TSTP Solution File: NUM584+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM584+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.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 : Thu Aug 31 11:31:38 EDT 2023
% Result : Theorem 10.01s 2.21s
% Output : CNFRefutation 10.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 22 unt; 0 def)
% Number of atoms : 223 ( 43 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 281 ( 108 ~; 105 |; 55 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-3 aty)
% Number of variables : 76 ( 0 sgn; 62 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(f57,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aSet0(X0) )
=> ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3418) ).
fof(f75,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(f76,axiom,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).
fof(f87,axiom,
xK = sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4007) ).
fof(f88,axiom,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4024) ).
fof(f89,conjecture,
aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f90,negated_conjecture,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
inference(negated_conjecture,[],[f89]) ).
fof(f98,plain,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
inference(flattening,[],[f90]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f173,plain,
! [X0,X1] :
( ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f174,plain,
! [X0,X1] :
( ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(flattening,[],[f173]) ).
fof(f218,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f105]) ).
fof(f219,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f218]) ).
fof(f220,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f219]) ).
fof(f221,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f222,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f220,f221]) ).
fof(f262,plain,
! [X0,X1] :
( ! [X2] :
( ( slbdtsldtrb0(X0,X1) = X2
| ? [X3] :
( ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f174]) ).
fof(f263,plain,
! [X0,X1] :
( ! [X2] :
( ( slbdtsldtrb0(X0,X1) = X2
| ? [X3] :
( ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(flattening,[],[f262]) ).
fof(f264,plain,
! [X0,X1] :
( ! [X2] :
( ( slbdtsldtrb0(X0,X1) = X2
| ? [X3] :
( ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0) )
& ( ( sbrdtbr0(X4) = X1
& aSubsetOf0(X4,X0) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(rectify,[],[f263]) ).
fof(f265,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
=> ( ( sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aSubsetOf0(sK14(X0,X1,X2),X0)
| ~ aElementOf0(sK14(X0,X1,X2),X2) )
& ( ( sbrdtbr0(sK14(X0,X1,X2)) = X1
& aSubsetOf0(sK14(X0,X1,X2),X0) )
| aElementOf0(sK14(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f266,plain,
! [X0,X1] :
( ! [X2] :
( ( slbdtsldtrb0(X0,X1) = X2
| ( ( sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aSubsetOf0(sK14(X0,X1,X2),X0)
| ~ aElementOf0(sK14(X0,X1,X2),X2) )
& ( ( sbrdtbr0(sK14(X0,X1,X2)) = X1
& aSubsetOf0(sK14(X0,X1,X2),X0) )
| aElementOf0(sK14(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0) )
& ( ( sbrdtbr0(X4) = X1
& aSubsetOf0(X4,X0) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f264,f265]) ).
fof(f298,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f222]) ).
fof(f336,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f394,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0)
| slbdtsldtrb0(X0,X1) != X2
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f436,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f437,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f75]) ).
fof(f440,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(cnf_transformation,[],[f76]) ).
fof(f461,plain,
xK = sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cnf_transformation,[],[f87]) ).
fof(f462,plain,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(cnf_transformation,[],[f88]) ).
fof(f463,plain,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
inference(cnf_transformation,[],[f98]) ).
fof(f481,plain,
! [X2,X0,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| slbdtsldtrb0(X0,sbrdtbr0(X4)) != X2
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f394]) ).
fof(f482,plain,
! [X0,X4] :
( aElementOf0(X4,slbdtsldtrb0(X0,sbrdtbr0(X4)))
| ~ aSubsetOf0(X4,X0)
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f481]) ).
cnf(c_59,plain,
( ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| aSet0(X0) ),
inference(cnf_transformation,[],[f298]) ).
cnf(c_95,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f336]) ).
cnf(c_152,plain,
( ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| aElementOf0(X0,slbdtsldtrb0(X1,sbrdtbr0(X0))) ),
inference(cnf_transformation,[],[f482]) ).
cnf(c_194,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f436]) ).
cnf(c_196,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f437]) ).
cnf(c_198,plain,
slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
inference(cnf_transformation,[],[f440]) ).
cnf(c_219,plain,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
inference(cnf_transformation,[],[f461]) ).
cnf(c_220,plain,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(cnf_transformation,[],[f462]) ).
cnf(c_221,negated_conjecture,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
inference(cnf_transformation,[],[f463]) ).
cnf(c_7958,plain,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xc)),
inference(demodulation,[status(thm)],[c_221,c_198]) ).
cnf(c_8058,plain,
( ~ aSet0(szNzAzT0)
| aSet0(xS) ),
inference(superposition,[status(thm)],[c_196,c_59]) ).
cnf(c_8231,plain,
( ~ aElementOf0(sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),szNzAzT0)
| ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),X0)
| ~ aSet0(X0)
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(X0,xK)) ),
inference(superposition,[status(thm)],[c_219,c_152]) ).
cnf(c_8272,plain,
( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),X0)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(X0)
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(X0,xK)) ),
inference(light_normalisation,[status(thm)],[c_8231,c_219]) ).
cnf(c_11059,plain,
( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xS)
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_198,c_8272]) ).
cnf(c_11065,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11059,c_8058,c_7958,c_220,c_194,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM584+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 16:46:18 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.01/2.21 % SZS status Started for theBenchmark.p
% 10.01/2.21 % SZS status Theorem for theBenchmark.p
% 10.01/2.21
% 10.01/2.21 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 10.01/2.21
% 10.01/2.21 ------ iProver source info
% 10.01/2.21
% 10.01/2.21 git: date: 2023-05-31 18:12:56 +0000
% 10.01/2.21 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 10.01/2.21 git: non_committed_changes: false
% 10.01/2.21 git: last_make_outside_of_git: false
% 10.01/2.21
% 10.01/2.21 ------ Parsing...
% 10.01/2.21 ------ Clausification by vclausify_rel & Parsing by iProver...
% 10.01/2.21
% 10.01/2.21 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e
% 10.01/2.21
% 10.01/2.21 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 10.01/2.21
% 10.01/2.21 ------ Preprocessing... sf_s rm: 1 0s sf_e
% 10.01/2.21 ------ Proving...
% 10.01/2.21 ------ Problem Properties
% 10.01/2.21
% 10.01/2.21
% 10.01/2.21 clauses 169
% 10.01/2.21 conjectures 1
% 10.01/2.21 EPR 39
% 10.01/2.21 Horn 130
% 10.01/2.21 unary 28
% 10.01/2.21 binary 21
% 10.01/2.21 lits 593
% 10.01/2.21 lits eq 93
% 10.01/2.21 fd_pure 0
% 10.01/2.21 fd_pseudo 0
% 10.01/2.21 fd_cond 10
% 10.01/2.21 fd_pseudo_cond 25
% 10.01/2.21 AC symbols 0
% 10.01/2.21
% 10.01/2.21 ------ Input Options Time Limit: Unbounded
% 10.01/2.21
% 10.01/2.21
% 10.01/2.21 ------
% 10.01/2.21 Current options:
% 10.01/2.21 ------
% 10.01/2.21
% 10.01/2.21
% 10.01/2.21
% 10.01/2.21
% 10.01/2.21 ------ Proving...
% 10.01/2.21
% 10.01/2.21
% 10.01/2.21 % SZS status Theorem for theBenchmark.p
% 10.01/2.21
% 10.01/2.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.01/2.21
% 10.01/2.21
%------------------------------------------------------------------------------