%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP134-2.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 12:32:50 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.59s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 38
% Syntax : Number of formulae : 219 ( 19 unt; 24 def)
% Number of atoms : 602 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 731 ( 348 ~; 359 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 28 ( 27 usr; 25 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 87 ( 87 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
~ equalish(e_3,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(Z1,Z2,Y)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f34,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f35,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(thm)],[f14]) ).
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,
! [Y,Z1,Z2] :
( product(Z1,Z2,Y)
| ! [X] :
( ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X1)
| ~ product(X1,X0,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(f83,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)],[f47,f29]) ).
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(f86,plain,
( ~ sQ9_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f85]) ).
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(f95,definition,
( sQ12_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ12_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,definition,
( sQ13_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f99,plain,
( ~ sQ13_spl
| product(e_2,e_2,e_2) ),
inference(component_clause,[status(thm)],[f98]) ).
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(f104,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f83,f95,f98,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(f117,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)],[f48,f28]) ).
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(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(f133,plain,
( sQ22_spl
| ~ product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f131]) ).
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(f141,definition,
( sQ25_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ25_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f141]) ).
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(f147,plain,
( sQ26_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f117,f138,f141,f144]) ).
fof(f151,plain,
! [X0] :
( ~ sQ8_spl
| product(X0,e_3,e_3)
| ~ product(e_1,e_3,X0) ),
inference(resolution,[status(thm)],[f79,f45]) ).
fof(f162,plain,
! [X0] :
( ~ sQ6_spl
| product(X0,e_1,e_3)
| ~ product(e_1,e_3,X0) ),
inference(resolution,[status(thm)],[f73,f45]) ).
fof(f166,plain,
! [X0] :
( ~ sQ5_spl
| product(X0,e_3,e_3)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f69,f45]) ).
fof(f170,plain,
! [X0] :
( ~ sQ4_spl
| product(X0,e_2,e_3)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f66,f45]) ).
fof(f174,plain,
! [X0] :
( ~ sQ3_spl
| product(X0,e_1,e_3)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f63,f45]) ).
fof(f184,plain,
! [X0] :
( ~ sQ17_spl
| product(X0,e_3,e_2)
| ~ product(e_1,e_2,X0) ),
inference(resolution,[status(thm)],[f112,f45]) ).
fof(f189,plain,
! [X0] :
( ~ sQ16_spl
| product(X0,e_2,e_2)
| ~ product(e_1,e_2,X0) ),
inference(resolution,[status(thm)],[f109,f45]) ).
fof(f194,plain,
! [X0] :
( ~ sQ15_spl
| product(X0,e_1,e_2)
| ~ product(e_1,e_2,X0) ),
inference(resolution,[status(thm)],[f106,f45]) ).
fof(f198,plain,
! [X0] :
( ~ sQ14_spl
| product(X0,e_3,e_2)
| ~ product(e_2,e_2,X0) ),
inference(resolution,[status(thm)],[f102,f45]) ).
fof(f199,plain,
( ~ sQ14_spl
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f198,f102]) ).
fof(f201,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_3)
| ~ product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f199,f43]) ).
fof(f202,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_3)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f199,f41]) ).
fof(f203,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_2)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f199,f39]) ).
fof(f214,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f202,f66]) ).
fof(f215,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f202,f76]) ).
fof(f216,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f214,f34]) ).
fof(f217,plain,
( ~ sQ4_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f216]) ).
fof(f227,plain,
! [X0] :
( ~ sQ12_spl
| product(X0,e_1,e_2)
| ~ product(e_2,e_2,X0) ),
inference(resolution,[status(thm)],[f96,f45]) ).
fof(f228,plain,
( ~ sQ12_spl
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f227,f96]) ).
fof(f238,plain,
! [X0] :
( ~ sQ12_spl
| equalish(X0,e_1)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f228,f43]) ).
fof(f240,plain,
! [X0] :
( ~ sQ12_spl
| equalish(X0,e_2)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f228,f39]) ).
fof(f259,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[f92,f174]) ).
fof(f260,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f92,f166]) ).
fof(f264,plain,
! [X0] :
( ~ sQ11_spl
| product(X0,e_3,e_2)
| ~ product(e_3,e_2,X0) ),
inference(resolution,[status(thm)],[f92,f45]) ).
fof(f265,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f264,f63]) ).
fof(f266,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f264,f69]) ).
fof(f286,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f203,f59]) ).
fof(f287,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f286,f36]) ).
fof(f288,plain,
( ~ sQ2_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f296,plain,
( ~ sQ16_spl
| ~ sQ12_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f238,f109]) ).
fof(f297,plain,
( ~ sQ16_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f296,f33]) ).
fof(f298,plain,
( ~ sQ16_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f297]) ).
fof(f299,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f89,f170]) ).
fof(f300,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f89,f166]) ).
fof(f304,plain,
! [X0] :
( ~ sQ10_spl
| product(X0,e_2,e_2)
| ~ product(e_3,e_2,X0) ),
inference(resolution,[status(thm)],[f89,f45]) ).
fof(f305,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f299,f101,f88,f65]) ).
fof(f306,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f300,f91,f88,f68]) ).
fof(f320,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f86,f174]) ).
fof(f324,plain,
! [X0] :
( ~ sQ9_spl
| product(X0,e_1,e_2)
| ~ product(e_3,e_2,X0) ),
inference(resolution,[status(thm)],[f86,f45]) ).
fof(f329,plain,
! [X0] :
( ~ sQ26_spl
| product(X0,e_3,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f145,f45]) ).
fof(f334,plain,
! [X0] :
( ~ sQ25_spl
| product(X0,e_2,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f142,f45]) ).
fof(f346,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f132,f194]) ).
fof(f359,plain,
( ~ sQ6_spl
| ~ sQ20_spl
| product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[f125,f162]) ).
fof(f368,plain,
( ~ sQ14_spl
| ~ sQ19_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f122,f201]) ).
fof(f372,plain,
! [X0] :
( ~ sQ19_spl
| product(X0,e_2,e_1)
| ~ product(e_3,e_1,X0) ),
inference(resolution,[status(thm)],[f122,f45]) ).
fof(f373,plain,
( ~ sQ14_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f368,f32]) ).
fof(f374,plain,
( ~ sQ14_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f373]) ).
fof(f385,plain,
( ~ sQ24_spl
| ~ sQ12_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f240,f139]) ).
fof(f387,plain,
( ~ sQ26_spl
| ~ sQ12_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f240,f145]) ).
fof(f388,plain,
( ~ sQ24_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f385,f31]) ).
fof(f389,plain,
( ~ sQ24_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f388]) ).
fof(f390,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f265,f121,f91,f62]) ).
fof(f391,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f260,f58,f91,f68]) ).
fof(f394,plain,
( ~ sQ26_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f329,f145]) ).
fof(f399,plain,
( ~ sQ26_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f387,f36]) ).
fof(f400,plain,
( ~ sQ26_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f399]) ).
fof(f425,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f320,f144,f85,f62]) ).
fof(f433,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f334,f228]) ).
fof(f438,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| equalish(X0,e_2)
| ~ product(X0,e_2,e_1) ),
inference(resolution,[status(thm)],[f433,f43]) ).
fof(f446,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f346,f108,f131,f105]) ).
fof(f473,plain,
! [X0] :
( ~ sQ0_spl
| product(X0,e_1,e_3)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f53,f45]) ).
fof(f483,plain,
! [X0] :
( ~ sQ1_spl
| product(X0,e_2,e_3)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f56,f45]) ).
fof(f484,plain,
( ~ sQ1_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f483,f56]) ).
fof(f485,plain,
( ~ sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f484,f101,f55]) ).
fof(f486,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f215,f32]) ).
fof(f487,plain,
( ~ sQ7_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f486]) ).
fof(f508,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f63,f304]) ).
fof(f509,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ3_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f63,f438]) ).
fof(f514,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f36]) ).
fof(f515,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f514]) ).
fof(f516,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f266,f55,f91,f68]) ).
fof(f528,plain,
! [X0] :
( ~ sQ26_spl
| equalish(X0,e_3)
| ~ product(X0,e_3,e_1) ),
inference(resolution,[status(thm)],[f394,f43]) ).
fof(f544,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f324,f66]) ).
fof(f545,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f544,f108,f85,f65]) ).
fof(f546,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f86,f166]) ).
fof(f554,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ9_spl
| equalish(X0,e_1)
| ~ product(X0,e_3,e_3) ),
inference(resolution,[status(thm)],[f546,f43]) ).
fof(f578,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[f264,f66]) ).
fof(f579,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f578,f88,f91,f65]) ).
fof(f594,plain,
( ~ sQ19_spl
| ~ sQ3_spl
| ~ sQ11_spl
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f259,f372]) ).
fof(f598,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ11_spl
| equalish(X0,e_1)
| ~ product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f259,f41]) ).
fof(f606,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ3_spl
| ~ sQ11_spl
| equalish(X0,e_2)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f594,f41]) ).
fof(f609,plain,
( ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ3_spl
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f508,f189]) ).
fof(f610,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ3_spl
| equalish(X0,e_1)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f508,f43]) ).
fof(f653,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ9_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f554,f59]) ).
fof(f654,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f653,f35]) ).
fof(f655,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f654]) ).
fof(f700,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ11_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f598,f59]) ).
fof(f701,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f700,f35]) ).
fof(f702,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f701]) ).
fof(f703,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f66,f324]) ).
fof(f711,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ4_spl
| equalish(X0,e_1)
| ~ product(e_2,X0,e_2) ),
inference(resolution,[status(thm)],[f703,f41]) ).
fof(f727,plain,
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ4_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f711,f99]) ).
fof(f728,plain,
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f727,f33]) ).
fof(f729,plain,
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f728]) ).
fof(f775,plain,
( ~ sQ6_spl
| ~ sQ20_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f359,f78,f124,f72]) ).
fof(f780,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_3)
| ~ product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f199,f43]) ).
fof(f799,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ8_spl
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f151,f546]) ).
fof(f800,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f799,f58,f78,f85,f68]) ).
fof(f843,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f546,f124,f85,f68]) ).
fof(f885,plain,
( ~ sQ0_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f53,f473]) ).
fof(f886,plain,
( ~ sQ19_spl
| ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ0_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f53,f606]) ).
fof(f891,plain,
( ~ sQ0_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f885,f144,f52]) ).
fof(f892,plain,
( ~ sQ19_spl
| ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f886,f36]) ).
fof(f893,plain,
( ~ sQ19_spl
| ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f892]) ).
fof(f917,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ17_spl
| product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[f184,f508]) ).
fof(f919,plain,
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ17_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f917,f780]) ).
fof(f921,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ17_spl
| equalish(X0,e_3)
| ~ product(e_2,X0,e_2) ),
inference(resolution,[status(thm)],[f917,f41]) ).
fof(f924,plain,
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f919,f34]) ).
fof(f925,plain,
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f924]) ).
fof(f940,plain,
( sQ22_spl
| ~ sQ10_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f508]) ).
fof(f941,plain,
( sQ22_spl
| ~ sQ10_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f940]) ).
fof(f946,plain,
( ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ3_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f610,f609]) ).
fof(f948,plain,
( ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f946,f33]) ).
fof(f949,plain,
( ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f948]) ).
fof(f985,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ13_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f99,f921]) ).
fof(f991,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f985,f34]) ).
fof(f992,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f991]) ).
fof(f1032,plain,
( ~ sQ9_spl
| ~ sQ26_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f528,f86]) ).
fof(f1033,plain,
( ~ sQ9_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1032,f34]) ).
fof(f1034,plain,
( ~ sQ9_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f1033]) ).
fof(f1035,plain,
$false,
inference(sat_refutation,[status(thm)],[f61,f71,f81,f94,f104,f114,f147,f217,f288,f298,f305,f306,f374,f389,f390,f391,f400,f425,f446,f485,f487,f515,f516,f545,f579,f655,f702,f729,f775,f800,f843,f891,f893,f925,f941,f949,f992,f1034]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP134-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 19:59:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.59 % Refutation found
% 0.13/0.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.60 % Elapsed time: 0.233563 seconds
% 0.13/0.60 % CPU time: 1.646008 seconds
% 0.13/0.60 % Total memory used: 23.387 MB
% 0.13/0.60 % Net memory used: 22.415 MB
%------------------------------------------------------------------------------