,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(f21,plain,
next(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
greater(e_3,e_2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
! [Y,X1] :
( ~ greater(Y,X1)
| ! [X] :
( ~ next(X,X1)
| ~ product(X,e_1,Y) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ greater(X1,X2)
| ~ next(X0,X2)
| ~ product(X0,e_1,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f29,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f30,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f31,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f32,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f33,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f36,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f37,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)],[f16]) ).
fof(f38,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X,Y,Z2] :
( product(Z2,Y,X)
| ! [Z1] :
( ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( product(X3,X1,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,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)],[f37,f30]) ).
fof(f47,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)],[f37,f29]) ).
fof(f48,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)],[f37,f28]) ).
fof(f49,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f46,f30]) ).
fof(f50,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)],[f46,f29]) ).
fof(f51,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)],[f46,f28]) ).
fof(f52,definition,
( sQ0_spl
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( ~ sQ0_spl
| product(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,definition,
( sQ1_spl
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ1_spl
| product(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,definition,
( sQ2_spl
<=> product(e_3,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ2_spl
| product(e_3,e_3,e_3) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f52,f55,f58]) ).
fof(f62,definition,
( sQ3_spl
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( ~ sQ3_spl
| product(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,definition,
( sQ4_spl
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ4_spl
| product(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,definition,
( sQ5_spl
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f69,plain,
( ~ sQ5_spl
| product(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( sQ5_spl
| sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f50,f62,f65,f68]) ).
fof(f72,definition,
( sQ6_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f73,plain,
( ~ sQ6_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,definition,
( sQ7_spl
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ7_spl
| product(e_3,e_1,e_2) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,definition,
( sQ8_spl
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( ~ sQ8_spl
| product(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( sQ8_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f51,f72,f75,f78]) ).
fof(f82,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)],[f47,f30]) ).
fof(f84,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)],[f47,f28]) ).
fof(f85,definition,
( sQ9_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f88,definition,
( sQ10_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( ~ sQ10_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,definition,
( sQ11_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ11_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( sQ11_spl
| sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f82,f85,f88,f91]) ).
fof(f101,definition,
( sQ14_spl
<=> product(e_2,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ14_spl
| product(e_2,e_2,e_3) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f103,plain,
( sQ14_spl
| ~ product(e_2,e_2,e_3) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f105,definition,
( sQ15_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ15_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,definition,
( sQ16_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f109,plain,
( ~ sQ16_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,definition,
( sQ17_spl
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ17_spl
| product(e_2,e_1,e_3) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( sQ17_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f84,f105,f108,f111]) ).
fof(f115,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)],[f48,f30]) ).
fof(f116,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)],[f48,f29]) ).
fof(f118,definition,
( sQ18_spl
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ18_spl
| product(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
( sQ19_spl
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ19_spl
| product(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,definition,
( sQ20_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ20_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ20_spl
| sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f115,f118,f121,f124]) ).
fof(f128,definition,
( sQ21_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( ~ sQ21_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f131,definition,
( sQ22_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ22_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,definition,
( sQ23_spl
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( ~ sQ23_spl
| product(e_1,e_2,e_3) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,plain,
( sQ23_spl
| sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f116,f128,f131,f134]) ).
fof(f138,definition,
( sQ24_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( ~ sQ24_spl
| product(e_1,e_1,e_1) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f144,definition,
( sQ26_spl
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( ~ sQ26_spl
| product(e_1,e_1,e_3) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f151,plain,
! [X0] :
( ~ sQ8_spl
| product(e_3,X0,e_3)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f79,f45]) ).
fof(f152,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)],[f46,f151]) ).
fof(f154,plain,
( ~ sQ8_spl
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f152,f29]) ).
fof(f157,plain,
( ~ sQ8_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f154,f65,f68,f78]) ).
fof(f169,plain,
! [X0] :
( ~ sQ7_spl
| product(e_2,X0,e_3)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f76,f45]) ).
fof(f173,plain,
! [X0] :
( ~ sQ5_spl
| product(e_3,X0,e_3)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f69,f45]) ).
fof(f174,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)],[f46,f173]) ).
fof(f176,plain,
( ~ sQ5_spl
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f174,f30]) ).
fof(f178,plain,
( ~ sQ5_spl
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f174,f28]) ).
fof(f179,plain,
( ~ sQ5_spl
| sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f176,f52,f58,f68]) ).
fof(f181,plain,
( ~ sQ5_spl
| sQ8_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f178,f72,f78,f68]) ).
fof(f191,plain,
! [X0] :
( ~ sQ4_spl
| product(e_2,X0,e_3)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f66,f45]) ).
fof(f192,plain,
( ~ sQ4_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f191,f66]) ).
fof(f193,plain,
! [X0] :
( ~ sQ4_spl
| equalish(X0,e_2)
| ~ product(X0,e_2,e_3) ),
inference(resolution,[status(thm)],[f192,f43]) ).
fof(f194,plain,
! [X0] :
( ~ sQ4_spl
| equalish(X0,e_2)
| ~ product(e_2,X0,e_3) ),
inference(resolution,[status(thm)],[f192,f41]) ).
fof(f196,plain,
! [X0] :
( ~ sQ4_spl
| product(e_3,X0,e_2)
| ~ product(e_2,X0,e_2) ),
inference(resolution,[status(thm)],[f192,f45]) ).
fof(f204,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f112,f194]) ).
fof(f210,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f31]) ).
fof(f211,plain,
( ~ sQ4_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f210]) ).
fof(f222,plain,
! [X0] :
( ~ sQ16_spl
| product(e_2,X0,e_2)
| ~ product(e_2,X0,e_1) ),
inference(resolution,[status(thm)],[f109,f45]) ).
fof(f223,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)],[f47,f222]) ).
fof(f224,plain,
( ~ sQ16_spl
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[f223,f30]) ).
fof(f227,plain,
( ~ sQ16_spl
| sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f224,f88,f91,f108]) ).
fof(f240,plain,
! [X0] :
( ~ sQ15_spl
| product(e_1,X0,e_2)
| ~ product(e_2,X0,e_1) ),
inference(resolution,[status(thm)],[f106,f45]) ).
fof(f241,plain,
( ~ sQ15_spl
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f240,f106]) ).
fof(f244,plain,
! [X0] :
( ~ sQ15_spl
| equalish(X0,e_1)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f241,f41]) ).
fof(f245,plain,
! [X0] :
( ~ sQ15_spl
| equalish(X0,e_2)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f241,f39]) ).
fof(f264,plain,
! [X0] :
( ~ sQ11_spl
| product(e_3,X0,e_2)
| ~ product(e_2,X0,e_3) ),
inference(resolution,[status(thm)],[f92,f45]) ).
fof(f265,plain,
( ~ sQ11_spl
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f264,f92]) ).
fof(f266,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f264,f102]) ).
fof(f267,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f266,f65,f91,f101]) ).
fof(f268,plain,
( ~ sQ15_spl
| ~ sQ26_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f145,f245]) ).
fof(f273,plain,
! [X0] :
( ~ sQ26_spl
| product(e_3,X0,e_1)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[f145,f45]) ).
fof(f274,plain,
( ~ sQ15_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f268,f36]) ).
fof(f275,plain,
( ~ sQ15_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f274]) ).
fof(f276,plain,
( ~ sQ15_spl
| ~ sQ24_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f139,f245]) ).
fof(f283,plain,
( ~ sQ15_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f276,f31]) ).
fof(f284,plain,
( ~ sQ15_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f283]) ).
fof(f304,plain,
( ~ sQ4_spl
| ~ sQ23_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f135,f193]) ).
fof(f308,plain,
! [X0] :
( ~ sQ23_spl
| product(e_3,X0,e_1)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f135,f45]) ).
fof(f309,plain,
( ~ sQ4_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f304,f31]) ).
fof(f310,plain,
( ~ sQ4_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f309]) ).
fof(f332,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f132,f244]) ).
fof(f336,plain,
! [X0] :
( ~ sQ22_spl
| product(e_2,X0,e_1)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f132,f45]) ).
fof(f337,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f33]) ).
fof(f338,plain,
( ~ sQ15_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f342,plain,
! [X0] :
( ~ sQ21_spl
| product(e_1,X0,e_1)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f129,f45]) ).
fof(f346,plain,
! [X0] :
( ~ sQ20_spl
| product(e_3,X0,e_1)
| ~ product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f125,f45]) ).
fof(f350,plain,
! [X0] :
( ~ sQ1_spl
| product(e_2,X0,e_3)
| ~ product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f56,f45]) ).
fof(f355,plain,
! [X0] :
( ~ sQ6_spl
| product(e_1,X0,e_3)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f73,f45]) ).
fof(f363,plain,
! [X0] :
( ~ sQ3_spl
| product(e_1,X0,e_3)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f63,f45]) ).
fof(f383,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f191,f56]) ).
fof(f384,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)],[f48,f342]) ).
fof(f385,plain,
( ~ sQ21_spl
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f384,f30]) ).
fof(f387,plain,
( ~ sQ21_spl
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f384,f28]) ).
fof(f388,plain,
( ~ sQ21_spl
| sQ20_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f385,f118,f124,f128]) ).
fof(f390,plain,
( ~ sQ21_spl
| sQ26_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f387,f138,f144,f128]) ).
fof(f391,plain,
( ~ sQ20_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f346,f125]) ).
fof(f401,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f383,f194]) ).
fof(f406,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f401,f36]) ).
fof(f407,plain,
( ~ sQ4_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f406]) ).
fof(f408,plain,
( ~ sQ6_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f355,f73]) ).
fof(f409,plain,
! [X0] :
( ~ sQ6_spl
| ~ greater(e_3,X0)
| ~ next(e_1,X0) ),
inference(resolution,[status(thm)],[f408,f27]) ).
fof(f414,plain,
( ~ sQ6_spl
| ~ next(e_1,e_2) ),
inference(resolution,[status(thm)],[f409,f25]) ).
fof(f416,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f414,f21]) ).
fof(f417,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f416]) ).
fof(f424,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f89,f196]) ).
fof(f429,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f424,f55,f88,f65]) ).
fof(f430,plain,
( ~ sQ11_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f265,f55,f91]) ).
fof(f431,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ8_spl
| product(e_3,X0,e_3)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f174,f151]) ).
fof(f445,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| product(e_3,e_2,e_3) ),
inference(resolution,[status(thm)],[f431,f29]) ).
fof(f446,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[f431,f28]) ).
fof(f448,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ8_spl
| equalish(X0,e_2)
| ~ product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f445,f41]) ).
fof(f458,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f350,f59]) ).
fof(f459,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f458,f91,f55,f58]) ).
fof(f461,plain,
( ~ sQ23_spl
| ~ sQ15_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f241,f308]) ).
fof(f467,plain,
( ~ sQ23_spl
| ~ sQ15_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f461,f72,f105,f134]) ).
fof(f471,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f448,f446]) ).
fof(f473,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f471,f31]) ).
fof(f474,plain,
( ~ sQ5_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f473]) ).
fof(f498,plain,
( ~ sQ26_spl
| ~ sQ18_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f119,f273]) ).
fof(f503,plain,
( ~ sQ7_spl
| ~ sQ26_spl
| ~ sQ18_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f498,f169]) ).
fof(f521,plain,
( ~ sQ7_spl
| ~ sQ20_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f391,f169]) ).
fof(f542,plain,
( ~ sQ7_spl
| ~ sQ26_spl
| ~ sQ18_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f503,f91,f118,f144,f75]) ).
fof(f543,plain,
( ~ sQ7_spl
| ~ sQ20_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f521,f91,f124,f75]) ).
fof(f551,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f76,f363]) ).
fof(f557,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f551,f144,f75,f62]) ).
fof(f558,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f53,f169]) ).
fof(f563,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f558,f91,f52,f75]) ).
fof(f564,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f63,f169]) ).
fof(f569,plain,
( ~ sQ22_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f132,f336]) ).
fof(f582,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ3_spl
| equalish(X0,e_3)
| ~ product(e_2,e_2,X0) ),
inference(resolution,[status(thm)],[f564,f39]) ).
fof(f590,plain,
( ~ sQ22_spl
| ~ sQ7_spl
| ~ sQ3_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f582,f569]) ).
fof(f592,plain,
( ~ sQ22_spl
| ~ sQ7_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f590,f32]) ).
fof(f593,plain,
( ~ sQ22_spl
| ~ sQ7_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f592]) ).
fof(f594,plain,
( ~ sQ23_spl
| ~ sQ19_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f122,f308]) ).
fof(f599,plain,
( ~ sQ23_spl
| ~ sQ19_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f594,f52,f121,f134]) ).
fof(f600,plain,
( sQ14_spl
| ~ sQ7_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f564]) ).
fof(f601,plain,
( sQ14_spl
| ~ sQ7_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f600]) ).
fof(f602,plain,
$false,
inference(sat_refutation,[status(thm)],[f61,f71,f81,f94,f114,f127,f137,f157,f179,f181,f211,f227,f267,f275,f284,f310,f338,f388,f390,f407,f417,f429,f430,f459,f467,f474,f542,f543,f557,f563,f593,f599,f601]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP130-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n026.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 20 20:04:08 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.14/0.51 % Refutation found
% 0.14/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.68/0.52 % Elapsed time: 0.149802 seconds
% 0.68/0.52 % CPU time: 0.934732 seconds
% 0.68/0.52 % Total memory used: 21.158 MB
% 0.68/0.52 % Net memory used: 20.609 MB
%------------------------------------------------------------------------------