%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP133-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:32:49 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.53s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 41
% Syntax : Number of formulae : 300 ( 19 unt; 27 def)
% Number of atoms : 832 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1034 ( 502 ~; 505 |; 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 : 106 ( 106 !; 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,X)
| ~ 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,
! [X,Z1,Z2] :
( product(Z1,Z2,X)
| ! [Y] :
( ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X0)
| ~ 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(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(f76,plain,
! [X0] :
( ~ sQ7_spl
| product(X0,e_2,e_1)
| ~ product(e_1,e_3,X0) ),
inference(resolution,[status(thm)],[f63,f32]) ).
fof(f80,plain,
! [X0] :
( ~ sQ6_spl
| product(X0,e_1,e_1)
| ~ 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_2)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f56,f32]) ).
fof(f154,plain,
! [X0] :
( ~ sQ4_spl
| product(X0,e_2,e_2)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f53,f32]) ).
fof(f158,plain,
! [X0] :
( ~ sQ3_spl
| product(X0,e_1,e_2)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f50,f32]) ).
fof(f162,plain,
! [X0] :
( ~ sQ2_spl
| product(X0,e_3,e_3)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f46,f32]) ).
fof(f167,plain,
! [X0] :
( ~ sQ17_spl
| product(X0,e_3,e_1)
| ~ product(e_1,e_2,X0) ),
inference(resolution,[status(thm)],[f111,f32]) ).
fof(f175,plain,
! [X0] :
( ~ sQ15_spl
| product(X0,e_1,e_1)
| ~ 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(f182,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_3)
| ~ product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f180,f30]) ).
fof(f183,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_3)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f180,f28]) ).
fof(f184,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_2)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f180,f26]) ).
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(f195,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f183,f53]) ).
fof(f196,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f183,f63]) ).
fof(f197,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f21]) ).
fof(f198,plain,
( ~ sQ4_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f197]) ).
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(f219,plain,
! [X0] :
( ~ sQ12_spl
| equalish(X0,e_1)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f209,f28]) ).
fof(f221,plain,
! [X0] :
( ~ sQ12_spl
| product(X0,e_2,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f209,f32]) ).
fof(f233,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f91,f150]) ).
fof(f237,plain,
! [X0] :
( ~ sQ11_spl
| product(X0,e_3,e_3)
| ~ 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_3) ),
inference(resolution,[status(thm)],[f237,f50]) ).
fof(f239,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f237,f56]) ).
fof(f242,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ11_spl
| equalish(X0,e_3)
| ~ product(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f233,f28]) ).
fof(f248,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ11_spl
| equalish(X0,e_1)
| ~ product(X0,e_3,e_3) ),
inference(resolution,[status(thm)],[f238,f30]) ).
fof(f259,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ11_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f242,f63]) ).
fof(f260,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f19]) ).
fof(f261,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f260]) ).
fof(f266,plain,
! [X0] :
( ~ sQ10_spl
| product(X0,e_2,e_3)
| ~ product(e_3,e_2,X0) ),
inference(resolution,[status(thm)],[f88,f32]) ).
fof(f267,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f266,f50]) ).
fof(f270,plain,
( ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ10_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f267,f167]) ).
fof(f272,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ10_spl
| equalish(X0,e_2)
| ~ product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f267,f28]) ).
fof(f275,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ10_spl
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f270,f162]) ).
fof(f288,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ10_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f272,f275]) ).
fof(f290,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f288,f23]) ).
fof(f291,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f290]) ).
fof(f292,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f85,f158]) ).
fof(f297,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ9_spl
| equalish(X0,e_1)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f292,f30]) ).
fof(f300,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ9_spl
| product(X0,e_2,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f292,f32]) ).
fof(f302,plain,
( ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ9_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f297,f108]) ).
fof(f303,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ9_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f297,f63]) ).
fof(f304,plain,
( ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f302,f20]) ).
fof(f305,plain,
( ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f304]) ).
fof(f306,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f154,f85]) ).
fof(f310,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ4_spl
| equalish(X0,e_1)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f306,f30]) ).
fof(f317,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f19]) ).
fof(f318,plain,
( ~ sQ7_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f317]) ).
fof(f326,plain,
( ~ sQ12_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f221,f209]) ).
fof(f328,plain,
! [X0] :
( ~ sQ12_spl
| equalish(X0,e_2)
| ~ product(X0,e_2,e_1) ),
inference(resolution,[status(thm)],[f326,f30]) ).
fof(f329,plain,
! [X0] :
( ~ sQ12_spl
| equalish(X0,e_2)
| ~ product(e_2,X0,e_1) ),
inference(resolution,[status(thm)],[f326,f28]) ).
fof(f334,plain,
( ~ sQ15_spl
| ~ sQ12_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f329,f105]) ).
fof(f335,plain,
( ~ sQ15_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f334,f18]) ).
fof(f336,plain,
( ~ sQ15_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f335]) ).
fof(f339,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_2)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f180,f26]) ).
fof(f348,plain,
! [X0] :
( ~ sQ26_spl
| product(X0,e_3,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f144,f32]) ).
fof(f352,plain,
! [X0] :
( ~ sQ25_spl
| product(X0,e_2,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f141,f32]) ).
fof(f356,plain,
! [X0] :
( ~ sQ24_spl
| product(X0,e_1,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f138,f32]) ).
fof(f360,plain,
! [X0] :
( ~ sQ22_spl
| product(X0,e_2,e_2)
| ~ product(e_2,e_1,X0) ),
inference(resolution,[status(thm)],[f131,f32]) ).
fof(f364,plain,
! [X0] :
( ~ sQ21_spl
| product(X0,e_1,e_2)
| ~ product(e_2,e_1,X0) ),
inference(resolution,[status(thm)],[f128,f32]) ).
fof(f369,plain,
! [X0] :
( ~ sQ20_spl
| product(X0,e_3,e_3)
| ~ product(e_3,e_1,X0) ),
inference(resolution,[status(thm)],[f124,f32]) ).
fof(f373,plain,
! [X0] :
( ~ sQ0_spl
| product(X0,e_1,e_3)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f40,f32]) ).
fof(f374,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f184,f40]) ).
fof(f376,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f374,f18]) ).
fof(f377,plain,
( ~ sQ0_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f376]) ).
fof(f384,plain,
( ~ sQ22_spl
| ~ sQ12_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f219,f131]) ).
fof(f385,plain,
( ~ sQ22_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f384,f20]) ).
fof(f386,plain,
( ~ sQ22_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f385]) ).
fof(f390,plain,
( ~ sQ26_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f348,f144]) ).
fof(f392,plain,
( ~ sQ26_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f390,f39,f143]) ).
fof(f398,plain,
( ~ sQ24_spl
| ~ sQ12_spl
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f209,f356]) ).
fof(f400,plain,
! [X0] :
( ~ sQ12_spl
| equalish(X0,e_1)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f209,f28]) ).
fof(f403,plain,
( ~ sQ24_spl
| ~ sQ12_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f398,f104,f94,f137]) ).
fof(f417,plain,
( ~ sQ21_spl
| ~ sQ12_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f328,f128]) ).
fof(f419,plain,
( ~ sQ21_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f417,f18]) ).
fof(f420,plain,
( ~ sQ21_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f419]) ).
fof(f442,plain,
( ~ sQ14_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f185,f180]) ).
fof(f445,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_2)
| ~ product(X0,e_2,e_3) ),
inference(resolution,[status(thm)],[f442,f30]) ).
fof(f454,plain,
( ~ sQ14_spl
| ~ sQ5_spl
| ~ sQ11_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f239,f339]) ).
fof(f459,plain,
( ~ sQ14_spl
| ~ sQ5_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f454,f23]) ).
fof(f460,plain,
( ~ sQ14_spl
| ~ sQ5_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f459]) ).
fof(f464,plain,
( ~ sQ15_spl
| ~ sQ23_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f134,f175]) ).
fof(f465,plain,
( ~ sQ14_spl
| ~ sQ23_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f134,f445]) ).
fof(f470,plain,
( ~ sQ14_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f18]) ).
fof(f471,plain,
( ~ sQ14_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f470]) ).
fof(f474,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f22]) ).
fof(f475,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f474]) ).
fof(f492,plain,
! [X0] :
( ~ sQ18_spl
| product(X0,e_1,e_3)
| ~ product(e_3,e_1,X0) ),
inference(resolution,[status(thm)],[f118,f32]) ).
fof(f500,plain,
! [X0] :
( ~ sQ0_spl
| product(X0,e_1,e_3)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f40,f32]) ).
fof(f509,plain,
( ~ sQ0_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f373,f40]) ).
fof(f510,plain,
( ~ sQ0_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f509,f143,f39]) ).
fof(f511,plain,
( ~ sQ18_spl
| ~ sQ6_spl
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f80,f118]) ).
fof(f521,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ6_spl
| equalish(X0,e_1)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[f511,f28]) ).
fof(f535,plain,
( ~ sQ18_spl
| ~ sQ6_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f521,f118]) ).
fof(f536,plain,
( ~ sQ18_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f535,f22]) ).
fof(f537,plain,
( ~ sQ18_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f557,plain,
! [X0] :
( ~ sQ1_spl
| product(X0,e_2,e_3)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f43,f32]) ).
fof(f558,plain,
( ~ sQ7_spl
| ~ sQ19_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f121,f76]) ).
fof(f559,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f121,f400]) ).
fof(f564,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f559,f22]) ).
fof(f565,plain,
( ~ sQ12_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f564]) ).
fof(f574,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f182,f88]) ).
fof(f576,plain,
( ~ sQ19_spl
| ~ sQ14_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f182,f121]) ).
fof(f577,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f574,f21]) ).
fof(f578,plain,
( ~ sQ10_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f583,plain,
! [X0] :
( ~ sQ12_spl
| equalish(X0,e_1)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f209,f30]) ).
fof(f589,plain,
( ~ sQ1_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f557,f43]) ).
fof(f590,plain,
( ~ sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f589,f100,f42]) ).
fof(f591,plain,
( ~ sQ19_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f576,f19]) ).
fof(f592,plain,
( ~ sQ19_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f591]) ).
fof(f618,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f53,f310]) ).
fof(f623,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f618,f22]) ).
fof(f624,plain,
( ~ sQ9_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f623]) ).
fof(f650,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f300,f292]) ).
fof(f651,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f650,f94,f84,f49]) ).
fof(f652,plain,
( ~ sQ9_spl
| ~ sQ5_spl
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f150,f85]) ).
fof(f653,plain,
( ~ sQ9_spl
| ~ sQ5_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f652,f120,f55,f84]) ).
fof(f654,plain,
( ~ sQ7_spl
| ~ sQ19_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f558,f94,f120,f62]) ).
fof(f655,plain,
( ~ sQ0_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f40,f500]) ).
fof(f665,plain,
( ~ sQ26_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f144,f348]) ).
fof(f675,plain,
( ~ sQ6_spl
| ~ sQ19_spl
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f121,f80]) ).
fof(f700,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ19_spl
| equalish(X0,e_2)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f675,f30]) ).
fof(f707,plain,
( ~ sQ6_spl
| ~ sQ19_spl
| ~ sQ22_spl
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f360,f675]) ).
fof(f716,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f88,f154]) ).
fof(f724,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ10_spl
| equalish(X0,e_2)
| ~ product(e_2,X0,e_2) ),
inference(resolution,[status(thm)],[f716,f28]) ).
fof(f729,plain,
( ~ sQ15_spl
| ~ sQ23_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f464,f59,f133,f104]) ).
fof(f732,plain,
( ~ sQ10_spl
| ~ sQ4_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f724,f88]) ).
fof(f733,plain,
( ~ sQ10_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f732,f23]) ).
fof(f734,plain,
( ~ sQ10_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f733]) ).
fof(f774,plain,
! [X0] :
( ~ sQ0_spl
| equalish(X0,e_1)
| ~ product(X0,e_1,e_3) ),
inference(resolution,[status(thm)],[f655,f30]) ).
fof(f780,plain,
! [X0] :
( ~ sQ26_spl
| equalish(X0,e_3)
| ~ product(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f665,f28]) ).
fof(f781,plain,
! [X0] :
( ~ sQ26_spl
| equalish(X0,e_1)
| ~ product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f665,f26]) ).
fof(f795,plain,
( ~ sQ21_spl
| ~ sQ15_spl
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f105,f364]) ).
fof(f800,plain,
( ~ sQ21_spl
| ~ sQ15_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f795,f140,f104,f127]) ).
fof(f810,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f91,f248]) ).
fof(f815,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f810,f20]) ).
fof(f816,plain,
( ~ sQ3_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f815]) ).
fof(f822,plain,
( ~ sQ11_spl
| ~ sQ4_spl
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f154,f91]) ).
fof(f825,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ4_spl
| equalish(X0,e_3)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f822,f30]) ).
fof(f842,plain,
( ~ sQ18_spl
| ~ sQ7_spl
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f63,f492]) ).
fof(f844,plain,
( ~ sQ12_spl
| ~ sQ7_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f63,f583]) ).
fof(f851,plain,
( ~ sQ6_spl
| ~ sQ19_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f675,f104,f120,f59]) ).
fof(f868,plain,
( ~ sQ15_spl
| ~ sQ23_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f134,f175]) ).
fof(f874,plain,
( ~ sQ6_spl
| ~ sQ19_spl
| ~ sQ15_spl
| ~ sQ23_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f868,f700]) ).
fof(f879,plain,
( ~ sQ6_spl
| ~ sQ19_spl
| ~ sQ15_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f874,f23]) ).
fof(f880,plain,
( ~ sQ6_spl
| ~ sQ19_spl
| ~ sQ15_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f879]) ).
fof(f894,plain,
( ~ sQ25_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f141,f352]) ).
fof(f913,plain,
( ~ sQ6_spl
| ~ sQ20_spl
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f369,f60]) ).
fof(f915,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ20_spl
| equalish(X0,e_1)
| ~ product(X0,e_3,e_3) ),
inference(resolution,[status(thm)],[f913,f30]) ).
fof(f920,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ20_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f915,f46]) ).
fof(f922,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f920,f22]) ).
fof(f923,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f922]) ).
fof(f926,plain,
( ~ sQ25_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f894,f94,f140]) ).
fof(f927,plain,
( ~ sQ12_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f844,f22]) ).
fof(f928,plain,
( ~ sQ12_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f927]) ).
fof(f929,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ19_spl
| ~ sQ22_spl
| equalish(X0,e_1)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f707,f30]) ).
fof(f961,plain,
( ~ sQ26_spl
| ~ sQ2_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f46,f781]) ).
fof(f963,plain,
( ~ sQ2_spl
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f46,f162]) ).
fof(f968,plain,
( ~ sQ26_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f961,f22]) ).
fof(f969,plain,
( ~ sQ26_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f968]) ).
fof(f987,plain,
( ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ13_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f98,f825]) ).
fof(f992,plain,
( ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f987,f21]) ).
fof(f993,plain,
( ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f992]) ).
fof(f994,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f267,f133,f87,f49]) ).
fof(f999,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f66,f774]) ).
fof(f1004,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f999,f22]) ).
fof(f1005,plain,
( ~ sQ0_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f1004]) ).
fof(f1015,plain,
! [X0] :
( ~ sQ2_spl
| equalish(X0,e_3)
| ~ product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f963,f28]) ).
fof(f1019,plain,
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ19_spl
| ~ sQ22_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f929,f98]) ).
fof(f1020,plain,
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ19_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1019,f20]) ).
fof(f1021,plain,
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ19_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f1020]) ).
fof(f1026,plain,
( ~ sQ6_spl
| ~ sQ20_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f913,f80]) ).
fof(f1041,plain,
( ~ sQ6_spl
| ~ sQ20_spl
| ~ sQ26_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f780,f1026]) ).
fof(f1043,plain,
( ~ sQ6_spl
| ~ sQ20_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1041,f19]) ).
fof(f1044,plain,
( ~ sQ6_spl
| ~ sQ20_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f1043]) ).
fof(f1068,plain,
( ~ sQ20_spl
| ~ sQ7_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f63,f369]) ).
fof(f1073,plain,
( ~ sQ20_spl
| ~ sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f1068,f90,f62,f123]) ).
fof(f1075,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| ~ sQ7_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f842,f774]) ).
fof(f1078,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ7_spl
| equalish(X0,e_3)
| ~ product(e_2,e_1,X0) ),
inference(resolution,[status(thm)],[f842,f26]) ).
fof(f1080,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1075,f20]) ).
fof(f1081,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1080]) ).
fof(f1091,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| ~ sQ7_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f1078,f108]) ).
fof(f1092,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1091,f21]) ).
fof(f1093,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1092]) ).
fof(f1098,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f56,f1015]) ).
fof(f1103,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1098,f21]) ).
fof(f1104,plain,
( ~ sQ2_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f1103]) ).
fof(f1135,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f66,f1015]) ).
fof(f1140,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1135,f19]) ).
fof(f1141,plain,
( ~ sQ2_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f1140]) ).
fof(f1142,plain,
$false,
inference(sat_refutation,[status(thm)],[f48,f58,f68,f93,f103,f113,f126,f136,f146,f198,f261,f291,f305,f318,f336,f377,f386,f392,f403,f420,f460,f471,f475,f510,f537,f565,f578,f590,f592,f624,f651,f653,f654,f729,f734,f800,f816,f851,f880,f923,f926,f928,f969,f993,f994,f1005,f1021,f1044,f1073,f1081,f1093,f1104,f1141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP133-1.003 : 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 : n011.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 20:01:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.53 % Refutation found
% 0.09/0.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.54 % Elapsed time: 0.181355 seconds
% 0.09/0.54 % CPU time: 1.235098 seconds
% 0.09/0.54 % Total memory used: 21.692 MB
% 0.09/0.54 % Net memory used: 20.961 MB
%------------------------------------------------------------------------------