%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET776+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 02:10:35 PM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 69 ( 15 unt; 11 def)
% Number of atoms : 304 ( 0 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 379 ( 144 ~; 132 |; 75 &)
% ( 17 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 11 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 111 ( 89 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [R,E] :
( pre_order(R,E)
<=> ( ! [X,Y,Z] :
( ( member(Z,E)
& member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,Z)
& apply(R,X,Y) )
=> apply(R,X,Z) ) )
& ! [X] :
( member(X,E)
=> apply(R,X,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [E,P,R] :
( ( ! [A,B] :
( ( member(B,E)
& member(A,E) )
=> ( apply(R,A,B)
<=> ( apply(P,B,A)
& apply(P,A,B) ) ) )
& pre_order(P,E) )
=> ! [X1,X2,Y1,Y2] :
( ( member(Y2,E)
& member(Y1,E)
& member(X2,E)
& member(X1,E) )
=> ( ( apply(P,X1,X2)
& apply(R,X2,Y2)
& apply(R,X1,Y1) )
=> apply(P,Y1,Y2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [E,P,R] :
( ( ! [A,B] :
( ( member(B,E)
& member(A,E) )
=> ( apply(R,A,B)
<=> ( apply(P,B,A)
& apply(P,A,B) ) ) )
& pre_order(P,E) )
=> ! [X1,X2,Y1,Y2] :
( ( member(Y2,E)
& member(Y1,E)
& member(X2,E)
& member(X1,E) )
=> ( ( apply(P,X1,X2)
& apply(R,X2,Y2)
& apply(R,X1,Y1) )
=> apply(P,Y1,Y2) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f112,plain,
! [R,E] :
( pre_order(R,E)
<=> ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] :
( apply(R,X,X)
| ~ member(X,E) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f113,definition,
! [R,E,X] :
( sP2_prd(X,E,R)
<=> ( apply(R,X,X)
| ~ member(X,E) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f114,plain,
! [R,E] :
( pre_order(R,E)
<=> ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP2_prd(X,E,R) ) ),
inference(formula_renaming,[status(thm)],[f112,f113]) ).
fof(f115,plain,
! [R,E] :
( ( ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,Y,Z)
& apply(R,X,Y)
& member(Z,E)
& member(Y,E)
& member(X,E) )
| ? [X] : ~ sP2_prd(X,E,R)
| pre_order(R,E) )
& ( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP2_prd(X,E,R) )
| ~ pre_order(R,E) ) ),
inference(NNF_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
( ! [R,E] :
( ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,Y,Z)
& apply(R,X,Y)
& member(Z,E)
& member(Y,E)
& member(X,E) )
| ? [X] : ~ sP2_prd(X,E,R)
| pre_order(R,E) )
& ! [R,E] :
( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP2_prd(X,E,R) )
| ~ pre_order(R,E) ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
( ! [R,E] :
( ( ~ apply(R,sK11_skl(E,R),sK13_skl(E,R))
& apply(R,sK12_skl(E,R),sK13_skl(E,R))
& apply(R,sK11_skl(E,R),sK12_skl(E,R))
& member(sK13_skl(E,R),E)
& member(sK12_skl(E,R),E)
& member(sK11_skl(E,R),E) )
| ~ sP2_prd(sK10_skl(E,R),E,R)
| pre_order(R,E) )
& ! [R,E] :
( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP2_prd(X,E,R) )
| ~ pre_order(R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(X,sK10_skl(E,R)),skolemize(X,sK11_skl(E,R)),skolemize(Y,sK12_skl(E,R)),skolemize(Z,sK13_skl(E,R))],[f116]) ).
fof(f119,plain,
! [X0,X1,X2,X3,X4] :
( apply(X0,X2,X4)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ pre_order(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f126,plain,
? [E,P,R] :
( ? [X1,X2,Y1,Y2] :
( ~ apply(P,Y1,Y2)
& apply(P,X1,X2)
& apply(R,X2,Y2)
& apply(R,X1,Y1)
& member(Y2,E)
& member(Y1,E)
& member(X2,E)
& member(X1,E) )
& ! [A,B] :
( ( apply(R,A,B)
<=> ( apply(P,B,A)
& apply(P,A,B) ) )
| ~ member(B,E)
| ~ member(A,E) )
& pre_order(P,E) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f127,plain,
? [E,P,R] :
( ? [X1,X2,Y1,Y2] :
( ~ apply(P,Y1,Y2)
& apply(P,X1,X2)
& apply(R,X2,Y2)
& apply(R,X1,Y1)
& member(Y2,E)
& member(Y1,E)
& member(X2,E)
& member(X1,E) )
& ! [A,B] :
( ( ( ~ apply(P,B,A)
| ~ apply(P,A,B)
| apply(R,A,B) )
& ( ( apply(P,B,A)
& apply(P,A,B) )
| ~ apply(R,A,B) ) )
| ~ member(B,E)
| ~ member(A,E) )
& pre_order(P,E) ),
inference(NNF_transformation,[status(thm)],[f126]) ).
fof(f128,plain,
( ~ apply(sK15_skl,sK19_skl,sK20_skl)
& apply(sK15_skl,sK17_skl,sK18_skl)
& apply(sK16_skl,sK18_skl,sK20_skl)
& apply(sK16_skl,sK17_skl,sK19_skl)
& member(sK20_skl,sK14_skl)
& member(sK19_skl,sK14_skl)
& member(sK18_skl,sK14_skl)
& member(sK17_skl,sK14_skl)
& ! [A,B] :
( ( ( ~ apply(sK15_skl,B,A)
| ~ apply(sK15_skl,A,B)
| apply(sK16_skl,A,B) )
& ( ( apply(sK15_skl,B,A)
& apply(sK15_skl,A,B) )
| ~ apply(sK16_skl,A,B) ) )
| ~ member(B,sK14_skl)
| ~ member(A,sK14_skl) )
& pre_order(sK15_skl,sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl,sK17_skl,sK18_skl,sK19_skl,sK20_skl]),skolemize(E,sK14_skl),skolemize(P,sK15_skl),skolemize(R,sK16_skl),skolemize(X1,sK17_skl),skolemize(X2,sK18_skl),skolemize(Y1,sK19_skl),skolemize(Y2,sK20_skl)],[f127]) ).
fof(f129,plain,
pre_order(sK15_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( apply(sK15_skl,X0,X1)
| ~ apply(sK16_skl,X0,X1)
| ~ member(X1,sK14_skl)
| ~ member(X0,sK14_skl) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f131,plain,
! [X0,X1] :
( apply(sK15_skl,X1,X0)
| ~ apply(sK16_skl,X0,X1)
| ~ member(X1,sK14_skl)
| ~ member(X0,sK14_skl) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f133,plain,
member(sK17_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f134,plain,
member(sK18_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f135,plain,
member(sK19_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f136,plain,
member(sK20_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f137,plain,
apply(sK16_skl,sK17_skl,sK19_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f138,plain,
apply(sK16_skl,sK18_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f139,plain,
apply(sK15_skl,sK17_skl,sK18_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f140,plain,
~ apply(sK15_skl,sK19_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f176,definition,
( sQ0_spl
<=> member(sK17_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( sQ0_spl
| ~ member(sK17_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,definition,
( sQ1_spl
<=> member(sK19_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ1_spl
| ~ member(sK19_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f186,plain,
( apply(sK15_skl,sK18_skl,sK20_skl)
| ~ member(sK20_skl,sK14_skl)
| ~ member(sK18_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f138,f130]) ).
fof(f187,definition,
( sQ3_spl
<=> member(sK18_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( sQ3_spl
| ~ member(sK18_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,definition,
( sQ4_spl
<=> member(sK20_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( sQ4_spl
| ~ member(sK20_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,definition,
( sQ5_spl
<=> apply(sK15_skl,sK18_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ5_spl
| apply(sK15_skl,sK18_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f186,f187,f190,f193]) ).
fof(f197,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f136]) ).
fof(f198,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f199,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f189,f134]) ).
fof(f200,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f199]) ).
fof(f201,plain,
! [X0,X1,X2] :
( apply(sK15_skl,X0,X2)
| ~ apply(sK15_skl,X1,X2)
| ~ apply(sK15_skl,X0,X1)
| ~ member(X2,sK14_skl)
| ~ member(X1,sK14_skl)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f119,f129]) ).
fof(f209,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f135]) ).
fof(f210,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f209]) ).
fof(f211,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f133]) ).
fof(f212,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f229,plain,
! [X0] :
( ~ apply(sK15_skl,X0,sK20_skl)
| ~ apply(sK15_skl,sK19_skl,X0)
| ~ member(sK20_skl,sK14_skl)
| ~ member(X0,sK14_skl)
| ~ member(sK19_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f201,f140]) ).
fof(f230,definition,
! [X0] :
( sQ10_spl
<=> ( ~ apply(sK15_skl,X0,sK20_skl)
| ~ apply(sK15_skl,sK19_skl,X0)
| ~ member(X0,sK14_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f231,plain,
! [X0] :
( ~ sQ10_spl
| ~ apply(sK15_skl,X0,sK20_skl)
| ~ apply(sK15_skl,sK19_skl,X0)
| ~ member(X0,sK14_skl) ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f233,plain,
( ~ sQ4_spl
| sQ10_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f229,f179,f230,f190]) ).
fof(f235,plain,
! [X0] :
( ~ sQ10_spl
| ~ apply(sK16_skl,X0,sK19_skl)
| ~ member(sK19_skl,sK14_skl)
| ~ member(X0,sK14_skl)
| ~ apply(sK15_skl,X0,sK20_skl)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f231,f131]) ).
fof(f240,definition,
! [X0] :
( sQ12_spl
<=> ( ~ apply(sK16_skl,X0,sK19_skl)
| ~ member(X0,sK14_skl)
| ~ apply(sK15_skl,X0,sK20_skl)
| ~ member(X0,sK14_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f241,plain,
! [X0] :
( ~ sQ12_spl
| ~ apply(sK16_skl,X0,sK19_skl)
| ~ member(X0,sK14_skl)
| ~ apply(sK15_skl,X0,sK20_skl)
| ~ member(X0,sK14_skl) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,plain,
( ~ sQ10_spl
| ~ sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f235,f240,f179,f230]) ).
fof(f245,plain,
! [X0] :
( ~ sQ12_spl
| ~ apply(sK16_skl,X0,sK19_skl)
| ~ apply(sK15_skl,X0,sK20_skl)
| ~ member(X0,sK14_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f241]) ).
fof(f263,plain,
( ~ sQ12_spl
| ~ apply(sK15_skl,sK17_skl,sK20_skl)
| ~ member(sK17_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f245,f137]) ).
fof(f265,definition,
( sQ15_spl
<=> apply(sK15_skl,sK17_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( sQ15_spl
| ~ apply(sK15_skl,sK17_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f265]) ).
fof(f268,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f263,f176,f265,f240]) ).
fof(f274,plain,
! [X0] :
( sQ15_spl
| ~ apply(sK15_skl,X0,sK20_skl)
| ~ apply(sK15_skl,sK17_skl,X0)
| ~ member(sK20_skl,sK14_skl)
| ~ member(X0,sK14_skl)
| ~ member(sK17_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f267,f201]) ).
fof(f276,definition,
! [X0] :
( sQ17_spl
<=> ( ~ apply(sK15_skl,X0,sK20_skl)
| ~ apply(sK15_skl,sK17_skl,X0)
| ~ member(X0,sK14_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f277,plain,
! [X0] :
( ~ sQ17_spl
| ~ apply(sK15_skl,X0,sK20_skl)
| ~ apply(sK15_skl,sK17_skl,X0)
| ~ member(X0,sK14_skl) ),
inference(component_clause,[status(thm)],[f276]) ).
fof(f279,plain,
( sQ15_spl
| ~ sQ4_spl
| sQ17_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f274,f176,f276,f190,f265]) ).
fof(f301,plain,
( ~ sQ5_spl
| ~ sQ17_spl
| ~ apply(sK15_skl,sK17_skl,sK18_skl)
| ~ member(sK18_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f277,f194]) ).
fof(f304,definition,
( sQ22_spl
<=> apply(sK15_skl,sK17_skl,sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( sQ22_spl
| ~ apply(sK15_skl,sK17_skl,sK18_skl) ),
inference(component_clause,[status(thm)],[f304]) ).
fof(f307,plain,
( ~ sQ5_spl
| ~ sQ17_spl
| ~ sQ22_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f301,f187,f304,f276,f193]) ).
fof(f316,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f139]) ).
fof(f317,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f316]) ).
fof(f318,plain,
$false,
inference(sat_refutation,[status(thm)],[f196,f198,f200,f210,f212,f233,f243,f268,f279,f307,f317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET776+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:37:13 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.41 % Elapsed time: 0.039626 seconds
% 0.08/0.41 % CPU time: 0.091732 seconds
% 0.08/0.41 % Total memory used: 18.696 MB
% 0.08/0.41 % Net memory used: 18.661 MB
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