%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP126-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 12:32:45 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 64
% Syntax : Number of formulae : 285 ( 65 unt; 46 def)
% Number of atoms : 637 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 626 ( 274 ~; 306 |; 0 &)
% ( 46 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 50 ( 49 usr; 47 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 109 ( 109 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( product(e_4,X,Y)
| product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( product(X,e_4,Y)
| product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y] :
( product(X,Y,e_4)
| 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(f22,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,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(f27,plain,
! [X0,X1] :
( product(e_4,X0,X1)
| product(e_3,X0,X1)
| product(e_2,X0,X1)
| product(e_1,X0,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f28,plain,
! [X0,X1] :
( product(X0,e_4,X1)
| product(X0,e_3,X1)
| product(X0,e_2,X1)
| product(X0,e_1,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f33,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f36,plain,
group_element(e_4),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f37,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f39,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f42,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f45,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f49,plain,
! [X0,X1] :
( product(X0,X1,e_4)
| 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)],[f21]) ).
fof(f50,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f57,plain,
! [Y,Z1,Z2] :
( product(Z1,Z2,Y)
| ! [X] :
( ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f69,plain,
! [X0] :
( product(X0,e_4,e_1)
| product(X0,e_3,e_1)
| product(X0,e_2,e_1)
| product(X0,e_1,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f33,f28]) ).
fof(f71,plain,
! [X0] :
( product(X0,e_4,e_2)
| product(X0,e_3,e_2)
| product(X0,e_2,e_2)
| product(X0,e_1,e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f34,f28]) ).
fof(f72,plain,
! [X0] :
( product(e_4,X0,e_2)
| product(e_3,X0,e_2)
| product(e_2,X0,e_2)
| product(e_1,X0,e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f34,f27]) ).
fof(f73,plain,
! [X0] :
( product(X0,e_4,e_3)
| product(X0,e_3,e_3)
| product(X0,e_2,e_3)
| product(X0,e_1,e_3)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f35,f28]) ).
fof(f74,plain,
! [X0] :
( product(e_4,X0,e_3)
| product(e_3,X0,e_3)
| product(e_2,X0,e_3)
| product(e_1,X0,e_3)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f35,f27]) ).
fof(f75,plain,
! [X0] :
( product(X0,e_4,e_4)
| product(X0,e_3,e_4)
| product(X0,e_2,e_4)
| product(X0,e_1,e_4)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f36,f28]) ).
fof(f77,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f37,f55]) ).
fof(f78,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f37,f53]) ).
fof(f79,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f37,f51]) ).
fof(f80,plain,
~ product(e_1,e_2,e_2),
inference(resolution,[status(thm)],[f77,f56]) ).
fof(f81,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f38,f55]) ).
fof(f82,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f38,f53]) ).
fof(f83,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f38,f51]) ).
fof(f84,plain,
~ product(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f78,f56]) ).
fof(f85,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f39,f55]) ).
fof(f86,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f39,f53]) ).
fof(f87,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f39,f51]) ).
fof(f91,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f41,f55]) ).
fof(f92,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f41,f53]) ).
fof(f93,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f41,f51]) ).
fof(f94,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f42,f55]) ).
fof(f95,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f42,f53]) ).
fof(f96,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f42,f51]) ).
fof(f97,plain,
~ product(e_2,e_2,e_1),
inference(resolution,[status(thm)],[f79,f56]) ).
fof(f98,plain,
~ product(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f81,f56]) ).
fof(f99,plain,
~ product(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f82,f56]) ).
fof(f106,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f45,f55]) ).
fof(f107,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f45,f53]) ).
fof(f108,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_3) ),
inference(resolution,[status(thm)],[f45,f51]) ).
fof(f118,plain,
~ product(e_3,e_3,e_1),
inference(resolution,[status(thm)],[f83,f56]) ).
fof(f119,plain,
! [X0] :
( product(X0,e_4,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f49,f36]) ).
fof(f120,plain,
! [X0] :
( product(X0,e_3,e_4)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f49,f35]) ).
fof(f121,plain,
! [X0] :
( product(X0,e_2,e_4)
| product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f49,f34]) ).
fof(f123,plain,
( product(e_4,e_4,e_1)
| product(e_4,e_3,e_1)
| product(e_4,e_2,e_1)
| product(e_4,e_1,e_1) ),
inference(resolution,[status(thm)],[f69,f36]) ).
fof(f124,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f69,f35]) ).
fof(f127,definition,
( sQ0_spl
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ0_spl
| product(e_4,e_1,e_1) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,definition,
( sQ1_spl
<=> product(e_4,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ1_spl
| product(e_4,e_2,e_1) ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ2_spl
<=> product(e_4,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ2_spl
| product(e_4,e_3,e_1) ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
( sQ3_spl
<=> product(e_4,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ3_spl
| product(e_4,e_4,e_1) ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( sQ3_spl
| sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f123,f127,f130,f133,f136]) ).
fof(f140,definition,
( sQ4_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( ~ sQ4_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,definition,
( sQ5_spl
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ5_spl
| product(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,definition,
( sQ6_spl
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( ~ sQ6_spl
| product(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,definition,
( sQ7_spl
<=> product(e_3,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ7_spl
| product(e_3,e_4,e_1) ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ7_spl
| sQ6_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f124,f140,f143,f146,f149]) ).
fof(f156,definition,
( sQ9_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( ~ sQ9_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,definition,
( sQ10_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ10_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f179,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f97]) ).
fof(f180,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f179]) ).
fof(f181,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f118]) ).
fof(f182,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f181]) ).
fof(f191,plain,
( product(e_4,e_4,e_2)
| product(e_4,e_3,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_1,e_2) ),
inference(resolution,[status(thm)],[f71,f36]) ).
fof(f192,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[f71,f35]) ).
fof(f195,definition,
( sQ16_spl
<=> product(e_4,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( ~ sQ16_spl
| product(e_4,e_1,e_2) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,definition,
( sQ17_spl
<=> product(e_4,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( ~ sQ17_spl
| product(e_4,e_2,e_2) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,definition,
( sQ18_spl
<=> product(e_4,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f202,plain,
( ~ sQ18_spl
| product(e_4,e_3,e_2) ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,definition,
( sQ19_spl
<=> product(e_4,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( ~ sQ19_spl
| product(e_4,e_4,e_2) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f191,f195,f198,f201,f204]) ).
fof(f208,definition,
( sQ20_spl
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( ~ sQ20_spl
| product(e_3,e_1,e_2) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
( sQ21_spl
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( ~ sQ21_spl
| product(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,definition,
( sQ22_spl
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f215,plain,
( ~ sQ22_spl
| product(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,definition,
( sQ23_spl
<=> product(e_3,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( ~ sQ23_spl
| product(e_3,e_4,e_2) ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,plain,
( sQ23_spl
| sQ22_spl
| sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f192,f208,f211,f214,f217]) ).
fof(f221,definition,
( sQ24_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( ~ sQ24_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,definition,
( sQ25_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f227,definition,
( sQ26_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( ~ sQ26_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f234,definition,
( sQ28_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f235,plain,
( ~ sQ28_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f237,definition,
( sQ29_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( ~ sQ29_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,definition,
( sQ30_spl
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f80]) ).
fof(f248,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f247]) ).
fof(f249,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f222,f84]) ).
fof(f250,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f249]) ).
fof(f251,plain,
~ product(e_1,e_4,e_4),
inference(resolution,[status(thm)],[f85,f56]) ).
fof(f252,plain,
~ product(e_4,e_1,e_4),
inference(resolution,[status(thm)],[f86,f56]) ).
fof(f253,plain,
~ product(e_4,e_4,e_1),
inference(resolution,[status(thm)],[f87,f56]) ).
fof(f254,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f137]) ).
fof(f255,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f254]) ).
fof(f257,plain,
( product(e_4,e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f72,f35]) ).
fof(f258,plain,
( product(e_4,e_2,e_2)
| product(e_3,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f72,f34]) ).
fof(f259,plain,
( product(e_4,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f72,f33]) ).
fof(f261,plain,
( sQ18_spl
| sQ22_spl
| sQ26_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f257,f240,f227,f214,f201]) ).
fof(f262,plain,
( sQ17_spl
| sQ21_spl
| sQ25_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f258,f237,f224,f211,f198]) ).
fof(f263,plain,
( sQ16_spl
| sQ20_spl
| sQ24_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f259,f234,f221,f208,f195]) ).
fof(f265,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_2,e_3)
| product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[f73,f35]) ).
fof(f274,definition,
( sQ34_spl
<=> product(e_4,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f277,definition,
( sQ35_spl
<=> product(e_4,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( ~ sQ35_spl
| product(e_4,e_4,e_3) ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f281,definition,
( sQ36_spl
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f282,plain,
( ~ sQ36_spl
| product(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,definition,
( sQ37_spl
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f285,plain,
( ~ sQ37_spl
| product(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f284]) ).
fof(f287,definition,
( sQ38_spl
<=> product(e_3,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f290,definition,
( sQ39_spl
<=> product(e_3,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( sQ39_spl
| sQ38_spl
| sQ37_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f265,f281,f284,f287,f290]) ).
fof(f300,definition,
( sQ42_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( ~ sQ42_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f300]) ).
fof(f313,definition,
( sQ46_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f314,plain,
( ~ sQ46_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f313]) ).
fof(f320,plain,
( ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f314,f98]) ).
fof(f321,plain,
~ sQ46_spl,
inference(contradiction_clause,[status(thm)],[f320]) ).
fof(f322,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f282,f99]) ).
fof(f323,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f322]) ).
fof(f325,plain,
( product(e_4,e_3,e_3)
| product(e_3,e_3,e_3)
| product(e_2,e_3,e_3)
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f74,f35]) ).
fof(f329,plain,
( sQ34_spl
| sQ38_spl
| sQ42_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f325,f313,f300,f287,f274]) ).
fof(f335,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_3,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_1,e_4) ),
inference(resolution,[status(thm)],[f75,f33]) ).
fof(f336,definition,
( sQ48_spl
<=> product(e_4,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( ~ sQ48_spl
| product(e_4,e_1,e_4) ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f339,definition,
( sQ49_spl
<=> product(e_4,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( ~ sQ49_spl
| product(e_4,e_2,e_4) ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f342,definition,
( sQ50_spl
<=> product(e_4,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( ~ sQ50_spl
| product(e_4,e_3,e_4) ),
inference(component_clause,[status(thm)],[f342]) ).
fof(f345,definition,
( sQ51_spl
<=> product(e_4,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f352,definition,
( sQ53_spl
<=> product(e_3,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( ~ sQ53_spl
| product(e_3,e_2,e_4) ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f355,definition,
( sQ54_spl
<=> product(e_3,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f358,definition,
( sQ55_spl
<=> product(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f359,plain,
( ~ sQ55_spl
| product(e_3,e_4,e_4) ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f362,definition,
( sQ56_spl
<=> product(e_2,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( ~ sQ56_spl
| product(e_2,e_1,e_4) ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f368,definition,
( sQ58_spl
<=> product(e_2,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f369,plain,
( ~ sQ58_spl
| product(e_2,e_3,e_4) ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f371,definition,
( sQ59_spl
<=> product(e_2,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( ~ sQ59_spl
| product(e_2,e_4,e_4) ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f375,definition,
( sQ60_spl
<=> product(e_1,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f376,plain,
( ~ sQ60_spl
| product(e_1,e_1,e_4) ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,definition,
( sQ61_spl
<=> product(e_1,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f380,plain,
( sQ61_spl
| ~ product(e_1,e_2,e_4) ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,definition,
( sQ62_spl
<=> product(e_1,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f382,plain,
( ~ sQ62_spl
| product(e_1,e_3,e_4) ),
inference(component_clause,[status(thm)],[f381]) ).
fof(f384,definition,
( sQ63_spl
<=> product(e_1,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f385,plain,
( ~ sQ63_spl
| product(e_1,e_4,e_4) ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f387,plain,
( sQ63_spl
| sQ62_spl
| sQ61_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f335,f375,f378,f381,f384]) ).
fof(f388,plain,
( ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f385,f251]) ).
fof(f389,plain,
~ sQ63_spl,
inference(contradiction_clause,[status(thm)],[f388]) ).
fof(f398,plain,
( ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f337,f252]) ).
fof(f399,plain,
~ sQ48_spl,
inference(contradiction_clause,[status(thm)],[f398]) ).
fof(f400,plain,
~ product(e_2,e_3,e_3),
inference(resolution,[status(thm)],[f91,f56]) ).
fof(f401,plain,
( ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f400,f301]) ).
fof(f402,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f401]) ).
fof(f403,plain,
~ product(e_3,e_2,e_3),
inference(resolution,[status(thm)],[f92,f56]) ).
fof(f404,plain,
( ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f403,f285]) ).
fof(f405,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f404]) ).
fof(f406,plain,
~ product(e_3,e_3,e_2),
inference(resolution,[status(thm)],[f93,f56]) ).
fof(f407,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f406,f215]) ).
fof(f408,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f407]) ).
fof(f409,plain,
~ product(e_2,e_4,e_4),
inference(resolution,[status(thm)],[f94,f56]) ).
fof(f410,plain,
( ~ sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f409,f372]) ).
fof(f411,plain,
~ sQ59_spl,
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f412,plain,
~ product(e_4,e_2,e_4),
inference(resolution,[status(thm)],[f95,f56]) ).
fof(f413,plain,
( ~ sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f412,f340]) ).
fof(f414,plain,
~ sQ49_spl,
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f415,plain,
~ product(e_4,e_4,e_2),
inference(resolution,[status(thm)],[f96,f56]) ).
fof(f416,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f415,f205]) ).
fof(f417,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f416]) ).
fof(f418,plain,
~ product(e_3,e_4,e_4),
inference(resolution,[status(thm)],[f106,f56]) ).
fof(f419,plain,
( ~ sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f418,f359]) ).
fof(f420,plain,
~ sQ55_spl,
inference(contradiction_clause,[status(thm)],[f419]) ).
fof(f421,plain,
~ product(e_4,e_3,e_4),
inference(resolution,[status(thm)],[f107,f56]) ).
fof(f422,plain,
( ~ sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f421,f343]) ).
fof(f423,plain,
~ sQ50_spl,
inference(contradiction_clause,[status(thm)],[f422]) ).
fof(f424,plain,
~ product(e_4,e_4,e_3),
inference(resolution,[status(thm)],[f108,f56]) ).
fof(f425,plain,
( ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f424,f278]) ).
fof(f426,plain,
~ sQ35_spl,
inference(contradiction_clause,[status(thm)],[f425]) ).
fof(f427,plain,
( product(e_4,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1) ),
inference(resolution,[status(thm)],[f119,f36]) ).
fof(f431,plain,
( sQ51_spl
| sQ35_spl
| sQ19_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f427,f136,f204,f277,f345]) ).
fof(f436,plain,
( product(e_3,e_3,e_4)
| 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)],[f120,f35]) ).
fof(f437,plain,
( product(e_2,e_3,e_4)
| 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)],[f120,f34]) ).
fof(f440,plain,
( sQ54_spl
| sQ38_spl
| sQ22_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f436,f146,f214,f287,f355]) ).
fof(f441,plain,
( sQ58_spl
| sQ42_spl
| sQ26_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f437,f159,f227,f300,f368]) ).
fof(f444,plain,
( product(e_3,e_2,e_4)
| 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)],[f121,f35]) ).
fof(f448,plain,
( sQ53_spl
| sQ37_spl
| sQ21_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f444,f143,f211,f284,f352]) ).
fof(f461,plain,
( ~ sQ0_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f128,f85]) ).
fof(f470,plain,
( ~ sQ1_spl
| ~ product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f131,f106]) ).
fof(f478,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f470,f144]) ).
fof(f479,plain,
( ~ sQ1_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f478]) ).
fof(f481,plain,
( ~ sQ2_spl
| ~ product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f134,f94]) ).
fof(f485,plain,
! [X0] :
( ~ sQ2_spl
| product(X0,e_1,e_4)
| ~ product(e_3,e_4,X0) ),
inference(resolution,[status(thm)],[f134,f58]) ).
fof(f489,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f481,f160]) ).
fof(f490,plain,
( ~ sQ2_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f489]) ).
fof(f497,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f461,f56]) ).
fof(f498,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f497]) ).
fof(f509,plain,
( ~ sQ28_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f235,f79]) ).
fof(f515,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f56]) ).
fof(f516,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f518,plain,
( ~ sQ26_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f228,f92]) ).
fof(f527,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f56]) ).
fof(f528,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f531,plain,
( ~ sQ21_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f212,f91]) ).
fof(f541,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f531,f56]) ).
fof(f542,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f545,plain,
( ~ sQ20_spl
| ~ product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f209,f79]) ).
fof(f550,plain,
( ~ sQ16_spl
| ~ product(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[f196,f106]) ).
fof(f558,plain,
( ~ sQ16_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f550,f209]) ).
fof(f559,plain,
( ~ sQ16_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f558]) ).
fof(f561,plain,
( ~ sQ17_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f199,f94]) ).
fof(f571,plain,
( ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f561,f56]) ).
fof(f572,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f571]) ).
fof(f575,plain,
( ~ sQ18_spl
| ~ product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f202,f85]) ).
fof(f577,plain,
( ~ sQ18_spl
| ~ product(e_4,e_1,e_2) ),
inference(resolution,[status(thm)],[f202,f82]) ).
fof(f578,plain,
( ~ sQ18_spl
| ~ product(e_4,e_3,e_1) ),
inference(resolution,[status(thm)],[f202,f79]) ).
fof(f579,plain,
! [X0] :
( ~ sQ18_spl
| product(X0,e_2,e_4)
| ~ product(e_3,e_4,X0) ),
inference(resolution,[status(thm)],[f202,f58]) ).
fof(f583,plain,
( ~ sQ18_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f575,f240,f201]) ).
fof(f617,plain,
( ~ sQ62_spl
| ~ product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f382,f96]) ).
fof(f629,plain,
( ~ sQ60_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f376,f87]) ).
fof(f636,plain,
( ~ sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f629,f56]) ).
fof(f637,plain,
~ sQ60_spl,
inference(contradiction_clause,[status(thm)],[f636]) ).
fof(f640,plain,
( ~ sQ58_spl
| ~ product(e_2,e_1,e_4) ),
inference(resolution,[status(thm)],[f369,f82]) ).
fof(f648,plain,
( ~ sQ58_spl
| ~ sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f640,f363]) ).
fof(f649,plain,
( ~ sQ58_spl
| ~ sQ56_spl ),
inference(contradiction_clause,[status(thm)],[f648]) ).
fof(f650,plain,
( ~ sQ18_spl
| ~ sQ7_spl
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[f150,f579]) ).
fof(f662,plain,
( ~ sQ4_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f545]) ).
fof(f663,plain,
( ~ sQ4_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f662]) ).
fof(f667,plain,
( ~ sQ18_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f577,f195,f201]) ).
fof(f668,plain,
( ~ sQ18_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f578,f133,f201]) ).
fof(f670,plain,
( ~ sQ53_spl
| ~ product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[f353,f81]) ).
fof(f680,plain,
( ~ sQ53_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f670,f378,f352]) ).
fof(f683,plain,
( sQ61_spl
| ~ sQ18_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f380,f650]) ).
fof(f684,plain,
( sQ61_spl
| ~ sQ18_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f683]) ).
fof(f689,plain,
( ~ sQ62_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f617,f240,f381]) ).
fof(f702,plain,
( ~ sQ2_spl
| ~ sQ23_spl
| product(e_2,e_1,e_4) ),
inference(resolution,[status(thm)],[f218,f485]) ).
fof(f713,plain,
( ~ sQ2_spl
| ~ sQ23_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f702,f362,f217,f133]) ).
fof(f716,plain,
$false,
inference(sat_refutation,[status(thm)],[f139,f152,f180,f182,f207,f220,f248,f250,f255,f261,f262,f263,f293,f321,f323,f329,f387,f389,f399,f402,f405,f408,f411,f414,f417,f420,f423,f426,f431,f440,f441,f448,f479,f490,f498,f516,f528,f542,f559,f572,f583,f637,f649,f663,f667,f668,f680,f684,f689,f713]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP126-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:02:29 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.44 % Refutation found
% 0.14/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.48 % Elapsed time: 0.095241 seconds
% 0.14/0.48 % CPU time: 0.389600 seconds
% 0.14/0.48 % Total memory used: 19.127 MB
% 0.14/0.48 % Net memory used: 18.959 MB
%------------------------------------------------------------------------------