%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET721+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 02:10:31 PM UTC 2026
% Result : Theorem 76.43s 10.28s
% Output : CNFRefutation 76.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of formulae : 70 ( 6 unt; 3 def)
% Number of atoms : 419 ( 35 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 586 ( 237 ~; 244 |; 87 &)
% ( 10 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-7 aty)
% Number of variables : 305 ( 272 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [F,A,B] :
( maps(F,A,B)
<=> ( ! [X,Y1,Y2] :
( ( member(Y2,B)
& member(Y1,B)
& member(X,A) )
=> ( ( apply(F,X,Y2)
& apply(F,X,Y1) )
=> Y1 = Y2 ) )
& ! [X] :
( member(X,A)
=> ? [Y] :
( apply(F,X,Y)
& member(Y,B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f17,axiom,
! [F,A,B] :
( injective(F,A,B)
<=> ! [X1,X2,Y] :
( ( member(Y,B)
& member(X2,A)
& member(X1,A) )
=> ( ( apply(F,X2,Y)
& apply(F,X1,Y) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [F,G,A,B,C] :
( ( injective(compose_function(G,F,A,B,C),A,C)
& maps(G,B,C)
& maps(F,A,B) )
=> injective(F,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [F,G,A,B,C] :
( ( injective(compose_function(G,F,A,B,C),A,C)
& maps(G,B,C)
& maps(F,A,B) )
=> injective(F,A,B) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f85,plain,
! [F,A,B] :
( maps(F,A,B)
<=> ( ! [X,Y1,Y2] :
( Y1 = Y2
| ~ apply(F,X,Y2)
| ~ apply(F,X,Y1)
| ~ member(Y2,B)
| ~ member(Y1,B)
| ~ member(X,A) )
& ! [X] :
( ? [Y] :
( apply(F,X,Y)
& member(Y,B) )
| ~ member(X,A) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f86,definition,
! [F,A,B,X] :
( sP0_prd(X,B,A,F)
<=> ( ? [Y] :
( apply(F,X,Y)
& member(Y,B) )
| ~ member(X,A) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f87,plain,
! [F,A,B] :
( maps(F,A,B)
<=> ( ! [X,Y1,Y2] :
( Y1 = Y2
| ~ apply(F,X,Y2)
| ~ apply(F,X,Y1)
| ~ member(Y2,B)
| ~ member(Y1,B)
| ~ member(X,A) )
& ! [X] : sP0_prd(X,B,A,F) ) ),
inference(formula_renaming,[status(thm)],[f85,f86]) ).
fof(f88,plain,
! [F,A,B] :
( ( ? [X,Y1,Y2] :
( Y1 != Y2
& apply(F,X,Y2)
& apply(F,X,Y1)
& member(Y2,B)
& member(Y1,B)
& member(X,A) )
| ? [X] : ~ sP0_prd(X,B,A,F)
| maps(F,A,B) )
& ( ( ! [X,Y1,Y2] :
( Y1 = Y2
| ~ apply(F,X,Y2)
| ~ apply(F,X,Y1)
| ~ member(Y2,B)
| ~ member(Y1,B)
| ~ member(X,A) )
& ! [X] : sP0_prd(X,B,A,F) )
| ~ maps(F,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
( ! [F,A,B] :
( ? [X,Y1,Y2] :
( Y1 != Y2
& apply(F,X,Y2)
& apply(F,X,Y1)
& member(Y2,B)
& member(Y1,B)
& member(X,A) )
| ? [X] : ~ sP0_prd(X,B,A,F)
| maps(F,A,B) )
& ! [F,A,B] :
( ( ! [X,Y1,Y2] :
( Y1 = Y2
| ~ apply(F,X,Y2)
| ~ apply(F,X,Y1)
| ~ member(Y2,B)
| ~ member(Y1,B)
| ~ member(X,A) )
& ! [X] : sP0_prd(X,B,A,F) )
| ~ maps(F,A,B) ) ),
inference(miniscoping,[status(thm)],[f88]) ).
fof(f90,plain,
( ! [F,A,B] :
( ( sK5_skl(B,A,F) != sK6_skl(B,A,F)
& apply(F,sK4_skl(B,A,F),sK6_skl(B,A,F))
& apply(F,sK4_skl(B,A,F),sK5_skl(B,A,F))
& member(sK6_skl(B,A,F),B)
& member(sK5_skl(B,A,F),B)
& member(sK4_skl(B,A,F),A) )
| ~ sP0_prd(sK3_skl(B,A,F),B,A,F)
| maps(F,A,B) )
& ! [F,A,B] :
( ( ! [X,Y1,Y2] :
( Y1 = Y2
| ~ apply(F,X,Y2)
| ~ apply(F,X,Y1)
| ~ member(Y2,B)
| ~ member(Y1,B)
| ~ member(X,A) )
& ! [X] : sP0_prd(X,B,A,F) )
| ~ maps(F,A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(X,sK3_skl(B,A,F)),skolemize(X,sK4_skl(B,A,F)),skolemize(Y1,sK5_skl(B,A,F)),skolemize(Y2,sK6_skl(B,A,F))],[f89]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( sP0_prd(X3,X2,X1,X0)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
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(f118,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ apply(X4,X7,X2)
| ~ apply(X5,X0,X7)
| ~ member(X7,X6)
| apply(compose_function(X4,X5,X1,X6,X3),X0,X2)
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f137,plain,
! [F,A,B] :
( injective(F,A,B)
<=> ! [X1,X2,Y] :
( X1 = X2
| ~ apply(F,X2,Y)
| ~ apply(F,X1,Y)
| ~ member(Y,B)
| ~ member(X2,A)
| ~ member(X1,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f138,plain,
! [F,A,B] :
( ( ? [X1,X2,Y] :
( X1 != X2
& apply(F,X2,Y)
& apply(F,X1,Y)
& member(Y,B)
& member(X2,A)
& member(X1,A) )
| injective(F,A,B) )
& ( ! [X1,X2,Y] :
( X1 = X2
| ~ apply(F,X2,Y)
| ~ apply(F,X1,Y)
| ~ member(Y,B)
| ~ member(X2,A)
| ~ member(X1,A) )
| ~ injective(F,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
( ! [F,A,B] :
( ? [X1,X2,Y] :
( X1 != X2
& apply(F,X2,Y)
& apply(F,X1,Y)
& member(Y,B)
& member(X2,A)
& member(X1,A) )
| injective(F,A,B) )
& ! [F,A,B] :
( ! [X1,X2,Y] :
( X1 = X2
| ~ apply(F,X2,Y)
| ~ apply(F,X1,Y)
| ~ member(Y,B)
| ~ member(X2,A)
| ~ member(X1,A) )
| ~ injective(F,A,B) ) ),
inference(miniscoping,[status(thm)],[f138]) ).
fof(f140,plain,
( ! [F,A,B] :
( ( sK16_skl(B,A,F) != sK17_skl(B,A,F)
& apply(F,sK17_skl(B,A,F),sK18_skl(B,A,F))
& apply(F,sK16_skl(B,A,F),sK18_skl(B,A,F))
& member(sK18_skl(B,A,F),B)
& member(sK17_skl(B,A,F),A)
& member(sK16_skl(B,A,F),A) )
| injective(F,A,B) )
& ! [F,A,B] :
( ! [X1,X2,Y] :
( X1 = X2
| ~ apply(F,X2,Y)
| ~ apply(F,X1,Y)
| ~ member(Y,B)
| ~ member(X2,A)
| ~ member(X1,A) )
| ~ injective(F,A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl,sK17_skl,sK18_skl]),skolemize(X1,sK16_skl(B,A,F)),skolemize(X2,sK17_skl(B,A,F)),skolemize(Y,sK18_skl(B,A,F))],[f139]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4,X5] :
( X3 = X4
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ injective(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f142,plain,
! [X0,X1,X2] :
( member(sK16_skl(X2,X1,X0),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f143,plain,
! [X0,X1,X2] :
( member(sK17_skl(X2,X1,X0),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f144,plain,
! [X0,X1,X2] :
( member(sK18_skl(X2,X1,X0),X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f145,plain,
! [X0,X1,X2] :
( apply(X0,sK16_skl(X2,X1,X0),sK18_skl(X2,X1,X0))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f146,plain,
! [X0,X1,X2] :
( apply(X0,sK17_skl(X2,X1,X0),sK18_skl(X2,X1,X0))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f147,plain,
! [X0,X1,X2] :
( sK16_skl(X2,X1,X0) != sK17_skl(X2,X1,X0)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f244,plain,
? [F,G,A,B,C] :
( ~ injective(F,A,B)
& injective(compose_function(G,F,A,B,C),A,C)
& maps(G,B,C)
& maps(F,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f245,plain,
? [F,A,B] :
( ~ injective(F,A,B)
& ? [G,C] :
( injective(compose_function(G,F,A,B,C),A,C)
& maps(G,B,C)
& maps(F,A,B) ) ),
inference(miniscoping,[status(thm)],[f244]) ).
fof(f246,plain,
( ~ injective(sK39_skl,sK40_skl,sK41_skl)
& injective(compose_function(sK42_skl,sK39_skl,sK40_skl,sK41_skl,sK43_skl),sK40_skl,sK43_skl)
& maps(sK42_skl,sK41_skl,sK43_skl)
& maps(sK39_skl,sK40_skl,sK41_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39_skl,sK40_skl,sK41_skl,sK42_skl,sK43_skl]),skolemize(F,sK39_skl),skolemize(A,sK40_skl),skolemize(B,sK41_skl),skolemize(G,sK42_skl),skolemize(C,sK43_skl)],[f245]) ).
fof(f248,plain,
maps(sK42_skl,sK41_skl,sK43_skl),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f249,plain,
injective(compose_function(sK42_skl,sK39_skl,sK40_skl,sK41_skl,sK43_skl),sK40_skl,sK43_skl),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f250,plain,
~ injective(sK39_skl,sK40_skl,sK41_skl),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f251,plain,
! [F,A,B,X] :
( ( ( ! [Y] :
( ~ apply(F,X,Y)
| ~ member(Y,B) )
& member(X,A) )
| sP0_prd(X,B,A,F) )
& ( ? [Y] :
( apply(F,X,Y)
& member(Y,B) )
| ~ member(X,A)
| ~ sP0_prd(X,B,A,F) ) ),
inference(NNF_transformation,[status(thm)],[f86]) ).
fof(f252,plain,
( ! [F,A,B,X] :
( ( ! [Y] :
( ~ apply(F,X,Y)
| ~ member(Y,B) )
& member(X,A) )
| sP0_prd(X,B,A,F) )
& ! [F,A,B,X] :
( ? [Y] :
( apply(F,X,Y)
& member(Y,B) )
| ~ member(X,A)
| ~ sP0_prd(X,B,A,F) ) ),
inference(miniscoping,[status(thm)],[f251]) ).
fof(f253,plain,
( ! [F,A,B,X] :
( ( ! [Y] :
( ~ apply(F,X,Y)
| ~ member(Y,B) )
& member(X,A) )
| sP0_prd(X,B,A,F) )
& ! [F,A,B,X] :
( ( apply(F,X,sK44_skl(X,B,A,F))
& member(sK44_skl(X,B,A,F),B) )
| ~ member(X,A)
| ~ sP0_prd(X,B,A,F) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44_skl]),skolemize(Y,sK44_skl(X,B,A,F))],[f252]) ).
fof(f254,plain,
! [X0,X1,X2,X3] :
( member(sK44_skl(X0,X1,X2,X3),X1)
| ~ member(X0,X2)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f255,plain,
! [X0,X1,X2,X3] :
( apply(X3,X0,sK44_skl(X0,X1,X2,X3))
| ~ member(X0,X2)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f269,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ apply(compose_function(sK42_skl,sK39_skl,sK40_skl,sK41_skl,sK43_skl),X1,X2)
| ~ apply(compose_function(sK42_skl,sK39_skl,sK40_skl,sK41_skl,sK43_skl),X0,X2)
| ~ member(X2,sK43_skl)
| ~ member(X1,sK40_skl)
| ~ member(X0,sK40_skl) ),
inference(resolution,[status(thm)],[f141,f249]) ).
fof(f270,plain,
! [X0,X1,X2,X3] :
( ~ apply(sK42_skl,X3,X2)
| ~ apply(sK39_skl,X1,X3)
| ~ member(X3,sK41_skl)
| ~ member(X2,sK43_skl)
| ~ member(X1,sK40_skl)
| X0 = X1
| ~ apply(compose_function(sK42_skl,sK39_skl,sK40_skl,sK41_skl,sK43_skl),X0,X2)
| ~ member(X2,sK43_skl)
| ~ member(X1,sK40_skl)
| ~ member(X0,sK40_skl) ),
inference(resolution,[status(thm)],[f269,f118]) ).
fof(f271,plain,
! [X0,X1,X2,X3] :
( ~ apply(sK42_skl,X3,X2)
| ~ apply(sK39_skl,X1,X3)
| ~ member(X3,sK41_skl)
| X0 = X1
| ~ apply(compose_function(sK42_skl,sK39_skl,sK40_skl,sK41_skl,sK43_skl),X0,X2)
| ~ member(X2,sK43_skl)
| ~ member(X1,sK40_skl)
| ~ member(X0,sK40_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f270]) ).
fof(f272,plain,
! [X0,X1,X2,X3,X4] :
( ~ apply(sK42_skl,X4,X2)
| ~ apply(sK39_skl,X0,X4)
| ~ member(X4,sK41_skl)
| ~ member(X2,sK43_skl)
| ~ member(X0,sK40_skl)
| ~ apply(sK42_skl,X3,X2)
| ~ apply(sK39_skl,X1,X3)
| ~ member(X3,sK41_skl)
| X0 = X1
| ~ member(X2,sK43_skl)
| ~ member(X1,sK40_skl)
| ~ member(X0,sK40_skl) ),
inference(resolution,[status(thm)],[f271,f118]) ).
fof(f273,plain,
! [X0,X1,X2,X3,X4] :
( ~ apply(sK42_skl,X4,X2)
| ~ apply(sK39_skl,X0,X4)
| ~ member(X4,sK41_skl)
| ~ apply(sK42_skl,X3,X2)
| ~ apply(sK39_skl,X1,X3)
| ~ member(X3,sK41_skl)
| X0 = X1
| ~ member(X2,sK43_skl)
| ~ member(X1,sK40_skl)
| ~ member(X0,sK40_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f272]) ).
fof(f274,plain,
! [X0,X1,X2,X3] :
( ~ apply(sK39_skl,X0,X3)
| ~ member(X3,sK41_skl)
| ~ apply(sK42_skl,X3,X2)
| ~ apply(sK39_skl,X1,X3)
| ~ member(X3,sK41_skl)
| X0 = X1
| ~ member(X2,sK43_skl)
| ~ member(X1,sK40_skl)
| ~ member(X0,sK40_skl) ),
inference(factoring,[status(thm)],[f273]) ).
fof(f275,plain,
! [X0,X1,X2,X3] :
( ~ apply(sK39_skl,X0,X3)
| ~ apply(sK42_skl,X3,X2)
| ~ apply(sK39_skl,X1,X3)
| ~ member(X3,sK41_skl)
| X0 = X1
| ~ member(X2,sK43_skl)
| ~ member(X1,sK40_skl)
| ~ member(X0,sK40_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f274]) ).
fof(f5167,plain,
! [X0,X1,X2,X3,X4] :
( ~ apply(sK39_skl,X3,X0)
| ~ apply(sK39_skl,X4,X0)
| ~ member(X0,sK41_skl)
| X3 = X4
| ~ member(sK44_skl(X0,X1,X2,sK42_skl),sK43_skl)
| ~ member(X4,sK40_skl)
| ~ member(X3,sK40_skl)
| ~ member(X0,X2)
| ~ sP0_prd(X0,X1,X2,sK42_skl) ),
inference(resolution,[status(thm)],[f255,f275]) ).
fof(f5762,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X1)
| ~ sP0_prd(X0,sK43_skl,X1,sK42_skl)
| ~ apply(sK39_skl,X2,X0)
| ~ apply(sK39_skl,X3,X0)
| ~ member(X0,sK41_skl)
| X2 = X3
| ~ member(X3,sK40_skl)
| ~ member(X2,sK40_skl)
| ~ member(X0,X1)
| ~ sP0_prd(X0,sK43_skl,X1,sK42_skl) ),
inference(resolution,[status(thm)],[f5167,f254]) ).
fof(f5763,plain,
! [X0,X1,X2,X3] :
( ~ apply(sK39_skl,X2,X0)
| ~ apply(sK39_skl,X3,X0)
| ~ member(X0,sK41_skl)
| X2 = X3
| ~ member(X3,sK40_skl)
| ~ member(X2,sK40_skl)
| ~ member(X0,X1)
| ~ sP0_prd(X0,sK43_skl,X1,sK42_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f5762]) ).
fof(f5765,plain,
! [X0,X1,X2,X3] :
( ~ maps(sK42_skl,X1,sK43_skl)
| ~ apply(sK39_skl,X2,X0)
| ~ apply(sK39_skl,X3,X0)
| ~ member(X0,sK41_skl)
| X2 = X3
| ~ member(X3,sK40_skl)
| ~ member(X2,sK40_skl)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f5763,f91]) ).
fof(f5767,plain,
! [X0,X1,X2] :
( ~ apply(sK39_skl,X1,X0)
| ~ apply(sK39_skl,X2,X0)
| ~ member(X0,sK41_skl)
| X1 = X2
| ~ member(X2,sK40_skl)
| ~ member(X1,sK40_skl)
| ~ member(X0,sK41_skl) ),
inference(resolution,[status(thm)],[f5765,f248]) ).
fof(f5768,plain,
! [X0,X1,X2] :
( ~ apply(sK39_skl,X1,X0)
| ~ apply(sK39_skl,X2,X0)
| X1 = X2
| ~ member(X2,sK40_skl)
| ~ member(X1,sK40_skl)
| ~ member(X0,sK41_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f5767]) ).
fof(f5785,plain,
! [X0,X1,X2] :
( injective(sK39_skl,X1,X0)
| ~ apply(sK39_skl,X2,sK18_skl(X0,X1,sK39_skl))
| X2 = sK17_skl(X0,X1,sK39_skl)
| ~ member(sK17_skl(X0,X1,sK39_skl),sK40_skl)
| ~ member(X2,sK40_skl)
| ~ member(sK18_skl(X0,X1,sK39_skl),sK41_skl) ),
inference(resolution,[status(thm)],[f5768,f146]) ).
fof(f6734,plain,
! [X0,X1] :
( injective(sK39_skl,X1,X0)
| injective(sK39_skl,X1,X0)
| sK16_skl(X0,X1,sK39_skl) = sK17_skl(X0,X1,sK39_skl)
| ~ member(sK17_skl(X0,X1,sK39_skl),sK40_skl)
| ~ member(sK16_skl(X0,X1,sK39_skl),sK40_skl)
| ~ member(sK18_skl(X0,X1,sK39_skl),sK41_skl) ),
inference(resolution,[status(thm)],[f5785,f145]) ).
fof(f6737,plain,
! [X0,X1] :
( injective(sK39_skl,X1,X0)
| sK16_skl(X0,X1,sK39_skl) = sK17_skl(X0,X1,sK39_skl)
| ~ member(sK17_skl(X0,X1,sK39_skl),sK40_skl)
| ~ member(sK16_skl(X0,X1,sK39_skl),sK40_skl)
| ~ member(sK18_skl(X0,X1,sK39_skl),sK41_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f6734]) ).
fof(f6738,plain,
! [X0,X1] :
( injective(sK39_skl,X1,X0)
| ~ member(sK17_skl(X0,X1,sK39_skl),sK40_skl)
| ~ member(sK16_skl(X0,X1,sK39_skl),sK40_skl)
| ~ member(sK18_skl(X0,X1,sK39_skl),sK41_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f6737,f147]) ).
fof(f6747,plain,
! [X0] :
( injective(sK39_skl,X0,sK41_skl)
| injective(sK39_skl,X0,sK41_skl)
| ~ member(sK17_skl(sK41_skl,X0,sK39_skl),sK40_skl)
| ~ member(sK16_skl(sK41_skl,X0,sK39_skl),sK40_skl) ),
inference(resolution,[status(thm)],[f6738,f144]) ).
fof(f6748,plain,
! [X0] :
( injective(sK39_skl,X0,sK41_skl)
| ~ member(sK17_skl(sK41_skl,X0,sK39_skl),sK40_skl)
| ~ member(sK16_skl(sK41_skl,X0,sK39_skl),sK40_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f6747]) ).
fof(f6749,plain,
( injective(sK39_skl,sK40_skl,sK41_skl)
| injective(sK39_skl,sK40_skl,sK41_skl)
| ~ member(sK16_skl(sK41_skl,sK40_skl,sK39_skl),sK40_skl) ),
inference(resolution,[status(thm)],[f6748,f143]) ).
fof(f6750,definition,
( sQ2_spl
<=> member(sK16_skl(sK41_skl,sK40_skl,sK39_skl),sK40_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f6752,plain,
( sQ2_spl
| ~ member(sK16_skl(sK41_skl,sK40_skl,sK39_skl),sK40_skl) ),
inference(component_clause,[status(thm)],[f6750]) ).
fof(f6753,definition,
( sQ3_spl
<=> injective(sK39_skl,sK40_skl,sK41_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f6754,plain,
( ~ sQ3_spl
| injective(sK39_skl,sK40_skl,sK41_skl) ),
inference(component_clause,[status(thm)],[f6753]) ).
fof(f6756,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f6749,f6750,f6753]) ).
fof(f6757,plain,
( sQ2_spl
| injective(sK39_skl,sK40_skl,sK41_skl) ),
inference(resolution,[status(thm)],[f6752,f142]) ).
fof(f6758,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6757,f250]) ).
fof(f6759,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f6758]) ).
fof(f6760,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6754,f250]) ).
fof(f6761,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f6760]) ).
fof(f6762,plain,
$false,
inference(sat_refutation,[status(thm)],[f6756,f6759,f6761]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET721+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n008.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 05:34:39 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 76.43/10.28 % Refutation found
% 76.43/10.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 76.43/10.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 76.43/10.35 % Elapsed time: 9.897984 seconds
% 76.43/10.35 % CPU time: 77.738732 seconds
% 76.43/10.35 % Total memory used: 302.928 MB
% 76.43/10.35 % Net memory used: 267.758 MB
%------------------------------------------------------------------------------