TSTP Solution File: SET724+4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET724+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:40:15 EDT 2024
% Result : Theorem 19.33s 2.81s
% Output : CNFRefutation 19.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 6
% Syntax : Number of formulae : 70 ( 6 unt; 0 def)
% Number of atoms : 400 ( 29 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 565 ( 235 ~; 240 |; 76 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 10 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-7 aty)
% Number of variables : 313 ( 282 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [G,F,A,B,C,X,Z] :
( ( member(X,A)
& member(Z,C) )
=> ( apply(compose_function(G,F,A,B,C),X,Z)
<=> ? [Y] :
( member(Y,B)
& apply(F,X,Y)
& apply(G,Y,Z) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [F,G,A,B] :
( equal_maps(F,G,A,B)
<=> ! [X,Y1,Y2] :
( ( member(X,A)
& member(Y1,B)
& member(Y2,B) )
=> ( ( apply(F,X,Y1)
& apply(G,X,Y2) )
=> Y1 = Y2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [F,A,B] :
( surjective(F,A,B)
<=> ! [Y] :
( member(Y,B)
=> ? [E] :
( member(E,A)
& apply(F,E,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [F,A,Y] :
( member(Y,image2(F,A))
<=> ? [X] :
( member(X,A)
& apply(F,X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [F,G,H,A,B,C] :
( ( maps(F,A,B)
& maps(G,B,C)
& maps(H,B,C)
& surjective(F,A,B)
& equal_maps(compose_function(G,F,A,B,C),compose_function(H,F,A,B,C),A,C) )
=> equal_maps(G,H,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [F,G,H,A,B,C] :
( ( maps(F,A,B)
& maps(G,B,C)
& maps(H,B,C)
& surjective(F,A,B)
& equal_maps(compose_function(G,F,A,B,C),compose_function(H,F,A,B,C),A,C) )
=> equal_maps(G,H,B,C) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f111,plain,
! [G,F,A,B,C,X,Z] :
( ~ member(X,A)
| ~ member(Z,C)
| ( apply(compose_function(G,F,A,B,C),X,Z)
<=> ? [Y] :
( member(Y,B)
& apply(F,X,Y)
& apply(G,Y,Z) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f112,plain,
! [G,F,A,B,C,X,Z] :
( ~ member(X,A)
| ~ member(Z,C)
| ( ( ~ apply(compose_function(G,F,A,B,C),X,Z)
| ? [Y] :
( member(Y,B)
& apply(F,X,Y)
& apply(G,Y,Z) ) )
& ( apply(compose_function(G,F,A,B,C),X,Z)
| ! [Y] :
( ~ member(Y,B)
| ~ apply(F,X,Y)
| ~ apply(G,Y,Z) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f111]) ).
fof(f113,plain,
! [A,C,X,Z] :
( ~ member(X,A)
| ~ member(Z,C)
| ( ! [G,F,B] :
( ~ apply(compose_function(G,F,A,B,C),X,Z)
| ? [Y] :
( member(Y,B)
& apply(F,X,Y)
& apply(G,Y,Z) ) )
& ! [G,F,B] :
( apply(compose_function(G,F,A,B,C),X,Z)
| ! [Y] :
( ~ member(Y,B)
| ~ apply(F,X,Y)
| ~ apply(G,Y,Z) ) ) ) ),
inference(miniscoping,[status(esa)],[f112]) ).
fof(f114,plain,
! [A,C,X,Z] :
( ~ member(X,A)
| ~ member(Z,C)
| ( ! [G,F,B] :
( ~ apply(compose_function(G,F,A,B,C),X,Z)
| ( member(sk0_11(B,F,G,Z,X,C,A),B)
& apply(F,X,sk0_11(B,F,G,Z,X,C,A))
& apply(G,sk0_11(B,F,G,Z,X,C,A),Z) ) )
& ! [G,F,B] :
( apply(compose_function(G,F,A,B,C),X,Z)
| ! [Y] :
( ~ member(Y,B)
| ~ apply(F,X,Y)
| ~ apply(G,Y,Z) ) ) ) ),
inference(skolemization,[status(esa)],[f113]) ).
fof(f118,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| apply(compose_function(X4,X5,X1,X6,X3),X0,X2)
| ~ member(X7,X6)
| ~ apply(X5,X0,X7)
| ~ apply(X4,X7,X2) ),
inference(cnf_transformation,[status(esa)],[f114]) ).
fof(f119,plain,
! [F,G,A,B] :
( equal_maps(F,G,A,B)
<=> ! [X,Y1,Y2] :
( ~ member(X,A)
| ~ member(Y1,B)
| ~ member(Y2,B)
| ~ apply(F,X,Y1)
| ~ apply(G,X,Y2)
| Y1 = Y2 ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f120,plain,
! [F,G,A,B] :
( ( ~ equal_maps(F,G,A,B)
| ! [X,Y1,Y2] :
( ~ member(X,A)
| ~ member(Y1,B)
| ~ member(Y2,B)
| ~ apply(F,X,Y1)
| ~ apply(G,X,Y2)
| Y1 = Y2 ) )
& ( equal_maps(F,G,A,B)
| ? [X,Y1,Y2] :
( member(X,A)
& member(Y1,B)
& member(Y2,B)
& apply(F,X,Y1)
& apply(G,X,Y2)
& Y1 != Y2 ) ) ),
inference(NNF_transformation,[status(esa)],[f119]) ).
fof(f121,plain,
( ! [F,G,A,B] :
( ~ equal_maps(F,G,A,B)
| ! [X,Y1,Y2] :
( ~ member(X,A)
| ~ member(Y1,B)
| ~ member(Y2,B)
| ~ apply(F,X,Y1)
| ~ apply(G,X,Y2)
| Y1 = Y2 ) )
& ! [F,G,A,B] :
( equal_maps(F,G,A,B)
| ? [X,Y1,Y2] :
( member(X,A)
& member(Y1,B)
& member(Y2,B)
& apply(F,X,Y1)
& apply(G,X,Y2)
& Y1 != Y2 ) ) ),
inference(miniscoping,[status(esa)],[f120]) ).
fof(f122,plain,
( ! [F,G,A,B] :
( ~ equal_maps(F,G,A,B)
| ! [X,Y1,Y2] :
( ~ member(X,A)
| ~ member(Y1,B)
| ~ member(Y2,B)
| ~ apply(F,X,Y1)
| ~ apply(G,X,Y2)
| Y1 = Y2 ) )
& ! [F,G,A,B] :
( equal_maps(F,G,A,B)
| ( member(sk0_12(B,A,G,F),A)
& member(sk0_13(B,A,G,F),B)
& member(sk0_14(B,A,G,F),B)
& apply(F,sk0_12(B,A,G,F),sk0_13(B,A,G,F))
& apply(G,sk0_12(B,A,G,F),sk0_14(B,A,G,F))
& sk0_13(B,A,G,F) != sk0_14(B,A,G,F) ) ) ),
inference(skolemization,[status(esa)],[f121]) ).
fof(f123,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ equal_maps(X0,X1,X2,X3)
| ~ member(X4,X2)
| ~ member(X5,X3)
| ~ member(X6,X3)
| ~ apply(X0,X4,X5)
| ~ apply(X1,X4,X6)
| X5 = X6 ),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| member(sk0_12(X3,X2,X1,X0),X2) ),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| member(sk0_13(X3,X2,X1,X0),X3) ),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f126,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| member(sk0_14(X3,X2,X1,X0),X3) ),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| apply(X0,sk0_12(X3,X2,X1,X0),sk0_13(X3,X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| apply(X1,sk0_12(X3,X2,X1,X0),sk0_14(X3,X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| sk0_13(X3,X2,X1,X0) != sk0_14(X3,X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f148,plain,
! [F,A,B] :
( surjective(F,A,B)
<=> ! [Y] :
( ~ member(Y,B)
| ? [E] :
( member(E,A)
& apply(F,E,Y) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f149,plain,
! [F,A,B] :
( ( ~ surjective(F,A,B)
| ! [Y] :
( ~ member(Y,B)
| ? [E] :
( member(E,A)
& apply(F,E,Y) ) ) )
& ( surjective(F,A,B)
| ? [Y] :
( member(Y,B)
& ! [E] :
( ~ member(E,A)
| ~ apply(F,E,Y) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f148]) ).
fof(f150,plain,
( ! [F,A,B] :
( ~ surjective(F,A,B)
| ! [Y] :
( ~ member(Y,B)
| ? [E] :
( member(E,A)
& apply(F,E,Y) ) ) )
& ! [F,A,B] :
( surjective(F,A,B)
| ? [Y] :
( member(Y,B)
& ! [E] :
( ~ member(E,A)
| ~ apply(F,E,Y) ) ) ) ),
inference(miniscoping,[status(esa)],[f149]) ).
fof(f151,plain,
( ! [F,A,B] :
( ~ surjective(F,A,B)
| ! [Y] :
( ~ member(Y,B)
| ( member(sk0_19(Y,B,A,F),A)
& apply(F,sk0_19(Y,B,A,F),Y) ) ) )
& ! [F,A,B] :
( surjective(F,A,B)
| ( member(sk0_20(B,A,F),B)
& ! [E] :
( ~ member(E,A)
| ~ apply(F,E,sk0_20(B,A,F)) ) ) ) ),
inference(skolemization,[status(esa)],[f150]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( ~ surjective(X0,X1,X2)
| ~ member(X3,X2)
| member(sk0_19(X3,X2,X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( ~ surjective(X0,X1,X2)
| ~ member(X3,X2)
| apply(X0,sk0_19(X3,X2,X1,X0),X3) ),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f176,plain,
! [F,A,Y] :
( ( ~ member(Y,image2(F,A))
| ? [X] :
( member(X,A)
& apply(F,X,Y) ) )
& ( member(Y,image2(F,A))
| ! [X] :
( ~ member(X,A)
| ~ apply(F,X,Y) ) ) ),
inference(NNF_transformation,[status(esa)],[f22]) ).
fof(f177,plain,
( ! [F,A,Y] :
( ~ member(Y,image2(F,A))
| ? [X] :
( member(X,A)
& apply(F,X,Y) ) )
& ! [F,A,Y] :
( member(Y,image2(F,A))
| ! [X] :
( ~ member(X,A)
| ~ apply(F,X,Y) ) ) ),
inference(miniscoping,[status(esa)],[f176]) ).
fof(f178,plain,
( ! [F,A,Y] :
( ~ member(Y,image2(F,A))
| ( member(sk0_23(Y,A,F),A)
& apply(F,sk0_23(Y,A,F),Y) ) )
& ! [F,A,Y] :
( member(Y,image2(F,A))
| ! [X] :
( ~ member(X,A)
| ~ apply(F,X,Y) ) ) ),
inference(skolemization,[status(esa)],[f177]) ).
fof(f179,plain,
! [X0,X1,X2] :
( ~ member(X0,image2(X1,X2))
| member(sk0_23(X0,X2,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f178]) ).
fof(f180,plain,
! [X0,X1,X2] :
( ~ member(X0,image2(X1,X2))
| apply(X1,sk0_23(X0,X2,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f178]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( member(X0,image2(X1,X2))
| ~ member(X3,X2)
| ~ apply(X1,X3,X0) ),
inference(cnf_transformation,[status(esa)],[f178]) ).
fof(f244,plain,
? [F,G,H,A,B,C] :
( maps(F,A,B)
& maps(G,B,C)
& maps(H,B,C)
& surjective(F,A,B)
& equal_maps(compose_function(G,F,A,B,C),compose_function(H,F,A,B,C),A,C)
& ~ equal_maps(G,H,B,C) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f245,plain,
? [G,H,B,C] :
( ? [F,A] :
( maps(F,A,B)
& maps(G,B,C)
& maps(H,B,C)
& surjective(F,A,B)
& equal_maps(compose_function(G,F,A,B,C),compose_function(H,F,A,B,C),A,C) )
& ~ equal_maps(G,H,B,C) ),
inference(miniscoping,[status(esa)],[f244]) ).
fof(f246,plain,
( maps(sk0_43,sk0_44,sk0_41)
& maps(sk0_39,sk0_41,sk0_42)
& maps(sk0_40,sk0_41,sk0_42)
& surjective(sk0_43,sk0_44,sk0_41)
& equal_maps(compose_function(sk0_39,sk0_43,sk0_44,sk0_41,sk0_42),compose_function(sk0_40,sk0_43,sk0_44,sk0_41,sk0_42),sk0_44,sk0_42)
& ~ equal_maps(sk0_39,sk0_40,sk0_41,sk0_42) ),
inference(skolemization,[status(esa)],[f245]) ).
fof(f250,plain,
surjective(sk0_43,sk0_44,sk0_41),
inference(cnf_transformation,[status(esa)],[f246]) ).
fof(f251,plain,
equal_maps(compose_function(sk0_39,sk0_43,sk0_44,sk0_41,sk0_42),compose_function(sk0_40,sk0_43,sk0_44,sk0_41,sk0_42),sk0_44,sk0_42),
inference(cnf_transformation,[status(esa)],[f246]) ).
fof(f252,plain,
~ equal_maps(sk0_39,sk0_40,sk0_41,sk0_42),
inference(cnf_transformation,[status(esa)],[f246]) ).
fof(f269,plain,
! [X0,X1,X2] :
( ~ member(X0,sk0_44)
| ~ member(X1,sk0_42)
| ~ member(X2,sk0_42)
| ~ apply(compose_function(sk0_39,sk0_43,sk0_44,sk0_41,sk0_42),X0,X1)
| ~ apply(compose_function(sk0_40,sk0_43,sk0_44,sk0_41,sk0_42),X0,X2)
| X1 = X2 ),
inference(resolution,[status(thm)],[f123,f251]) ).
fof(f270,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,sk0_44)
| ~ member(X1,sk0_42)
| ~ member(X2,sk0_41)
| ~ apply(sk0_43,X0,X2)
| ~ apply(sk0_40,X2,X1)
| ~ member(X0,sk0_44)
| ~ member(X3,sk0_42)
| ~ member(X1,sk0_42)
| ~ apply(compose_function(sk0_39,sk0_43,sk0_44,sk0_41,sk0_42),X0,X3)
| X3 = X1 ),
inference(resolution,[status(thm)],[f118,f269]) ).
fof(f271,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,sk0_44)
| ~ member(X1,sk0_42)
| ~ member(X2,sk0_41)
| ~ apply(sk0_43,X0,X2)
| ~ apply(sk0_40,X2,X1)
| ~ member(X3,sk0_42)
| ~ apply(compose_function(sk0_39,sk0_43,sk0_44,sk0_41,sk0_42),X0,X3)
| X3 = X1 ),
inference(duplicate_literals_removal,[status(esa)],[f270]) ).
fof(f274,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X0,sk0_44)
| ~ member(X1,sk0_42)
| ~ member(X2,sk0_41)
| ~ apply(sk0_43,X0,X2)
| ~ apply(sk0_40,X2,X1)
| ~ member(X3,sk0_42)
| X3 = X1
| ~ member(X0,sk0_44)
| ~ member(X3,sk0_42)
| ~ member(X4,sk0_41)
| ~ apply(sk0_43,X0,X4)
| ~ apply(sk0_39,X4,X3) ),
inference(resolution,[status(thm)],[f271,f118]) ).
fof(f275,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X0,sk0_44)
| ~ member(X1,sk0_42)
| ~ member(X2,sk0_41)
| ~ apply(sk0_43,X0,X2)
| ~ apply(sk0_40,X2,X1)
| ~ member(X3,sk0_42)
| X3 = X1
| ~ member(X4,sk0_41)
| ~ apply(sk0_43,X0,X4)
| ~ apply(sk0_39,X4,X3) ),
inference(duplicate_literals_removal,[status(esa)],[f274]) ).
fof(f2493,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X0,image2(sk0_43,X1))
| ~ member(sk0_23(X0,X1,sk0_43),sk0_44)
| ~ member(X2,sk0_42)
| ~ member(X3,sk0_41)
| ~ apply(sk0_43,sk0_23(X0,X1,sk0_43),X3)
| ~ apply(sk0_40,X3,X2)
| ~ member(X4,sk0_42)
| X4 = X2
| ~ member(X0,sk0_41)
| ~ apply(sk0_39,X0,X4) ),
inference(resolution,[status(thm)],[f180,f275]) ).
fof(f2528,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,image2(sk0_43,X1))
| ~ member(sk0_23(X0,X1,sk0_43),sk0_44)
| ~ member(X2,sk0_42)
| ~ member(X0,sk0_41)
| ~ apply(sk0_40,X0,X2)
| ~ member(X3,sk0_42)
| X3 = X2
| ~ member(X0,sk0_41)
| ~ apply(sk0_39,X0,X3)
| ~ member(X0,image2(sk0_43,X1)) ),
inference(resolution,[status(thm)],[f2493,f180]) ).
fof(f2529,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,image2(sk0_43,X1))
| ~ member(sk0_23(X0,X1,sk0_43),sk0_44)
| ~ member(X2,sk0_42)
| ~ member(X0,sk0_41)
| ~ apply(sk0_40,X0,X2)
| ~ member(X3,sk0_42)
| X3 = X2
| ~ apply(sk0_39,X0,X3) ),
inference(duplicate_literals_removal,[status(esa)],[f2528]) ).
fof(f2532,plain,
! [X0,X1,X2] :
( ~ member(X0,image2(sk0_43,sk0_44))
| ~ member(X1,sk0_42)
| ~ member(X0,sk0_41)
| ~ apply(sk0_40,X0,X1)
| ~ member(X2,sk0_42)
| X2 = X1
| ~ apply(sk0_39,X0,X2)
| ~ member(X0,image2(sk0_43,sk0_44)) ),
inference(resolution,[status(thm)],[f2529,f179]) ).
fof(f2533,plain,
! [X0,X1,X2] :
( ~ member(X0,image2(sk0_43,sk0_44))
| ~ member(X1,sk0_42)
| ~ member(X0,sk0_41)
| ~ apply(sk0_40,X0,X1)
| ~ member(X2,sk0_42)
| X2 = X1
| ~ apply(sk0_39,X0,X2) ),
inference(duplicate_literals_removal,[status(esa)],[f2532]) ).
fof(f2555,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,sk0_42)
| ~ member(X1,sk0_41)
| ~ apply(sk0_40,X1,X0)
| ~ member(X2,sk0_42)
| X2 = X0
| ~ apply(sk0_39,X1,X2)
| ~ member(X3,sk0_44)
| ~ apply(sk0_43,X3,X1) ),
inference(resolution,[status(thm)],[f2533,f181]) ).
fof(f2559,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X0,sk0_42)
| ~ member(X1,sk0_41)
| ~ apply(sk0_40,X1,X0)
| ~ member(X2,sk0_42)
| X2 = X0
| ~ apply(sk0_39,X1,X2)
| ~ member(sk0_19(X1,X3,X4,sk0_43),sk0_44)
| ~ surjective(sk0_43,X4,X3)
| ~ member(X1,X3) ),
inference(resolution,[status(thm)],[f2555,f153]) ).
fof(f2748,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,sk0_42)
| ~ member(X1,sk0_41)
| ~ apply(sk0_40,X1,X0)
| ~ member(X2,sk0_42)
| X2 = X0
| ~ apply(sk0_39,X1,X2)
| ~ surjective(sk0_43,sk0_44,X3)
| ~ member(X1,X3)
| ~ surjective(sk0_43,sk0_44,X3)
| ~ member(X1,X3) ),
inference(resolution,[status(thm)],[f2559,f152]) ).
fof(f2749,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,sk0_42)
| ~ member(X1,sk0_41)
| ~ apply(sk0_40,X1,X0)
| ~ member(X2,sk0_42)
| X2 = X0
| ~ apply(sk0_39,X1,X2)
| ~ surjective(sk0_43,sk0_44,X3)
| ~ member(X1,X3) ),
inference(duplicate_literals_removal,[status(esa)],[f2748]) ).
fof(f2751,plain,
! [X0,X1,X2] :
( ~ member(X0,sk0_42)
| ~ member(X1,sk0_41)
| ~ apply(sk0_40,X1,X0)
| ~ member(X2,sk0_42)
| X2 = X0
| ~ apply(sk0_39,X1,X2)
| ~ member(X1,sk0_41) ),
inference(resolution,[status(thm)],[f2749,f250]) ).
fof(f2752,plain,
! [X0,X1,X2] :
( ~ member(X0,sk0_42)
| ~ member(X1,sk0_41)
| ~ apply(sk0_40,X1,X0)
| ~ member(X2,sk0_42)
| X2 = X0
| ~ apply(sk0_39,X1,X2) ),
inference(duplicate_literals_removal,[status(esa)],[f2751]) ).
fof(f2765,plain,
! [X0,X1,X2,X3] :
( ~ member(sk0_14(X0,X1,sk0_40,X2),sk0_42)
| ~ member(sk0_12(X0,X1,sk0_40,X2),sk0_41)
| ~ member(X3,sk0_42)
| X3 = sk0_14(X0,X1,sk0_40,X2)
| ~ apply(sk0_39,sk0_12(X0,X1,sk0_40,X2),X3)
| equal_maps(X2,sk0_40,X1,X0) ),
inference(resolution,[status(thm)],[f2752,f128]) ).
fof(f2797,plain,
! [X0,X1] :
( ~ member(sk0_14(X0,X1,sk0_40,sk0_39),sk0_42)
| ~ member(sk0_12(X0,X1,sk0_40,sk0_39),sk0_41)
| ~ member(sk0_13(X0,X1,sk0_40,sk0_39),sk0_42)
| sk0_13(X0,X1,sk0_40,sk0_39) = sk0_14(X0,X1,sk0_40,sk0_39)
| equal_maps(sk0_39,sk0_40,X1,X0)
| equal_maps(sk0_39,sk0_40,X1,X0) ),
inference(resolution,[status(thm)],[f2765,f127]) ).
fof(f2798,plain,
! [X0,X1] :
( ~ member(sk0_14(X0,X1,sk0_40,sk0_39),sk0_42)
| ~ member(sk0_12(X0,X1,sk0_40,sk0_39),sk0_41)
| ~ member(sk0_13(X0,X1,sk0_40,sk0_39),sk0_42)
| sk0_13(X0,X1,sk0_40,sk0_39) = sk0_14(X0,X1,sk0_40,sk0_39)
| equal_maps(sk0_39,sk0_40,X1,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f2797]) ).
fof(f2799,plain,
! [X0,X1] :
( ~ member(sk0_14(X0,X1,sk0_40,sk0_39),sk0_42)
| ~ member(sk0_12(X0,X1,sk0_40,sk0_39),sk0_41)
| ~ member(sk0_13(X0,X1,sk0_40,sk0_39),sk0_42)
| equal_maps(sk0_39,sk0_40,X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2798,f129]) ).
fof(f2802,plain,
! [X0] :
( ~ member(sk0_12(sk0_42,X0,sk0_40,sk0_39),sk0_41)
| ~ member(sk0_13(sk0_42,X0,sk0_40,sk0_39),sk0_42)
| equal_maps(sk0_39,sk0_40,X0,sk0_42)
| equal_maps(sk0_39,sk0_40,X0,sk0_42) ),
inference(resolution,[status(thm)],[f2799,f126]) ).
fof(f2803,plain,
! [X0] :
( ~ member(sk0_12(sk0_42,X0,sk0_40,sk0_39),sk0_41)
| ~ member(sk0_13(sk0_42,X0,sk0_40,sk0_39),sk0_42)
| equal_maps(sk0_39,sk0_40,X0,sk0_42) ),
inference(duplicate_literals_removal,[status(esa)],[f2802]) ).
fof(f2804,plain,
! [X0] :
( ~ member(sk0_12(sk0_42,X0,sk0_40,sk0_39),sk0_41)
| equal_maps(sk0_39,sk0_40,X0,sk0_42) ),
inference(forward_subsumption_resolution,[status(thm)],[f2803,f125]) ).
fof(f2806,plain,
( spl0_51
<=> equal_maps(sk0_39,sk0_40,sk0_41,sk0_42) ),
introduced(split_symbol_definition) ).
fof(f2807,plain,
( equal_maps(sk0_39,sk0_40,sk0_41,sk0_42)
| ~ spl0_51 ),
inference(component_clause,[status(thm)],[f2806]) ).
fof(f2809,plain,
( equal_maps(sk0_39,sk0_40,sk0_41,sk0_42)
| equal_maps(sk0_39,sk0_40,sk0_41,sk0_42) ),
inference(resolution,[status(thm)],[f2804,f124]) ).
fof(f2810,plain,
spl0_51,
inference(split_clause,[status(thm)],[f2809,f2806]) ).
fof(f2812,plain,
( $false
| ~ spl0_51 ),
inference(forward_subsumption_resolution,[status(thm)],[f2807,f252]) ).
fof(f2813,plain,
~ spl0_51,
inference(contradiction_clause,[status(thm)],[f2812]) ).
fof(f2814,plain,
$false,
inference(sat_refutation,[status(thm)],[f2810,f2813]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET724+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.05/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Apr 29 21:36:05 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.14/0.32 % Drodi V3.6.0
% 19.33/2.81 % Refutation found
% 19.33/2.81 % SZS status Theorem for theBenchmark: Theorem is valid
% 19.33/2.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 19.33/2.86 % Elapsed time: 2.536492 seconds
% 19.33/2.86 % CPU time: 19.936518 seconds
% 19.33/2.86 % Total memory used: 150.386 MB
% 19.33/2.86 % Net memory used: 146.298 MB
%------------------------------------------------------------------------------