%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP128-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 12:32:46 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.51s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 39
% Syntax : Number of formulae : 211 ( 17 unt; 27 def)
% Number of atoms : 548 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 620 ( 283 ~; 310 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 31 ( 30 usr; 28 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 84 ( 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
! [X,Y,Z1,Z2] :
( product(X,Z1,Z2)
| ~ product(Z1,Y,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox2/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(f21,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f7]) ).
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,Z1,Z2] :
( product(X,Z1,Z2)
| ! [Y] :
( ~ product(Z1,Y,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( product(X0,X2,X3)
| ~ product(X2,X1,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(f36,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)],[f33,f17]) ).
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(f42,definition,
( sQ1_spl
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( ~ sQ1_spl
| product(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f42]) ).
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(f48,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f39,f42,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(X0,e_3,e_3)
| ~ product(X0,e_1,e_3) ),
inference(resolution,[status(thm)],[f66,f32]) ).
fof(f76,plain,
! [X0] :
( ~ sQ7_spl
| product(X0,e_3,e_2)
| ~ product(X0,e_1,e_3) ),
inference(resolution,[status(thm)],[f63,f32]) ).
fof(f77,plain,
! [X0] :
( ~ sQ6_spl
| equalish(X0,e_3)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f60,f30]) ).
fof(f80,plain,
! [X0] :
( ~ sQ6_spl
| product(X0,e_3,e_1)
| ~ product(X0,e_1,e_3) ),
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(f99,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(f116,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)],[f35,f15]) ).
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(f121,plain,
( ~ sQ19_spl
| product(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f120]) ).
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(f140,definition,
( sQ25_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( ~ sQ25_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f140]) ).
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(f146,plain,
( sQ26_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f116,f137,f140,f143]) ).
fof(f147,plain,
( ~ sQ8_spl
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f72,f66]) ).
fof(f149,plain,
! [X0] :
( ~ sQ8_spl
| equalish(X0,e_3)
| ~ product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f147,f28]) ).
fof(f154,plain,
( ~ sQ8_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f149,f66]) ).
fof(f155,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f19]) ).
fof(f156,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f155]) ).
fof(f160,plain,
! [X0] :
( ~ sQ5_spl
| product(X0,e_3,e_3)
| ~ product(X0,e_2,e_3) ),
inference(resolution,[status(thm)],[f56,f32]) ).
fof(f161,plain,
( ~ sQ5_spl
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f160,f56]) ).
fof(f163,plain,
! [X0] :
( ~ sQ5_spl
| equalish(X0,e_3)
| ~ product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f161,f28]) ).
fof(f168,plain,
( ~ sQ5_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f163,f56]) ).
fof(f169,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f21]) ).
fof(f170,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f169]) ).
fof(f178,plain,
! [X0] :
( ~ sQ3_spl
| product(X0,e_3,e_1)
| ~ product(X0,e_2,e_3) ),
inference(resolution,[status(thm)],[f50,f32]) ).
fof(f179,plain,
! [X0] :
( ~ sQ2_spl
| equalish(X0,e_3)
| ~ product(X0,e_3,e_3) ),
inference(resolution,[status(thm)],[f46,f30]) ).
fof(f184,plain,
( ~ sQ7_spl
| ~ sQ17_spl
| product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[f111,f76]) ).
fof(f194,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ17_spl
| equalish(X0,e_3)
| ~ product(e_2,X0,e_2) ),
inference(resolution,[status(thm)],[f184,f28]) ).
fof(f206,plain,
! [X0] :
( ~ sQ16_spl
| product(X0,e_2,e_2)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f108,f32]) ).
fof(f207,plain,
( ~ sQ16_spl
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f206,f108]) ).
fof(f208,plain,
! [X0] :
( ~ sQ16_spl
| equalish(X0,e_2)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f207,f30]) ).
fof(f213,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f208,f53]) ).
fof(f214,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f23]) ).
fof(f215,plain,
( ~ sQ4_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f214]) ).
fof(f219,plain,
! [X0] :
( ~ sQ15_spl
| product(X0,e_2,e_1)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f105,f32]) ).
fof(f220,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f101,f178]) ).
fof(f226,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ14_spl
| equalish(X0,e_3)
| ~ product(e_2,X0,e_1) ),
inference(resolution,[status(thm)],[f220,f28]) ).
fof(f231,plain,
( ~ sQ15_spl
| ~ sQ3_spl
| ~ sQ14_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f226,f105]) ).
fof(f232,plain,
( ~ sQ15_spl
| ~ sQ3_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f19]) ).
fof(f233,plain,
( ~ sQ15_spl
| ~ sQ3_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f232]) ).
fof(f241,plain,
! [X0] :
( ~ sQ12_spl
| product(X0,e_2,e_1)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f95,f32]) ).
fof(f246,plain,
! [X0] :
( ~ sQ11_spl
| product(X0,e_2,e_3)
| ~ product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f91,f32]) ).
fof(f251,plain,
! [X0] :
( ~ sQ10_spl
| product(X0,e_2,e_2)
| ~ product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f88,f32]) ).
fof(f256,plain,
! [X0] :
( ~ sQ9_spl
| product(X0,e_2,e_1)
| ~ product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f85,f32]) ).
fof(f257,plain,
( ~ sQ6_spl
| ~ sQ26_spl
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f144,f80]) ).
fof(f261,plain,
! [X0] :
( ~ sQ26_spl
| product(X0,e_1,e_3)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f144,f32]) ).
fof(f270,plain,
( ~ sQ15_spl
| ~ sQ25_spl
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f141,f219]) ).
fof(f274,plain,
! [X0] :
( ~ sQ25_spl
| product(X0,e_1,e_2)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f141,f32]) ).
fof(f288,plain,
( ~ sQ3_spl
| ~ sQ23_spl
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f134,f178]) ).
fof(f292,plain,
! [X0] :
( ~ sQ23_spl
| product(X0,e_1,e_3)
| ~ product(X0,e_2,e_1) ),
inference(resolution,[status(thm)],[f134,f32]) ).
fof(f294,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ23_spl
| equalish(X0,e_3)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[f288,f28]) ).
fof(f309,plain,
! [X0] :
( ~ sQ21_spl
| product(X0,e_1,e_1)
| ~ product(X0,e_2,e_1) ),
inference(resolution,[status(thm)],[f128,f32]) ).
fof(f314,plain,
! [X0] :
( ~ sQ20_spl
| product(X0,e_1,e_3)
| ~ product(X0,e_3,e_1) ),
inference(resolution,[status(thm)],[f124,f32]) ).
fof(f315,plain,
( ~ sQ9_spl
| ~ sQ20_spl
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f314,f85]) ).
fof(f316,plain,
( ~ sQ9_spl
| ~ sQ20_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f315,f110,f123,f84]) ).
fof(f317,plain,
( ~ sQ9_spl
| ~ sQ19_spl
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f121,f256]) ).
fof(f322,plain,
( ~ sQ9_spl
| ~ sQ19_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f317,f127,f120,f84]) ).
fof(f325,plain,
( ~ sQ6_spl
| ~ sQ25_spl
| product(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[f274,f60]) ).
fof(f330,plain,
! [X0] :
( ~ sQ18_spl
| product(X0,e_1,e_1)
| ~ product(X0,e_3,e_1) ),
inference(resolution,[status(thm)],[f118,f32]) ).
fof(f331,plain,
( ~ sQ18_spl
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f330,f118]) ).
fof(f332,plain,
( ~ sQ9_spl
| ~ sQ18_spl
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f330,f85]) ).
fof(f341,plain,
( ~ sQ24_spl
| ~ sQ6_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f77,f138]) ).
fof(f344,plain,
( ~ sQ24_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f341,f19]) ).
fof(f345,plain,
( ~ sQ24_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f344]) ).
fof(f347,plain,
( ~ sQ18_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f331,f137,f117]) ).
fof(f352,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ25_spl
| equalish(X0,e_2)
| ~ product(e_3,e_1,X0) ),
inference(resolution,[status(thm)],[f325,f26]) ).
fof(f360,plain,
( ~ sQ6_spl
| ~ sQ25_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f352,f60]) ).
fof(f361,plain,
( ~ sQ6_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f360,f18]) ).
fof(f362,plain,
( ~ sQ6_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f361]) ).
fof(f364,plain,
( ~ sQ6_spl
| ~ sQ26_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f257,f117,f143,f59]) ).
fof(f368,plain,
( ~ sQ16_spl
| ~ sQ22_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f131,f208]) ).
fof(f373,plain,
( ~ sQ16_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f368,f18]) ).
fof(f374,plain,
( ~ sQ16_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f373]) ).
fof(f375,plain,
( ~ sQ11_spl
| ~ sQ1_spl
| product(e_3,e_2,e_3) ),
inference(resolution,[status(thm)],[f43,f246]) ).
fof(f380,plain,
( ~ sQ11_spl
| ~ sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f375,f55,f42,f90]) ).
fof(f381,plain,
( ~ sQ18_spl
| ~ sQ0_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f40,f330]) ).
fof(f385,plain,
! [X0] :
( ~ sQ0_spl
| product(X0,e_3,e_1)
| ~ product(X0,e_3,e_3) ),
inference(resolution,[status(thm)],[f40,f32]) ).
fof(f386,plain,
( ~ sQ18_spl
| ~ sQ0_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f381,f59,f39,f117]) ).
fof(f387,plain,
( ~ sQ21_spl
| ~ sQ3_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f50,f309]) ).
fof(f392,plain,
( ~ sQ21_spl
| ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f387,f59,f49,f127]) ).
fof(f393,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ18_spl
| equalish(X0,e_2)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f332,f30]) ).
fof(f404,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ17_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f194,f98]) ).
fof(f405,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f21]) ).
fof(f406,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f405]) ).
fof(f411,plain,
( ~ sQ18_spl
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f118,f330]) ).
fof(f416,plain,
( ~ sQ15_spl
| ~ sQ7_spl
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f63,f219]) ).
fof(f421,plain,
( ~ sQ15_spl
| ~ sQ7_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f416,f49,f62,f104]) ).
fof(f435,plain,
( ~ sQ12_spl
| ~ sQ22_spl
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f131,f241]) ).
fof(f440,plain,
( ~ sQ12_spl
| ~ sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f435,f127,f130,f94]) ).
fof(f445,plain,
( ~ sQ11_spl
| ~ sQ2_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f179,f91]) ).
fof(f447,plain,
( ~ sQ11_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f445,f21]) ).
fof(f448,plain,
( ~ sQ11_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f447]) ).
fof(f449,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f385,f91]) ).
fof(f450,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f449,f84,f39,f90]) ).
fof(f452,plain,
( ~ sQ24_spl
| ~ sQ9_spl
| ~ sQ18_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f393,f138]) ).
fof(f453,plain,
( ~ sQ24_spl
| ~ sQ9_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f452,f18]) ).
fof(f454,plain,
( ~ sQ24_spl
| ~ sQ9_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f453]) ).
fof(f455,plain,
( ~ sQ15_spl
| ~ sQ26_spl
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f261,f105]) ).
fof(f456,plain,
( ~ sQ15_spl
| ~ sQ26_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f455,f110,f143,f104]) ).
fof(f457,plain,
( ~ sQ15_spl
| ~ sQ25_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f270,f127,f140,f104]) ).
fof(f477,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f219,f63]) ).
fof(f479,plain,
( ~ sQ10_spl
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f88,f251]) ).
fof(f502,plain,
! [X0] :
( ~ sQ10_spl
| equalish(X0,e_2)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f479,f30]) ).
fof(f506,plain,
( ~ sQ22_spl
| ~ sQ10_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f502,f131]) ).
fof(f508,plain,
( ~ sQ22_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f506,f18]) ).
fof(f509,plain,
( ~ sQ22_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f508]) ).
fof(f511,plain,
( ~ sQ3_spl
| ~ sQ23_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f288,f117,f133,f49]) ).
fof(f512,plain,
( sQ13_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f479]) ).
fof(f513,plain,
( sQ13_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f512]) ).
fof(f514,plain,
( ~ sQ7_spl
| ~ sQ17_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f184,f87,f110,f62]) ).
fof(f528,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ23_spl
| product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[f292,f477]) ).
fof(f529,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ23_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f528,f65,f133,f104,f62]) ).
fof(f530,plain,
( ~ sQ18_spl
| ~ sQ3_spl
| ~ sQ23_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f294,f411]) ).
fof(f531,plain,
( ~ sQ18_spl
| ~ sQ3_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f530,f19]) ).
fof(f532,plain,
( ~ sQ18_spl
| ~ sQ3_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f531]) ).
fof(f533,plain,
$false,
inference(sat_refutation,[status(thm)],[f48,f58,f68,f93,f103,f113,f126,f136,f146,f156,f170,f215,f233,f316,f322,f345,f347,f362,f364,f374,f380,f386,f392,f406,f421,f440,f448,f450,f454,f456,f457,f509,f511,f513,f514,f529,f532]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP128-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:00:47 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.51 % Refutation found
% 0.12/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.53 % Elapsed time: 0.165214 seconds
% 0.13/0.53 % CPU time: 1.116940 seconds
% 0.13/0.53 % Total memory used: 20.136 MB
% 0.13/0.53 % Net memory used: 19.622 MB
%------------------------------------------------------------------------------