%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP133-2.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:32:50 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.58s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 38
% Syntax : Number of formulae : 197 ( 24 unt; 21 def)
% Number of atoms : 512 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 605 ( 290 ~; 294 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 27 ( 26 usr; 22 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(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,X)
| ~ product(Y,X,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(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,
! [X,Z1,Z2] :
( product(Z1,Z2,X)
| ! [Y] :
( ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X0)
| ~ 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(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(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(f90,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(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(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(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(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(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(f170,plain,
! [X0] :
( ~ sQ4_spl
| product(X0,e_2,e_2)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f66,f45]) ).
fof(f174,plain,
! [X0] :
( ~ sQ3_spl
| product(X0,e_1,e_2)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f63,f45]) ).
fof(f184,plain,
! [X0] :
( ~ sQ17_spl
| product(X0,e_3,e_1)
| ~ product(e_1,e_2,X0) ),
inference(resolution,[status(thm)],[f112,f45]) ).
fof(f189,plain,
! [X0] :
( ~ sQ16_spl
| product(X0,e_2,e_1)
| ~ product(e_1,e_2,X0) ),
inference(resolution,[status(thm)],[f109,f45]) ).
fof(f194,plain,
! [X0] :
( ~ sQ15_spl
| product(X0,e_1,e_1)
| ~ 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(f202,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_3)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f199,f41]) ).
fof(f214,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f202,f66]) ).
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(f239,plain,
! [X0] :
( ~ sQ12_spl
| equalish(X0,e_1)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f228,f41]) ).
fof(f240,plain,
! [X0] :
( ~ sQ12_spl
| equalish(X0,e_2)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f228,f39]) ).
fof(f241,plain,
! [X0] :
( ~ sQ12_spl
| product(X0,e_2,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f228,f45]) ).
fof(f265,plain,
! [X0] :
( ~ sQ11_spl
| product(X0,e_3,e_3)
| ~ product(e_3,e_2,X0) ),
inference(resolution,[status(thm)],[f92,f45]) ).
fof(f280,plain,
! [X0] :
( ~ sQ10_spl
| product(X0,e_2,e_3)
| ~ product(e_3,e_2,X0) ),
inference(resolution,[status(thm)],[f89,f45]) ).
fof(f322,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f170,f86]) ).
fof(f326,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ4_spl
| equalish(X0,e_1)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f322,f43]) ).
fof(f343,plain,
( ~ sQ12_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f241,f228]) ).
fof(f346,plain,
! [X0] :
( ~ sQ12_spl
| equalish(X0,e_2)
| ~ product(X0,e_2,e_1) ),
inference(resolution,[status(thm)],[f343,f43]) ).
fof(f356,plain,
! [X0] :
( ~ sQ26_spl
| product(X0,e_3,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f145,f45]) ).
fof(f361,plain,
( ~ sQ12_spl
| ~ sQ24_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f139,f240]) ).
fof(f363,plain,
! [X0] :
( ~ sQ24_spl
| equalish(X0,e_1)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f139,f43]) ).
fof(f364,plain,
! [X0] :
( ~ sQ24_spl
| equalish(X0,e_1)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[f139,f41]) ).
fof(f367,plain,
( ~ sQ12_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f361,f31]) ).
fof(f368,plain,
( ~ sQ12_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f367]) ).
fof(f369,plain,
( ~ sQ15_spl
| ~ sQ23_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f135,f194]) ).
fof(f373,plain,
! [X0] :
( ~ sQ23_spl
| product(X0,e_3,e_2)
| ~ product(e_2,e_1,X0) ),
inference(resolution,[status(thm)],[f135,f45]) ).
fof(f378,plain,
! [X0] :
( ~ sQ22_spl
| product(X0,e_2,e_2)
| ~ product(e_2,e_1,X0) ),
inference(resolution,[status(thm)],[f132,f45]) ).
fof(f397,plain,
( ~ sQ22_spl
| ~ sQ16_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f189,f132]) ).
fof(f398,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f189,f135]) ).
fof(f399,plain,
( ~ sQ22_spl
| ~ sQ16_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f397,f95,f108,f131]) ).
fof(f401,plain,
! [X0] :
( ~ sQ23_spl
| ~ sQ16_spl
| equalish(X0,e_3)
| ~ product(X0,e_2,e_1) ),
inference(resolution,[status(thm)],[f398,f43]) ).
fof(f428,plain,
( ~ sQ15_spl
| ~ sQ23_spl
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f373,f106]) ).
fof(f445,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ23_spl
| equalish(X0,e_3)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f369,f43]) ).
fof(f463,plain,
( ~ sQ15_spl
| ~ sQ23_spl
| ~ sQ12_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f239,f428]) ).
fof(f466,plain,
( ~ sQ15_spl
| ~ sQ23_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f463,f35]) ).
fof(f467,plain,
( ~ sQ15_spl
| ~ sQ23_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f466]) ).
fof(f470,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f398,f62,f108,f134]) ).
fof(f480,plain,
( ~ sQ12_spl
| ~ sQ23_spl
| ~ sQ16_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f401,f343]) ).
fof(f481,plain,
( ~ sQ12_spl
| ~ sQ23_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f34]) ).
fof(f482,plain,
( ~ sQ12_spl
| ~ sQ23_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f481]) ).
fof(f502,plain,
! [X0] :
( ~ sQ0_spl
| product(X0,e_1,e_3)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f53,f45]) ).
fof(f503,plain,
( ~ sQ17_spl
| ~ sQ23_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f135,f184]) ).
fof(f534,plain,
( ~ sQ17_spl
| ~ sQ23_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f503,f52,f134,f111]) ).
fof(f565,plain,
! [X0] :
( ~ sQ1_spl
| product(X0,e_2,e_3)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f56,f45]) ).
fof(f566,plain,
( ~ sQ1_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f565,f56]) ).
fof(f567,plain,
( ~ sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f566,f101,f55]) ).
fof(f584,plain,
! [X0] :
( ~ sQ25_spl
| product(X0,e_2,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f142,f45]) ).
fof(f665,plain,
( ~ sQ0_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f53,f502]) ).
fof(f672,plain,
! [X0] :
( ~ sQ0_spl
| ~ greater(e_3,X0)
| ~ next(e_1,X0) ),
inference(resolution,[status(thm)],[f665,f27]) ).
fof(f697,plain,
( ~ sQ12_spl
| ~ sQ21_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f129,f346]) ).
fof(f702,plain,
( ~ sQ12_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f697,f31]) ).
fof(f703,plain,
( ~ sQ12_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f702]) ).
fof(f755,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f132,f194]) ).
fof(f756,plain,
( ~ sQ12_spl
| ~ sQ22_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f132,f239]) ).
fof(f761,plain,
( ~ sQ12_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f756,f33]) ).
fof(f762,plain,
( ~ sQ12_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f761]) ).
fof(f776,plain,
( ~ sQ0_spl
| ~ next(e_1,e_2) ),
inference(resolution,[status(thm)],[f672,f25]) ).
fof(f778,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f776,f21]) ).
fof(f779,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f778]) ).
fof(f835,plain,
( ~ sQ26_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f145,f356]) ).
fof(f841,plain,
( ~ sQ26_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f835,f52,f144]) ).
fof(f860,plain,
( ~ sQ17_spl
| ~ sQ22_spl
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f378,f112]) ).
fof(f861,plain,
( ~ sQ17_spl
| ~ sQ22_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f860,f65,f131,f111]) ).
fof(f909,plain,
( ~ sQ10_spl
| ~ sQ4_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f66,f280]) ).
fof(f914,plain,
( ~ sQ10_spl
| ~ sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f909,f101,f65,f88]) ).
fof(f934,plain,
( ~ sQ16_spl
| ~ sQ23_spl
| product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[f373,f109]) ).
fof(f935,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f174,f89]) ).
fof(f970,plain,
( ~ sQ18_spl
| ~ sQ24_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f364,f119]) ).
fof(f972,plain,
( ~ sQ18_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f970,f35]) ).
fof(f973,plain,
( ~ sQ18_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f972]) ).
fof(f980,plain,
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ4_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f326,f99]) ).
fof(f981,plain,
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f980,f33]) ).
fof(f982,plain,
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f981]) ).
fof(f1004,plain,
( ~ sQ24_spl
| ~ sQ21_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f129,f364]) ).
fof(f1009,plain,
( ~ sQ24_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1004,f33]) ).
fof(f1010,plain,
( ~ sQ24_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f1009]) ).
fof(f1022,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ3_spl
| equalish(X0,e_1)
| ~ product(e_2,X0,e_2) ),
inference(resolution,[status(thm)],[f935,f41]) ).
fof(f1040,plain,
( ~ sQ16_spl
| ~ sQ23_spl
| ~ sQ10_spl
| ~ sQ3_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f1022,f934]) ).
fof(f1043,plain,
( ~ sQ16_spl
| ~ sQ23_spl
| ~ sQ10_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1040,f35]) ).
fof(f1044,plain,
( ~ sQ16_spl
| ~ sQ23_spl
| ~ sQ10_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f1043]) ).
fof(f1045,plain,
( sQ10_spl
| ~ sQ16_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f90,f934]) ).
fof(f1046,plain,
( sQ10_spl
| ~ sQ16_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f1045]) ).
fof(f1053,plain,
( ~ sQ24_spl
| ~ sQ15_spl
| ~ sQ23_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f445,f139]) ).
fof(f1054,plain,
( ~ sQ24_spl
| ~ sQ15_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1053,f32]) ).
fof(f1055,plain,
( ~ sQ24_spl
| ~ sQ15_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f1054]) ).
fof(f1057,plain,
( ~ sQ24_spl
| ~ sQ15_spl
| ~ sQ22_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f755,f363]) ).
fof(f1063,plain,
( ~ sQ24_spl
| ~ sQ15_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1057,f33]) ).
fof(f1064,plain,
( ~ sQ24_spl
| ~ sQ15_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f1063]) ).
fof(f1065,plain,
( ~ sQ11_spl
| ~ sQ4_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f66,f265]) ).
fof(f1071,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ4_spl
| equalish(X0,e_2)
| ~ product(X0,e_3,e_3) ),
inference(resolution,[status(thm)],[f1065,f43]) ).
fof(f1075,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ4_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f1071,f59]) ).
fof(f1077,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1075,f36]) ).
fof(f1078,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1077]) ).
fof(f1114,plain,
( ~ sQ25_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f142,f584]) ).
fof(f1120,plain,
( ~ sQ25_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f1114,f95,f141]) ).
fof(f1121,plain,
$false,
inference(sat_refutation,[status(thm)],[f61,f94,f104,f114,f137,f147,f217,f368,f399,f467,f470,f482,f534,f567,f703,f762,f779,f841,f861,f914,f973,f982,f1010,f1044,f1046,f1055,f1064,f1078,f1120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP133-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 20:04:16 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.12/0.58 % Refutation found
% 0.12/0.58 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.60 % Elapsed time: 0.239190 seconds
% 0.12/0.60 % CPU time: 1.595212 seconds
% 0.12/0.60 % Total memory used: 23.179 MB
% 0.12/0.60 % Net memory used: 22.219 MB
%------------------------------------------------------------------------------