%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET734+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 02:10:32 PM UTC 2026
% Result : Theorem 46.43s 6.72s
% Output : CNFRefutation 46.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 8 unt; 2 def)
% Number of atoms : 180 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 213 ( 80 ~; 76 |; 44 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-7 aty)
% Number of variables : 162 ( 142 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [G,F,A,B,C,X,Z] :
( ( member(Z,C)
& member(X,A) )
=> ( apply(compose_function(G,F,A,B,C),X,Z)
<=> ? [Y] :
( apply(G,Y,Z)
& apply(F,X,Y)
& member(Y,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [F,A] :
( identity(F,A)
<=> ! [X] :
( member(X,A)
=> apply(F,X,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [F,A,B] :
( surjective(F,A,B)
<=> ! [Y] :
( member(Y,B)
=> ? [E] :
( apply(F,E,Y)
& member(E,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [F,G,A,B] :
( ( identity(compose_function(G,F,B,A,B),B)
& maps(F,B,A)
& maps(G,A,B) )
=> surjective(G,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [F,G,A,B] :
( ( identity(compose_function(G,F,B,A,B),B)
& maps(F,B,A)
& maps(G,A,B) )
=> surjective(G,A,B) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f111,plain,
! [G,F,A,B,C,X,Z] :
( ( apply(compose_function(G,F,A,B,C),X,Z)
<=> ? [Y] :
( apply(G,Y,Z)
& apply(F,X,Y)
& member(Y,B) ) )
| ~ member(Z,C)
| ~ member(X,A) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f112,plain,
! [G,F,A,B,C,X,Z] :
( ( ( ! [Y] :
( ~ apply(G,Y,Z)
| ~ apply(F,X,Y)
| ~ member(Y,B) )
| apply(compose_function(G,F,A,B,C),X,Z) )
& ( ? [Y] :
( apply(G,Y,Z)
& apply(F,X,Y)
& member(Y,B) )
| ~ apply(compose_function(G,F,A,B,C),X,Z) ) )
| ~ member(Z,C)
| ~ member(X,A) ),
inference(NNF_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [A,C,X,Z] :
( ( ! [G,F,B] :
( ! [Y] :
( ~ apply(G,Y,Z)
| ~ apply(F,X,Y)
| ~ member(Y,B) )
| apply(compose_function(G,F,A,B,C),X,Z) )
& ! [G,F,B] :
( ? [Y] :
( apply(G,Y,Z)
& apply(F,X,Y)
& member(Y,B) )
| ~ apply(compose_function(G,F,A,B,C),X,Z) ) )
| ~ member(Z,C)
| ~ member(X,A) ),
inference(miniscoping,[status(thm)],[f112]) ).
fof(f114,plain,
! [A,C,X,Z] :
( ( ! [G,F,B] :
( ! [Y] :
( ~ apply(G,Y,Z)
| ~ apply(F,X,Y)
| ~ member(Y,B) )
| apply(compose_function(G,F,A,B,C),X,Z) )
& ! [G,F,B] :
( ( apply(G,sK11_skl(B,F,G,Z,X,C,A),Z)
& apply(F,X,sK11_skl(B,F,G,Z,X,C,A))
& member(sK11_skl(B,F,G,Z,X,C,A),B) )
| ~ apply(compose_function(G,F,A,B,C),X,Z) ) )
| ~ member(Z,C)
| ~ member(X,A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(Y,sK11_skl(B,F,G,Z,X,C,A))],[f113]) ).
fof(f115,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( member(sK11_skl(X6,X5,X4,X2,X0,X3,X1),X6)
| ~ apply(compose_function(X4,X5,X1,X6,X3),X0,X2)
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ apply(compose_function(X2,X4,X1,X3,X6),X0,X5)
| ~ member(X5,X6)
| apply(X2,sK11_skl(X3,X4,X2,X5,X0,X6,X1),X5)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f130,plain,
! [F,A] :
( identity(F,A)
<=> ! [X] :
( apply(F,X,X)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f131,plain,
! [F,A] :
( ( ? [X] :
( ~ apply(F,X,X)
& member(X,A) )
| identity(F,A) )
& ( ! [X] :
( apply(F,X,X)
| ~ member(X,A) )
| ~ identity(F,A) ) ),
inference(NNF_transformation,[status(thm)],[f130]) ).
fof(f132,plain,
( ! [F,A] :
( ? [X] :
( ~ apply(F,X,X)
& member(X,A) )
| identity(F,A) )
& ! [F,A] :
( ! [X] :
( apply(F,X,X)
| ~ member(X,A) )
| ~ identity(F,A) ) ),
inference(miniscoping,[status(thm)],[f131]) ).
fof(f133,plain,
( ! [F,A] :
( ( ~ apply(F,sK15_skl(A,F),sK15_skl(A,F))
& member(sK15_skl(A,F),A) )
| identity(F,A) )
& ! [F,A] :
( ! [X] :
( apply(F,X,X)
| ~ member(X,A) )
| ~ identity(F,A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(X,sK15_skl(A,F))],[f132]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ member(X1,X2)
| ~ identity(X0,X2)
| apply(X0,X1,X1) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f148,plain,
! [F,A,B] :
( surjective(F,A,B)
<=> ! [Y] :
( ? [E] :
( apply(F,E,Y)
& member(E,A) )
| ~ member(Y,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f149,plain,
! [F,A,B] :
( ( ? [Y] :
( ! [E] :
( ~ apply(F,E,Y)
| ~ member(E,A) )
& member(Y,B) )
| surjective(F,A,B) )
& ( ! [Y] :
( ? [E] :
( apply(F,E,Y)
& member(E,A) )
| ~ member(Y,B) )
| ~ surjective(F,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f148]) ).
fof(f150,plain,
( ! [F,A,B] :
( ? [Y] :
( ! [E] :
( ~ apply(F,E,Y)
| ~ member(E,A) )
& member(Y,B) )
| surjective(F,A,B) )
& ! [F,A,B] :
( ! [Y] :
( ? [E] :
( apply(F,E,Y)
& member(E,A) )
| ~ member(Y,B) )
| ~ surjective(F,A,B) ) ),
inference(miniscoping,[status(thm)],[f149]) ).
fof(f151,plain,
( ! [F,A,B] :
( ( ! [E] :
( ~ apply(F,E,sK20_skl(B,A,F))
| ~ member(E,A) )
& member(sK20_skl(B,A,F),B) )
| surjective(F,A,B) )
& ! [F,A,B] :
( ! [Y] :
( ( apply(F,sK19_skl(Y,B,A,F),Y)
& member(sK19_skl(Y,B,A,F),A) )
| ~ member(Y,B) )
| ~ surjective(F,A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(E,sK19_skl(Y,B,A,F)),skolemize(Y,sK20_skl(B,A,F))],[f150]) ).
fof(f154,plain,
! [X0,X1,X2] :
( member(sK20_skl(X2,X1,X0),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f155,plain,
! [X0,X1,X2,X3] :
( ~ apply(X2,X0,sK20_skl(X3,X1,X2))
| surjective(X2,X1,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f244,plain,
? [F,G,A,B] :
( ~ surjective(G,A,B)
& identity(compose_function(G,F,B,A,B),B)
& maps(F,B,A)
& maps(G,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f245,plain,
? [G,A,B] :
( ~ surjective(G,A,B)
& ? [F] :
( identity(compose_function(G,F,B,A,B),B)
& maps(F,B,A)
& maps(G,A,B) ) ),
inference(miniscoping,[status(thm)],[f244]) ).
fof(f246,plain,
( ~ surjective(sK39_skl,sK40_skl,sK41_skl)
& identity(compose_function(sK39_skl,sK42_skl,sK41_skl,sK40_skl,sK41_skl),sK41_skl)
& maps(sK42_skl,sK41_skl,sK40_skl)
& maps(sK39_skl,sK40_skl,sK41_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39_skl,sK40_skl,sK41_skl,sK42_skl]),skolemize(G,sK39_skl),skolemize(A,sK40_skl),skolemize(B,sK41_skl),skolemize(F,sK42_skl)],[f245]) ).
fof(f249,plain,
identity(compose_function(sK39_skl,sK42_skl,sK41_skl,sK40_skl,sK41_skl),sK41_skl),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f250,plain,
~ surjective(sK39_skl,sK40_skl,sK41_skl),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f279,plain,
member(sK20_skl(sK41_skl,sK40_skl,sK39_skl),sK41_skl),
inference(resolution,[status(thm)],[f154,f250]) ).
fof(f283,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( member(sK11_skl(X6,X5,X4,X0,X0,X2,X3),X6)
| ~ identity(compose_function(X4,X5,X3,X6,X2),X1)
| ~ member(X0,X3)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f115,f134]) ).
fof(f289,plain,
! [X0] :
( member(sK11_skl(sK40_skl,sK42_skl,sK39_skl,X0,X0,sK41_skl,sK41_skl),sK40_skl)
| ~ member(X0,sK41_skl)
| ~ member(X0,sK41_skl)
| ~ member(X0,sK41_skl) ),
inference(resolution,[status(thm)],[f283,f249]) ).
fof(f291,plain,
! [X0] :
( member(sK11_skl(sK40_skl,sK42_skl,sK39_skl,X0,X0,sK41_skl,sK41_skl),sK40_skl)
| ~ member(X0,sK41_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f289]) ).
fof(f297,plain,
member(sK11_skl(sK40_skl,sK42_skl,sK39_skl,sK20_skl(sK41_skl,sK40_skl,sK39_skl),sK20_skl(sK41_skl,sK40_skl,sK39_skl),sK41_skl,sK41_skl),sK40_skl),
inference(resolution,[status(thm)],[f291,f279]) ).
fof(f328,definition,
( sQ5_spl
<=> member(sK11_skl(sK40_skl,sK42_skl,sK39_skl,sK20_skl(sK41_skl,sK40_skl,sK39_skl),sK20_skl(sK41_skl,sK40_skl,sK39_skl),sK41_skl,sK41_skl),sK40_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( sQ5_spl
| ~ member(sK11_skl(sK40_skl,sK42_skl,sK39_skl,sK20_skl(sK41_skl,sK40_skl,sK39_skl),sK20_skl(sK41_skl,sK40_skl,sK39_skl),sK41_skl,sK41_skl),sK40_skl) ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f528,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ identity(compose_function(X4,X6,X2,X5,X3),X1)
| apply(X4,sK11_skl(X5,X6,X4,X0,X0,X3,X2),X0)
| ~ member(X0,X3)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f117,f134]) ).
fof(f530,plain,
! [X0] :
( apply(sK39_skl,sK11_skl(sK40_skl,sK42_skl,sK39_skl,X0,X0,sK41_skl,sK41_skl),X0)
| ~ member(X0,sK41_skl)
| ~ member(X0,sK41_skl)
| ~ member(X0,sK41_skl) ),
inference(resolution,[status(thm)],[f528,f249]) ).
fof(f532,plain,
! [X0] :
( apply(sK39_skl,sK11_skl(sK40_skl,sK42_skl,sK39_skl,X0,X0,sK41_skl,sK41_skl),X0)
| ~ member(X0,sK41_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f530]) ).
fof(f545,plain,
apply(sK39_skl,sK11_skl(sK40_skl,sK42_skl,sK39_skl,sK20_skl(sK41_skl,sK40_skl,sK39_skl),sK20_skl(sK41_skl,sK40_skl,sK39_skl),sK41_skl,sK41_skl),sK20_skl(sK41_skl,sK40_skl,sK39_skl)),
inference(resolution,[status(thm)],[f532,f279]) ).
fof(f1670,definition,
( sQ52_spl
<=> surjective(sK39_skl,sK40_skl,sK41_skl) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1671,plain,
( ~ sQ52_spl
| surjective(sK39_skl,sK40_skl,sK41_skl) ),
inference(component_clause,[status(thm)],[f1670]) ).
fof(f1674,plain,
( ~ sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1671,f250]) ).
fof(f1675,plain,
~ sQ52_spl,
inference(contradiction_clause,[status(thm)],[f1674]) ).
fof(f2659,plain,
( surjective(sK39_skl,sK40_skl,sK41_skl)
| ~ member(sK11_skl(sK40_skl,sK42_skl,sK39_skl,sK20_skl(sK41_skl,sK40_skl,sK39_skl),sK20_skl(sK41_skl,sK40_skl,sK39_skl),sK41_skl,sK41_skl),sK40_skl) ),
inference(resolution,[status(thm)],[f545,f155]) ).
fof(f2671,plain,
( sQ52_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2659,f328,f1670]) ).
fof(f2674,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f330,f297]) ).
fof(f2675,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f2674]) ).
fof(f2676,plain,
$false,
inference(sat_refutation,[status(thm)],[f1675,f2671,f2675]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET734+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 05:35:55 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 46.43/6.72 % Refutation found
% 46.43/6.72 % SZS status Theorem for theBenchmark: Theorem is valid
% 46.43/6.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.01/7.52 % Elapsed time: 7.134163 seconds
% 4.01/7.52 % CPU time: 50.701313 seconds
% 4.01/7.52 % Total memory used: 267.101 MB
% 4.01/7.52 % Net memory used: 235.991 MB
%------------------------------------------------------------------------------