%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP134-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 0.53s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 41
% Syntax : Number of formulae : 331 ( 19 unt; 27 def)
% Number of atoms : 992 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1292 ( 631 ~; 634 |; 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 : 108 ( 108 !; 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(f6,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
~ equalish(e_3,e_1),
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(Z1,Z2,Y)
| ~ product(Y,X,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(f20,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(thm)],[f8]) ).
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,
! [Y,Z1,Z2] :
( product(Z1,Z2,Y)
| ! [X] :
( ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0] :
( product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f24,f17]) ).
fof(f34,plain,
! [X0] :
( product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f24,f16]) ).
fof(f35,plain,
! [X0] :
( product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f24,f15]) ).
fof(f37,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f33,f16]) ).
fof(f38,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f33,f15]) ).
fof(f39,definition,
( sQ0_spl
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( ~ sQ0_spl
| product(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(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(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(f61,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(f64,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(e_1,e_3,X0) ),
inference(resolution,[status(thm)],[f66,f32]) ).
fof(f76,plain,
! [X0] :
( ~ sQ7_spl
| product(X0,e_2,e_3)
| ~ product(e_1,e_3,X0) ),
inference(resolution,[status(thm)],[f63,f32]) ).
fof(f80,plain,
! [X0] :
( ~ sQ6_spl
| product(X0,e_1,e_3)
| ~ product(e_1,e_3,X0) ),
inference(resolution,[status(thm)],[f60,f32]) ).
fof(f81,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f34,f17]) ).
fof(f82,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f34,f16]) ).
fof(f83,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f34,f15]) ).
fof(f84,definition,
( sQ9_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( ~ sQ9_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,definition,
( sQ10_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ10_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,definition,
( sQ11_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ11_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( sQ11_spl
| sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f81,f84,f87,f90]) ).
fof(f94,definition,
( sQ12_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ12_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
( sQ13_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ13_spl
| product(e_2,e_2,e_2) ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,definition,
( sQ14_spl
<=> product(e_2,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( ~ sQ14_spl
| product(e_2,e_2,e_3) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f82,f94,f97,f100]) ).
fof(f104,definition,
( sQ15_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( ~ sQ15_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,definition,
( sQ16_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ16_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,definition,
( sQ17_spl
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ17_spl
| product(e_2,e_1,e_3) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( sQ17_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f83,f104,f107,f110]) ).
fof(f114,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f35,f17]) ).
fof(f115,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f35,f16]) ).
fof(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(f150,plain,
! [X0] :
( ~ sQ5_spl
| product(X0,e_3,e_3)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f56,f32]) ).
fof(f154,plain,
! [X0] :
( ~ sQ4_spl
| product(X0,e_2,e_3)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f53,f32]) ).
fof(f158,plain,
! [X0] :
( ~ sQ3_spl
| product(X0,e_1,e_3)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f50,f32]) ).
fof(f167,plain,
! [X0] :
( ~ sQ17_spl
| product(X0,e_3,e_2)
| ~ product(e_1,e_2,X0) ),
inference(resolution,[status(thm)],[f111,f32]) ).
fof(f171,plain,
! [X0] :
( ~ sQ16_spl
| product(X0,e_2,e_2)
| ~ product(e_1,e_2,X0) ),
inference(resolution,[status(thm)],[f108,f32]) ).
fof(f175,plain,
! [X0] :
( ~ sQ15_spl
| product(X0,e_1,e_2)
| ~ product(e_1,e_2,X0) ),
inference(resolution,[status(thm)],[f105,f32]) ).
fof(f179,plain,
! [X0] :
( ~ sQ14_spl
| product(X0,e_3,e_2)
| ~ product(e_2,e_2,X0) ),
inference(resolution,[status(thm)],[f101,f32]) ).
fof(f180,plain,
( ~ sQ14_spl
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f179,f101]) ).
fof(f183,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_3)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f180,f28]) ).
fof(f185,plain,
! [X0] :
( ~ sQ14_spl
| product(X0,e_2,e_3)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f180,f32]) ).
fof(f196,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f183,f63]) ).
fof(f202,plain,
! [X0] :
( ~ sQ13_spl
| product(X0,e_2,e_2)
| ~ product(e_2,e_2,X0) ),
inference(resolution,[status(thm)],[f98,f32]) ).
fof(f204,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f95,f202]) ).
fof(f208,plain,
! [X0] :
( ~ sQ12_spl
| product(X0,e_1,e_2)
| ~ product(e_2,e_2,X0) ),
inference(resolution,[status(thm)],[f95,f32]) ).
fof(f209,plain,
( ~ sQ12_spl
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f208,f95]) ).
fof(f214,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ12_spl
| equalish(X0,e_1)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f204,f30]) ).
fof(f218,plain,
! [X0] :
( ~ sQ12_spl
| equalish(X0,e_1)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f209,f30]) ).
fof(f219,plain,
! [X0] :
( ~ sQ12_spl
| equalish(X0,e_1)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f209,f28]) ).
fof(f220,plain,
! [X0] :
( ~ sQ12_spl
| equalish(X0,e_2)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f209,f26]) ).
fof(f229,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f214,f98]) ).
fof(f230,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f229,f20]) ).
fof(f231,plain,
( ~ sQ13_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f230]) ).
fof(f232,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[f91,f158]) ).
fof(f233,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f91,f150]) ).
fof(f237,plain,
! [X0] :
( ~ sQ11_spl
| product(X0,e_3,e_2)
| ~ product(e_3,e_2,X0) ),
inference(resolution,[status(thm)],[f91,f32]) ).
fof(f238,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f237,f50]) ).
fof(f239,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f237,f56]) ).
fof(f240,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ11_spl
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f238,f80]) ).
fof(f241,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ11_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f238,f76]) ).
fof(f243,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ11_spl
| equalish(X0,e_1)
| ~ product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f238,f30]) ).
fof(f244,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ11_spl
| equalish(X0,e_3)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f238,f28]) ).
fof(f247,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f241,f100,f90,f49,f62]) ).
fof(f267,plain,
( ~ sQ16_spl
| ~ sQ12_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f218,f108]) ).
fof(f268,plain,
( ~ sQ16_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f267,f20]) ).
fof(f269,plain,
( ~ sQ16_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f268]) ).
fof(f270,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f88,f154]) ).
fof(f271,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f88,f150]) ).
fof(f275,plain,
! [X0] :
( ~ sQ10_spl
| product(X0,e_2,e_2)
| ~ product(e_3,e_2,X0) ),
inference(resolution,[status(thm)],[f88,f32]) ).
fof(f276,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f270,f100,f87,f52]) ).
fof(f277,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f271,f90,f87,f55]) ).
fof(f285,plain,
( ~ sQ14_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f185,f180]) ).
fof(f287,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_2)
| ~ product(X0,e_2,e_3) ),
inference(resolution,[status(thm)],[f285,f30]) ).
fof(f288,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_2)
| ~ product(e_2,X0,e_3) ),
inference(resolution,[status(thm)],[f285,f28]) ).
fof(f293,plain,
( ~ sQ17_spl
| ~ sQ14_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f288,f111]) ).
fof(f294,plain,
( ~ sQ17_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f293,f18]) ).
fof(f295,plain,
( ~ sQ17_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f294]) ).
fof(f298,plain,
! [X0] :
( ~ sQ12_spl
| equalish(X0,e_2)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f209,f26]) ).
fof(f309,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f85,f158]) ).
fof(f313,plain,
! [X0] :
( ~ sQ9_spl
| product(X0,e_1,e_2)
| ~ product(e_3,e_2,X0) ),
inference(resolution,[status(thm)],[f85,f32]) ).
fof(f315,plain,
( ~ sQ12_spl
| ~ sQ26_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f144,f220]) ).
fof(f319,plain,
! [X0] :
( ~ sQ26_spl
| product(X0,e_3,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f144,f32]) ).
fof(f320,plain,
( ~ sQ12_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f315,f23]) ).
fof(f321,plain,
( ~ sQ12_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f320]) ).
fof(f325,plain,
! [X0] :
( ~ sQ25_spl
| product(X0,e_2,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f141,f32]) ).
fof(f329,plain,
! [X0] :
( ~ sQ24_spl
| product(X0,e_1,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f138,f32]) ).
fof(f330,plain,
( ~ sQ15_spl
| ~ sQ23_spl
| product(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[f134,f175]) ).
fof(f334,plain,
! [X0] :
( ~ sQ23_spl
| product(X0,e_3,e_1)
| ~ product(e_2,e_1,X0) ),
inference(resolution,[status(thm)],[f134,f32]) ).
fof(f335,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f131,f175]) ).
fof(f339,plain,
! [X0] :
( ~ sQ22_spl
| product(X0,e_2,e_1)
| ~ product(e_2,e_1,X0) ),
inference(resolution,[status(thm)],[f131,f32]) ).
fof(f340,plain,
( ~ sQ15_spl
| ~ sQ21_spl
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f128,f175]) ).
fof(f344,plain,
! [X0] :
( ~ sQ21_spl
| product(X0,e_1,e_1)
| ~ product(e_2,e_1,X0) ),
inference(resolution,[status(thm)],[f128,f32]) ).
fof(f349,plain,
! [X0] :
( ~ sQ20_spl
| product(X0,e_3,e_1)
| ~ product(e_3,e_1,X0) ),
inference(resolution,[status(thm)],[f124,f32]) ).
fof(f350,plain,
( ~ sQ8_spl
| ~ sQ19_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f121,f72]) ).
fof(f354,plain,
! [X0] :
( ~ sQ19_spl
| product(X0,e_2,e_1)
| ~ product(e_3,e_1,X0) ),
inference(resolution,[status(thm)],[f121,f32]) ).
fof(f355,plain,
( ~ sQ8_spl
| ~ sQ19_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f350,f90,f120,f65]) ).
fof(f357,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ9_spl
| equalish(X0,e_1)
| ~ product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f309,f28]) ).
fof(f360,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ23_spl
| equalish(X0,e_3)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f330,f30]) ).
fof(f365,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ22_spl
| equalish(X0,e_1)
| ~ product(e_2,X0,e_2) ),
inference(resolution,[status(thm)],[f335,f28]) ).
fof(f370,plain,
( ~ sQ23_spl
| ~ sQ3_spl
| ~ sQ9_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f357,f134]) ).
fof(f374,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f240,f110,f90,f49,f59]) ).
fof(f375,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f19]) ).
fof(f376,plain,
( ~ sQ7_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f375]) ).
fof(f377,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f335,f107,f130,f104]) ).
fof(f378,plain,
( sQ7_spl
| ~ sQ15_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f64,f330]) ).
fof(f379,plain,
( sQ7_spl
| ~ sQ15_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f378]) ).
fof(f381,plain,
( ~ sQ25_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f325,f141]) ).
fof(f384,plain,
( ~ sQ15_spl
| ~ sQ21_spl
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f344,f105]) ).
fof(f396,plain,
( ~ sQ24_spl
| ~ sQ12_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f298,f138]) ).
fof(f398,plain,
( ~ sQ24_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f396,f18]) ).
fof(f399,plain,
( ~ sQ24_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f398]) ).
fof(f400,plain,
( ~ sQ25_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f381,f94,f140]) ).
fof(f401,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f233,f45,f90,f55]) ).
fof(f402,plain,
( ~ sQ15_spl
| ~ sQ21_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f384,f137,f127,f104]) ).
fof(f419,plain,
( ~ sQ6_spl
| ~ sQ18_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f118,f80]) ).
fof(f423,plain,
! [X0] :
( ~ sQ18_spl
| product(X0,e_1,e_1)
| ~ product(e_3,e_1,X0) ),
inference(resolution,[status(thm)],[f118,f32]) ).
fof(f424,plain,
( ~ sQ24_spl
| ~ sQ6_spl
| ~ sQ18_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f419,f329]) ).
fof(f427,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ18_spl
| equalish(X0,e_3)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f419,f26]) ).
fof(f439,plain,
( ~ sQ24_spl
| ~ sQ6_spl
| ~ sQ18_spl
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f423,f424]) ).
fof(f440,plain,
( ~ sQ6_spl
| ~ sQ18_spl
| ~ sQ24_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f439,f427]) ).
fof(f447,plain,
( ~ sQ6_spl
| ~ sQ18_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f440,f19]) ).
fof(f448,plain,
( ~ sQ6_spl
| ~ sQ18_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f447]) ).
fof(f449,plain,
( ~ sQ18_spl
| ~ sQ7_spl
| product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f76,f118]) ).
fof(f472,plain,
! [X0] :
( ~ sQ0_spl
| product(X0,e_1,e_3)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f40,f32]) ).
fof(f473,plain,
( ~ sQ0_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f472,f40]) ).
fof(f479,plain,
( ~ sQ24_spl
| ~ sQ0_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f473,f329]) ).
fof(f480,plain,
! [X0] :
( ~ sQ0_spl
| equalish(X0,e_1)
| ~ product(X0,e_1,e_3) ),
inference(resolution,[status(thm)],[f473,f30]) ).
fof(f491,plain,
( ~ sQ17_spl
| ~ sQ21_spl
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f128,f167]) ).
fof(f492,plain,
( ~ sQ16_spl
| ~ sQ21_spl
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f128,f171]) ).
fof(f497,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ21_spl
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f491,f80]) ).
fof(f524,plain,
( ~ sQ22_spl
| ~ sQ17_spl
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f111,f339]) ).
fof(f535,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ11_spl
| equalish(X0,e_3)
| ~ product(X0,e_1,e_3) ),
inference(resolution,[status(thm)],[f232,f30]) ).
fof(f536,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ11_spl
| equalish(X0,e_1)
| ~ product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f232,f28]) ).
fof(f547,plain,
( ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ11_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f535,f111]) ).
fof(f549,plain,
( ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f547,f21]) ).
fof(f550,plain,
( ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f551,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ22_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f365,f98]) ).
fof(f552,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f551,f20]) ).
fof(f553,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f554,plain,
( ~ sQ22_spl
| ~ sQ17_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f524,f49,f110,f130]) ).
fof(f556,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ21_spl
| equalish(X0,e_3)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f491,f28]) ).
fof(f560,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ11_spl
| equalish(X0,e_3)
| ~ product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f239,f30]) ).
fof(f562,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ11_spl
| equalish(X0,e_2)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f239,f26]) ).
fof(f604,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ1_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f43,f243]) ).
fof(f609,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f604,f22]) ).
fof(f610,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f609]) ).
fof(f612,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ22_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f131,f244]) ).
fof(f617,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f612,f21]) ).
fof(f618,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f617]) ).
fof(f619,plain,
( ~ sQ16_spl
| ~ sQ21_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f492,f130,f127,f107]) ).
fof(f620,plain,
( ~ sQ15_spl
| ~ sQ21_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f340,f140,f127,f104]) ).
fof(f622,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ2_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f46,f536]) ).
fof(f628,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f622,f22]) ).
fof(f629,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f628]) ).
fof(f641,plain,
( ~ sQ22_spl
| ~ sQ16_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f108,f339]) ).
fof(f646,plain,
( ~ sQ22_spl
| ~ sQ16_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f641,f94,f107,f130]) ).
fof(f647,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ19_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f121,f560]) ).
fof(f652,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f647,f19]) ).
fof(f653,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f652]) ).
fof(f654,plain,
( ~ sQ24_spl
| ~ sQ0_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f479,f59,f39,f137]) ).
fof(f661,plain,
! [X0] :
( ~ sQ0_spl
| equalish(X0,e_1)
| ~ product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f473,f28]) ).
fof(f677,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ21_spl
| ~ sQ0_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f480,f497]) ).
fof(f679,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ21_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f677,f20]) ).
fof(f680,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ21_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f679]) ).
fof(f683,plain,
( ~ sQ11_spl
| ~ sQ4_spl
| product(e_3,e_2,e_3) ),
inference(resolution,[status(thm)],[f154,f91]) ).
fof(f684,plain,
( ~ sQ11_spl
| ~ sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f683,f55,f52,f90]) ).
fof(f685,plain,
( ~ sQ19_spl
| ~ sQ15_spl
| ~ sQ23_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f330,f354]) ).
fof(f690,plain,
( ~ sQ19_spl
| ~ sQ15_spl
| ~ sQ23_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f685,f94,f133,f104,f120]) ).
fof(f706,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f472,f180]) ).
fof(f707,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f706,f110,f39,f100]) ).
fof(f718,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f50,f275]) ).
fof(f723,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f718,f130,f49,f87]) ).
fof(f724,plain,
( ~ sQ19_spl
| ~ sQ6_spl
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f60,f354]) ).
fof(f729,plain,
( ~ sQ19_spl
| ~ sQ6_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f724,f127,f59,f120]) ).
fof(f733,plain,
( ~ sQ14_spl
| ~ sQ23_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f134,f287]) ).
fof(f739,plain,
( ~ sQ14_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f733,f18]) ).
fof(f740,plain,
( ~ sQ14_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f739]) ).
fof(f756,plain,
( ~ sQ21_spl
| ~ sQ17_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f111,f344]) ).
fof(f770,plain,
! [X0] :
( ~ sQ21_spl
| ~ sQ17_spl
| equalish(X0,e_3)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f756,f30]) ).
fof(f787,plain,
( ~ sQ24_spl
| ~ sQ21_spl
| ~ sQ17_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f770,f138]) ).
fof(f788,plain,
( ~ sQ24_spl
| ~ sQ21_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f787,f19]) ).
fof(f789,plain,
( ~ sQ24_spl
| ~ sQ21_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f788]) ).
fof(f794,plain,
( ~ sQ17_spl
| ~ sQ21_spl
| ~ sQ12_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f209,f556]) ).
fof(f799,plain,
( ~ sQ17_spl
| ~ sQ21_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f794,f19]) ).
fof(f800,plain,
( ~ sQ17_spl
| ~ sQ21_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f799]) ).
fof(f803,plain,
( ~ sQ9_spl
| ~ sQ5_spl
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f150,f85]) ).
fof(f804,plain,
( ~ sQ9_spl
| ~ sQ5_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f803,f123,f55,f84]) ).
fof(f805,plain,
( ~ sQ17_spl
| ~ sQ22_spl
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f339,f111]) ).
fof(f806,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ22_spl
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f805,f275]) ).
fof(f814,plain,
( sQ6_spl
| ~ sQ21_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f756]) ).
fof(f815,plain,
( sQ6_spl
| ~ sQ21_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f814]) ).
fof(f830,plain,
( ~ sQ26_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f144,f319]) ).
fof(f836,plain,
( ~ sQ26_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f830,f39,f143]) ).
fof(f840,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f309,f143,f84,f49]) ).
fof(f846,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ22_spl
| equalish(X0,e_1)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f806,f30]) ).
fof(f861,plain,
( ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ22_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f846,f98]) ).
fof(f862,plain,
( ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f861,f20]) ).
fof(f863,plain,
( ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f862]) ).
fof(f869,plain,
( ~ sQ17_spl
| ~ sQ23_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f334,f111]) ).
fof(f870,plain,
( ~ sQ17_spl
| ~ sQ23_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f869,f39,f133,f110]) ).
fof(f888,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ23_spl
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f330,f423]) ).
fof(f894,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ23_spl
| equalish(X0,e_2)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f888,f30]) ).
fof(f903,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ11_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f562,f46]) ).
fof(f904,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f903,f23]) ).
fof(f905,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f904]) ).
fof(f933,plain,
( ~ sQ18_spl
| ~ sQ8_spl
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f72,f118]) ).
fof(f934,plain,
( ~ sQ8_spl
| ~ sQ18_spl
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f933,f72]) ).
fof(f935,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ8_spl
| equalish(X0,e_1)
| ~ product(X0,e_3,e_3) ),
inference(resolution,[status(thm)],[f933,f30]) ).
fof(f940,plain,
( ~ sQ2_spl
| ~ sQ18_spl
| ~ sQ8_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f935,f46]) ).
fof(f941,plain,
( ~ sQ2_spl
| ~ sQ18_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f940,f22]) ).
fof(f942,plain,
( ~ sQ2_spl
| ~ sQ18_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f941]) ).
fof(f943,plain,
( ~ sQ8_spl
| ~ sQ18_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f934,f45,f117,f65]) ).
fof(f944,plain,
( ~ sQ16_spl
| ~ sQ23_spl
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f134,f171]) ).
fof(f950,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ23_spl
| equalish(X0,e_3)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f944,f30]) ).
fof(f965,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ23_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f950,f98]) ).
fof(f966,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f965,f21]) ).
fof(f967,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f966]) ).
fof(f968,plain,
( ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ23_spl
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f330,f349]) ).
fof(f990,plain,
( ~ sQ24_spl
| ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ23_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f894,f138]) ).
fof(f992,plain,
( ~ sQ24_spl
| ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f990,f18]) ).
fof(f993,plain,
( ~ sQ24_spl
| ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f992]) ).
fof(f995,plain,
( ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ23_spl
| ~ sQ5_spl
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f150,f968]) ).
fof(f1001,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ23_spl
| ~ sQ5_spl
| equalish(X0,e_3)
| ~ product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f995,f28]) ).
fof(f1011,plain,
( ~ sQ23_spl
| ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ5_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f1001,f134]) ).
fof(f1012,plain,
( ~ sQ23_spl
| ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1011,f21]) ).
fof(f1013,plain,
( ~ sQ23_spl
| ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f1012]) ).
fof(f1020,plain,
( ~ sQ7_spl
| ~ sQ20_spl
| product(e_3,e_2,e_3) ),
inference(resolution,[status(thm)],[f124,f76]) ).
fof(f1025,plain,
( ~ sQ7_spl
| ~ sQ20_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f1020,f55,f123,f62]) ).
fof(f1026,plain,
( ~ sQ0_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f473,f143,f39]) ).
fof(f1057,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ22_spl
| ~ sQ12_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f219,f806]) ).
fof(f1059,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ22_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1057,f20]) ).
fof(f1060,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ22_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1059]) ).
fof(f1085,plain,
( ~ sQ20_spl
| ~ sQ0_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f661,f124]) ).
fof(f1086,plain,
( ~ sQ20_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1085,f22]) ).
fof(f1087,plain,
( ~ sQ20_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1086]) ).
fof(f1088,plain,
( ~ sQ23_spl
| ~ sQ3_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f370,f20]) ).
fof(f1089,plain,
( ~ sQ23_spl
| ~ sQ3_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1088]) ).
fof(f1092,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| ~ sQ7_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f449,f661]) ).
fof(f1097,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1092,f20]) ).
fof(f1098,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1097]) ).
fof(f1129,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ23_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f360,f209]) ).
fof(f1130,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1129,f19]) ).
fof(f1131,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f1130]) ).
fof(f1132,plain,
( ~ sQ9_spl
| ~ sQ17_spl
| ~ sQ22_spl
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f805,f313]) ).
fof(f1137,plain,
( ~ sQ9_spl
| ~ sQ17_spl
| ~ sQ22_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f1132,f140,f130,f110,f84]) ).
fof(f1160,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f154,f85]) ).
fof(f1161,plain,
( ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ4_spl
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f1160,f167]) ).
fof(f1169,plain,
( ~ sQ0_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ4_spl
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f1161,f472]) ).
fof(f1185,plain,
( ~ sQ0_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ4_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f480,f1169]) ).
fof(f1187,plain,
( ~ sQ0_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1185,f20]) ).
fof(f1188,plain,
( ~ sQ0_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1187]) ).
fof(f1189,plain,
$false,
inference(sat_refutation,[status(thm)],[f58,f68,f93,f103,f113,f126,f136,f146,f231,f247,f269,f276,f277,f295,f321,f355,f374,f376,f377,f379,f399,f400,f401,f402,f448,f550,f553,f554,f610,f618,f619,f620,f629,f646,f653,f654,f680,f684,f690,f707,f723,f729,f740,f789,f800,f804,f815,f836,f840,f863,f870,f905,f942,f943,f967,f993,f1013,f1025,f1026,f1060,f1087,f1089,f1098,f1131,f1137,f1188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP134-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n003.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 20:03:30 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.13/0.53 % Refutation found
% 0.13/0.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.55 % Elapsed time: 0.194513 seconds
% 0.13/0.55 % CPU time: 1.288260 seconds
% 0.13/0.55 % Total memory used: 22.054 MB
% 0.13/0.55 % Net memory used: 21.180 MB
%------------------------------------------------------------------------------