%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP129-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:32:47 PM UTC 2026
% Result : Unsatisfiable 1.17s 0.59s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 41
% Syntax : Number of formulae : 277 ( 19 unt; 27 def)
% Number of atoms : 811 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1019 ( 485 ~; 507 |; 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 : 94 ( 94 !; 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,
! [Y,X,Z1,Z2] :
( product(Z1,Y,Z2)
| ~ product(X,Z1,Z2)
| ~ product(Y,X,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,Y,Z2)
| ! [X] :
( ~ product(X,Z1,Z2)
| ~ product(Y,X,Z1) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( product(X2,X0,X3)
| ~ product(X1,X2,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(e_1,X0,e_3)
| ~ product(X0,e_3,e_1) ),
inference(resolution,[status(thm)],[f66,f32]) ).
fof(f76,plain,
! [X0] :
( ~ sQ7_spl
| product(e_1,X0,e_2)
| ~ product(X0,e_3,e_1) ),
inference(resolution,[status(thm)],[f63,f32]) ).
fof(f80,plain,
! [X0] :
( ~ sQ6_spl
| product(e_1,X0,e_1)
| ~ product(X0,e_3,e_1) ),
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(f92,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(f106,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(e_2,X0,e_3)
| ~ product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f56,f32]) ).
fof(f154,plain,
! [X0] :
( ~ sQ4_spl
| product(e_2,X0,e_2)
| ~ product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f53,f32]) ).
fof(f158,plain,
! [X0] :
( ~ sQ3_spl
| product(e_2,X0,e_1)
| ~ product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f50,f32]) ).
fof(f167,plain,
! [X0] :
( ~ sQ17_spl
| product(e_1,X0,e_3)
| ~ product(X0,e_2,e_1) ),
inference(resolution,[status(thm)],[f111,f32]) ).
fof(f181,plain,
! [X0] :
( ~ sQ16_spl
| product(e_1,X0,e_2)
| ~ product(X0,e_2,e_1) ),
inference(resolution,[status(thm)],[f108,f32]) ).
fof(f185,plain,
! [X0] :
( ~ sQ15_spl
| product(e_1,X0,e_1)
| ~ product(X0,e_2,e_1) ),
inference(resolution,[status(thm)],[f105,f32]) ).
fof(f189,plain,
! [X0] :
( ~ sQ14_spl
| product(e_2,X0,e_3)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f101,f32]) ).
fof(f190,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f189,f53]) ).
fof(f192,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ14_spl
| equalish(X0,e_2)
| ~ product(X0,e_3,e_3) ),
inference(resolution,[status(thm)],[f190,f30]) ).
fof(f197,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ14_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f192,f46]) ).
fof(f198,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f197,f23]) ).
fof(f199,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f198]) ).
fof(f203,plain,
! [X0] :
( ~ sQ13_spl
| product(e_2,X0,e_2)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f98,f32]) ).
fof(f205,plain,
( ~ sQ15_spl
| ~ sQ12_spl
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f95,f185]) ).
fof(f206,plain,
( ~ sQ16_spl
| ~ sQ12_spl
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f95,f181]) ).
fof(f210,plain,
! [X0] :
( ~ sQ12_spl
| product(e_2,X0,e_1)
| ~ product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f95,f32]) ).
fof(f214,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ12_spl
| equalish(X0,e_1)
| ~ product(X0,e_2,e_1) ),
inference(resolution,[status(thm)],[f205,f30]) ).
fof(f218,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f206,f210]) ).
fof(f233,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f214,f95]) ).
fof(f234,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f233,f20]) ).
fof(f235,plain,
( ~ sQ12_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f234]) ).
fof(f239,plain,
! [X0] :
( ~ sQ11_spl
| product(e_3,X0,e_3)
| ~ product(X0,e_2,e_3) ),
inference(resolution,[status(thm)],[f91,f32]) ).
fof(f242,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f88,f150]) ).
fof(f246,plain,
! [X0] :
( ~ sQ10_spl
| product(e_3,X0,e_2)
| ~ product(X0,e_2,e_3) ),
inference(resolution,[status(thm)],[f88,f32]) ).
fof(f247,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f242,f100,f87,f55]) ).
fof(f259,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f218,f104,f107,f94]) ).
fof(f260,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f85,f72]) ).
fof(f264,plain,
! [X0] :
( ~ sQ9_spl
| product(e_3,X0,e_1)
| ~ product(X0,e_2,e_3) ),
inference(resolution,[status(thm)],[f85,f32]) ).
fof(f272,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f264,f260]) ).
fof(f275,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| equalish(X0,e_1)
| ~ product(e_3,e_1,X0) ),
inference(resolution,[status(thm)],[f272,f26]) ).
fof(f280,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f275,f66]) ).
fof(f281,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f280,f22]) ).
fof(f282,plain,
( ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f281]) ).
fof(f286,plain,
! [X0] :
( ~ sQ26_spl
| product(e_1,X0,e_3)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f144,f32]) ).
fof(f290,plain,
! [X0] :
( ~ sQ25_spl
| product(e_1,X0,e_2)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f141,f32]) ).
fof(f296,plain,
! [X0] :
( ~ sQ24_spl
| product(e_1,X0,e_1)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f138,f32]) ).
fof(f302,plain,
! [X0] :
( ~ sQ23_spl
| product(e_2,X0,e_3)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f134,f32]) ).
fof(f311,plain,
( ~ sQ13_spl
| ~ sQ22_spl
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f131,f203]) ).
fof(f315,plain,
! [X0] :
( ~ sQ22_spl
| product(e_2,X0,e_2)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f131,f32]) ).
fof(f317,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ22_spl
| equalish(X0,e_1)
| ~ product(e_2,X0,e_2) ),
inference(resolution,[status(thm)],[f311,f28]) ).
fof(f320,plain,
( ~ sQ13_spl
| ~ sQ22_spl
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f315,f311]) ).
fof(f322,plain,
( ~ sQ15_spl
| ~ sQ21_spl
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f128,f185]) ).
fof(f326,plain,
! [X0] :
( ~ sQ21_spl
| product(e_2,X0,e_1)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f128,f32]) ).
fof(f330,plain,
! [X0] :
( ~ sQ20_spl
| product(e_3,X0,e_3)
| ~ product(X0,e_1,e_3) ),
inference(resolution,[status(thm)],[f124,f32]) ).
fof(f331,plain,
( ~ sQ3_spl
| ~ sQ19_spl
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f121,f158]) ).
fof(f335,plain,
! [X0] :
( ~ sQ19_spl
| product(e_3,X0,e_2)
| ~ product(X0,e_1,e_3) ),
inference(resolution,[status(thm)],[f121,f32]) ).
fof(f336,plain,
( ~ sQ6_spl
| ~ sQ18_spl
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f118,f80]) ).
fof(f337,plain,
( ~ sQ7_spl
| ~ sQ18_spl
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f118,f76]) ).
fof(f341,plain,
! [X0] :
( ~ sQ18_spl
| product(e_3,X0,e_1)
| ~ product(X0,e_1,e_3) ),
inference(resolution,[status(thm)],[f118,f32]) ).
fof(f343,plain,
( ~ sQ22_spl
| ~ sQ7_spl
| product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[f63,f315]) ).
fof(f350,plain,
( ~ sQ24_spl
| ~ sQ6_spl
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f60,f296]) ).
fof(f351,plain,
( ~ sQ26_spl
| ~ sQ6_spl
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f60,f286]) ).
fof(f356,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f43,f158]) ).
fof(f361,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f356,f84,f42,f49]) ).
fof(f364,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ6_spl
| equalish(X0,e_3)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[f350,f28]) ).
fof(f370,plain,
( ~ sQ24_spl
| ~ sQ6_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f364,f138]) ).
fof(f373,plain,
( ~ sQ15_spl
| ~ sQ21_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f322,f137,f127,f104]) ).
fof(f383,plain,
( ~ sQ13_spl
| ~ sQ22_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f317,f320]) ).
fof(f385,plain,
( ~ sQ13_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f383,f20]) ).
fof(f386,plain,
( ~ sQ13_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f385]) ).
fof(f387,plain,
( ~ sQ6_spl
| ~ sQ18_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f336,f137,f117,f59]) ).
fof(f388,plain,
( ~ sQ26_spl
| ~ sQ20_spl
| product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[f330,f144]) ).
fof(f389,plain,
( ~ sQ26_spl
| ~ sQ20_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f388,f65,f123,f143]) ).
fof(f390,plain,
( ~ sQ6_spl
| ~ sQ25_spl
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f290,f60]) ).
fof(f391,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ25_spl
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f390,f150]) ).
fof(f393,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ25_spl
| equalish(X0,e_3)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f390,f28]) ).
fof(f396,plain,
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ25_spl
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f391,f335]) ).
fof(f397,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ25_spl
| equalish(X0,e_2)
| ~ product(X0,e_1,e_3) ),
inference(resolution,[status(thm)],[f391,f30]) ).
fof(f401,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ25_spl
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f396,f210]) ).
fof(f406,plain,
( ~ sQ6_spl
| ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ25_spl
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f401,f80]) ).
fof(f411,plain,
( ~ sQ17_spl
| ~ sQ6_spl
| ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ25_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f406,f167]) ).
fof(f430,plain,
( ~ sQ17_spl
| ~ sQ6_spl
| ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ25_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f397,f411]) ).
fof(f431,plain,
( ~ sQ17_spl
| ~ sQ6_spl
| ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f430,f18]) ).
fof(f432,plain,
( ~ sQ17_spl
| ~ sQ6_spl
| ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f431]) ).
fof(f433,plain,
( ~ sQ26_spl
| ~ sQ6_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f351,f123,f59,f143]) ).
fof(f434,plain,
( ~ sQ6_spl
| ~ sQ25_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f390,f120,f140,f59]) ).
fof(f435,plain,
( ~ sQ24_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f370,f19]) ).
fof(f436,plain,
( ~ sQ24_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f435]) ).
fof(f442,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f40,f72]) ).
fof(f446,plain,
! [X0] :
( ~ sQ0_spl
| product(e_3,X0,e_1)
| ~ product(X0,e_3,e_3) ),
inference(resolution,[status(thm)],[f40,f32]) ).
fof(f454,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f446,f442]) ).
fof(f455,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f454,f59,f39,f65]) ).
fof(f470,plain,
( ~ sQ7_spl
| ~ sQ18_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f337,f140,f117,f62]) ).
fof(f477,plain,
( ~ sQ22_spl
| ~ sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f343,f87,f62,f130]) ).
fof(f478,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f85,f76]) ).
fof(f483,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f478,f130,f84,f62]) ).
fof(f484,plain,
( ~ sQ21_spl
| ~ sQ7_spl
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f63,f326]) ).
fof(f489,plain,
( ~ sQ21_spl
| ~ sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f484,f84,f62,f127]) ).
fof(f490,plain,
( ~ sQ7_spl
| ~ sQ22_spl
| product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[f315,f63]) ).
fof(f491,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ22_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f490,f158]) ).
fof(f494,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ22_spl
| equalish(X0,e_2)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f490,f26]) ).
fof(f496,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ22_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f491,f94,f130,f62,f49]) ).
fof(f505,plain,
( ~ sQ22_spl
| ~ sQ25_spl
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f141,f315]) ).
fof(f506,plain,
( ~ sQ21_spl
| ~ sQ25_spl
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f141,f326]) ).
fof(f511,plain,
( ~ sQ22_spl
| ~ sQ25_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f505,f107,f140,f130]) ).
fof(f512,plain,
( ~ sQ21_spl
| ~ sQ25_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f506,f104,f140,f127]) ).
fof(f526,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ22_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f494,f85]) ).
fof(f528,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f18]) ).
fof(f529,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f528]) ).
fof(f530,plain,
( ~ sQ7_spl
| ~ sQ22_spl
| ~ sQ5_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f150,f490]) ).
fof(f531,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ22_spl
| ~ sQ5_spl
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f530,f246]) ).
fof(f536,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ22_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f531,f52,f55,f130,f62,f87]) ).
fof(f538,plain,
( ~ sQ7_spl
| ~ sQ23_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f302,f63]) ).
fof(f540,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f190,f90,f100,f52]) ).
fof(f551,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ23_spl
| equalish(X0,e_2)
| ~ product(X0,e_3,e_3) ),
inference(resolution,[status(thm)],[f538,f30]) ).
fof(f552,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ23_spl
| equalish(X0,e_3)
| ~ product(e_2,X0,e_3) ),
inference(resolution,[status(thm)],[f538,f28]) ).
fof(f558,plain,
( ~ sQ25_spl
| ~ sQ23_spl
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f302,f141]) ).
fof(f561,plain,
( ~ sQ7_spl
| ~ sQ23_spl
| ~ sQ25_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f558,f552]) ).
fof(f567,plain,
( ~ sQ7_spl
| ~ sQ23_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f561,f19]) ).
fof(f568,plain,
( ~ sQ7_spl
| ~ sQ23_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f567]) ).
fof(f569,plain,
( sQ11_spl
| ~ sQ7_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f92,f538]) ).
fof(f570,plain,
( sQ11_spl
| ~ sQ7_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f569]) ).
fof(f595,plain,
( ~ sQ7_spl
| ~ sQ22_spl
| ~ sQ4_spl
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f154,f490]) ).
fof(f596,plain,
( ~ sQ7_spl
| ~ sQ22_spl
| ~ sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f595,f97,f52,f130,f62]) ).
fof(f613,plain,
( ~ sQ7_spl
| ~ sQ23_spl
| ~ sQ20_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f124,f551]) ).
fof(f619,plain,
( ~ sQ7_spl
| ~ sQ23_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f613,f18]) ).
fof(f620,plain,
( ~ sQ7_spl
| ~ sQ23_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f619]) ).
fof(f686,plain,
( sQ15_spl
| ~ sQ3_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f331]) ).
fof(f687,plain,
( sQ15_spl
| ~ sQ3_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f686]) ).
fof(f689,plain,
( ~ sQ14_spl
| ~ sQ22_spl
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f131,f189]) ).
fof(f694,plain,
( ~ sQ14_spl
| ~ sQ22_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f689,f110,f130,f100]) ).
fof(f696,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f43,f150]) ).
fof(f701,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f696,f90,f42,f55]) ).
fof(f702,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f56,f239]) ).
fof(f710,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ5_spl
| equalish(X0,e_3)
| ~ product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f702,f28]) ).
fof(f714,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f710,f56]) ).
fof(f716,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f714,f21]) ).
fof(f717,plain,
( ~ sQ5_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f716]) ).
fof(f727,plain,
( ~ sQ11_spl
| ~ sQ23_spl
| product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[f134,f239]) ).
fof(f738,plain,
( ~ sQ15_spl
| ~ sQ3_spl
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f50,f185]) ).
fof(f743,plain,
( ~ sQ15_spl
| ~ sQ3_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f738,f117,f49,f104]) ).
fof(f754,plain,
( ~ sQ8_spl
| ~ sQ18_spl
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f341,f66]) ).
fof(f755,plain,
( ~ sQ8_spl
| ~ sQ18_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f754,f39,f117,f65]) ).
fof(f767,plain,
( ~ sQ8_spl
| ~ sQ19_spl
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f335,f66]) ).
fof(f769,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ19_spl
| equalish(X0,e_3)
| ~ product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f767,f30]) ).
fof(f774,plain,
( ~ sQ19_spl
| ~ sQ25_spl
| ~ sQ23_spl
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f558,f335]) ).
fof(f779,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ25_spl
| ~ sQ23_spl
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f774,f210]) ).
fof(f797,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ25_spl
| ~ sQ23_spl
| ~ sQ6_spl
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f80,f779]) ).
fof(f798,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ25_spl
| ~ sQ23_spl
| ~ sQ6_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f797,f127,f59,f133,f140,f120,f94]) ).
fof(f799,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ19_spl
| product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[f767,f154]) ).
fof(f807,plain,
( ~ sQ8_spl
| ~ sQ19_spl
| ~ sQ4_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f799,f769]) ).
fof(f813,plain,
( ~ sQ8_spl
| ~ sQ19_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f807,f21]) ).
fof(f814,plain,
( ~ sQ8_spl
| ~ sQ19_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f813]) ).
fof(f815,plain,
( ~ sQ20_spl
| ~ sQ17_spl
| product(e_3,e_2,e_3) ),
inference(resolution,[status(thm)],[f111,f330]) ).
fof(f820,plain,
( ~ sQ20_spl
| ~ sQ17_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f815,f55,f110,f123]) ).
fof(f831,plain,
( ~ sQ17_spl
| ~ sQ19_spl
| product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f335,f111]) ).
fof(f834,plain,
( ~ sQ13_spl
| ~ sQ4_spl
| product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[f53,f203]) ).
fof(f839,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f834,f154]) ).
fof(f841,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ4_spl
| equalish(X0,e_3)
| ~ product(e_2,X0,e_2) ),
inference(resolution,[status(thm)],[f834,f28]) ).
fof(f850,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f841,f839]) ).
fof(f852,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f850,f21]) ).
fof(f853,plain,
( ~ sQ4_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f852]) ).
fof(f854,plain,
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ25_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f396,f52,f140,f59,f55,f120]) ).
fof(f855,plain,
( ~ sQ17_spl
| ~ sQ19_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f831,f52,f120,f110]) ).
fof(f856,plain,
( ~ sQ8_spl
| ~ sQ19_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f767,f42,f120,f65]) ).
fof(f886,plain,
( ~ sQ20_spl
| ~ sQ8_spl
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f66,f330]) ).
fof(f893,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ8_spl
| equalish(X0,e_3)
| ~ product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f886,f28]) ).
fof(f898,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f893,f66]) ).
fof(f899,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f898,f19]) ).
fof(f900,plain,
( ~ sQ8_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f899]) ).
fof(f901,plain,
( ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ22_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f131,f393]) ).
fof(f907,plain,
( ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f901,f21]) ).
fof(f908,plain,
( ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f907]) ).
fof(f909,plain,
( ~ sQ11_spl
| ~ sQ23_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f727,f65,f133,f90]) ).
fof(f910,plain,
$false,
inference(sat_refutation,[status(thm)],[f48,f58,f68,f93,f103,f113,f126,f136,f146,f199,f235,f247,f259,f282,f361,f373,f386,f387,f389,f432,f433,f434,f436,f455,f470,f477,f483,f489,f496,f511,f512,f529,f536,f540,f568,f570,f596,f620,f687,f694,f701,f717,f743,f755,f798,f814,f820,f853,f854,f855,f856,f900,f908,f909]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP129-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:00:18 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 1.17/0.59 % Refutation found
% 1.17/0.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.17/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.17/0.61 % Elapsed time: 0.225982 seconds
% 1.17/0.61 % CPU time: 1.546155 seconds
% 1.17/0.61 % Total memory used: 22.388 MB
% 1.17/0.61 % Net memory used: 21.542 MB
%------------------------------------------------------------------------------