TSTP Solution File: NUM623+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM623+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 11:31:57 EDT 2023
% Result : Theorem 7.83s 1.66s
% Output : CNFRefutation 7.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 73 ( 26 unt; 0 def)
% Number of atoms : 221 ( 85 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 257 ( 109 ~; 121 |; 20 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn; 29 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( slcrc0 = X0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f9,axiom,
! [X0] :
( ( isCountable0(X0)
& aSet0(X0) )
=> slcrc0 != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(f49,axiom,
! [X0,X1] :
( ( slcrc0 != X1
& slcrc0 != X0
& aSubsetOf0(X1,szNzAzT0)
& aSubsetOf0(X0,szNzAzT0) )
=> ( ( aElementOf0(szmzizndt0(X1),X0)
& aElementOf0(szmzizndt0(X0),X1) )
=> szmzizndt0(X0) = szmzizndt0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMinMin) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f100,axiom,
( slcrc0 != xQ
& aSubsetOf0(xQ,xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
fof(f101,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5106) ).
fof(f103,axiom,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(f115,axiom,
( xx = sdtlpdtrp0(xe,xm)
& aElementOf0(xm,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5389) ).
fof(f116,axiom,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5401) ).
fof(f119,axiom,
( aElementOf0(xx,xQ)
& aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5481) ).
fof(f120,conjecture,
xp = xx,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f121,negated_conjecture,
xp != xx,
inference(negated_conjecture,[],[f120]) ).
fof(f129,plain,
xp != xx,
inference(flattening,[],[f121]) ).
fof(f131,plain,
! [X0] :
( slcrc0 = X0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f134,plain,
! [X0] :
( slcrc0 != X0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f135,plain,
! [X0] :
( slcrc0 != X0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(flattening,[],[f134]) ).
fof(f193,plain,
! [X0,X1] :
( szmzizndt0(X0) = szmzizndt0(X1)
| ~ aElementOf0(szmzizndt0(X1),X0)
| ~ aElementOf0(szmzizndt0(X0),X1)
| slcrc0 = X1
| slcrc0 = X0
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f194,plain,
! [X0,X1] :
( szmzizndt0(X0) = szmzizndt0(X1)
| ~ aElementOf0(szmzizndt0(X1),X0)
| ~ aElementOf0(szmzizndt0(X0),X1)
| slcrc0 = X1
| slcrc0 = X0
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(flattening,[],[f193]) ).
fof(f233,plain,
! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f259,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f131]) ).
fof(f260,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f259]) ).
fof(f261,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f260]) ).
fof(f262,plain,
! [X0] :
( ? [X1] : aElementOf0(X1,X0)
=> aElementOf0(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f263,plain,
! [X0] :
( ( slcrc0 = X0
| aElementOf0(sK4(X0),X0)
| ~ aSet0(X0) )
& ( ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f261,f262]) ).
fof(f345,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f263]) ).
fof(f350,plain,
! [X0] :
( slcrc0 != X0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f426,plain,
! [X0,X1] :
( szmzizndt0(X0) = szmzizndt0(X1)
| ~ aElementOf0(szmzizndt0(X1),X0)
| ~ aElementOf0(szmzizndt0(X0),X1)
| slcrc0 = X1
| slcrc0 = X0
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f508,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f233]) ).
fof(f509,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f233]) ).
fof(f545,plain,
slcrc0 != xQ,
inference(cnf_transformation,[],[f100]) ).
fof(f546,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f101]) ).
fof(f548,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f103]) ).
fof(f564,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f115]) ).
fof(f566,plain,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f116]) ).
fof(f569,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f119]) ).
fof(f570,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f119]) ).
fof(f571,plain,
xp != xx,
inference(cnf_transformation,[],[f129]) ).
fof(f573,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f345]) ).
fof(f574,plain,
( ~ isCountable0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(equality_resolution,[],[f350]) ).
cnf(c_52,plain,
aSet0(slcrc0),
inference(cnf_transformation,[],[f573]) ).
cnf(c_55,plain,
( ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0) ),
inference(cnf_transformation,[],[f574]) ).
cnf(c_131,plain,
( ~ aElementOf0(szmzizndt0(X0),X1)
| ~ aElementOf0(szmzizndt0(X1),X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aSubsetOf0(X1,szNzAzT0)
| szmzizndt0(X0) = szmzizndt0(X1)
| X0 = slcrc0
| X1 = slcrc0 ),
inference(cnf_transformation,[],[f426]) ).
cnf(c_213,plain,
( ~ aElementOf0(X0,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f509]) ).
cnf(c_214,plain,
( ~ aElementOf0(X0,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f508]) ).
cnf(c_249,plain,
slcrc0 != xQ,
inference(cnf_transformation,[],[f545]) ).
cnf(c_251,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f546]) ).
cnf(c_253,plain,
szmzizndt0(xQ) = xp,
inference(cnf_transformation,[],[f548]) ).
cnf(c_270,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f564]) ).
cnf(c_271,plain,
szmzizndt0(sdtlpdtrp0(xN,xm)) = xx,
inference(cnf_transformation,[],[f566]) ).
cnf(c_274,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f570]) ).
cnf(c_275,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f569]) ).
cnf(c_276,negated_conjecture,
xp != xx,
inference(cnf_transformation,[],[f571]) ).
cnf(c_18477,plain,
( ~ aElementOf0(szmzizndt0(X0),xQ)
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aSubsetOf0(xQ,szNzAzT0)
| szmzizndt0(X0) = szmzizndt0(xQ)
| X0 = slcrc0
| slcrc0 = xQ ),
inference(superposition,[status(thm)],[c_253,c_131]) ).
cnf(c_18660,plain,
( X0 = slcrc0
| szmzizndt0(X0) = szmzizndt0(xQ)
| ~ aElementOf0(szmzizndt0(X0),xQ)
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_18477,c_251,c_249,c_18477]) ).
cnf(c_18661,plain,
( ~ aElementOf0(szmzizndt0(X0),xQ)
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| szmzizndt0(X0) = szmzizndt0(xQ)
| X0 = slcrc0 ),
inference(renaming,[status(thm)],[c_18660]) ).
cnf(c_18668,plain,
( ~ aElementOf0(szmzizndt0(X0),xQ)
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| szmzizndt0(X0) = xp
| X0 = slcrc0 ),
inference(light_normalisation,[status(thm)],[c_18661,c_253]) ).
cnf(c_18681,plain,
( ~ aElementOf0(xp,sdtlpdtrp0(xN,xm))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(xx,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xm)) = xp
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(superposition,[status(thm)],[c_271,c_18668]) ).
cnf(c_18904,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,xm)) = xp
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(global_subsumption_just,[status(thm)],[c_18681,c_274,c_275,c_18681]) ).
cnf(c_19736,plain,
( ~ aElementOf0(szmzizndt0(X0),xQ)
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aSubsetOf0(xQ,szNzAzT0)
| szmzizndt0(X0) = szmzizndt0(xQ)
| X0 = slcrc0
| slcrc0 = xQ ),
inference(superposition,[status(thm)],[c_253,c_131]) ).
cnf(c_19737,plain,
( ~ aElementOf0(szmzizndt0(X0),sdtlpdtrp0(xN,xm))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(X0)
| sdtlpdtrp0(xN,xm) = slcrc0
| X0 = slcrc0 ),
inference(superposition,[status(thm)],[c_271,c_131]) ).
cnf(c_21857,plain,
( X0 = slcrc0
| szmzizndt0(X0) = szmzizndt0(xQ)
| ~ aElementOf0(szmzizndt0(X0),xQ)
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_19736,c_18661]) ).
cnf(c_21858,plain,
( ~ aElementOf0(szmzizndt0(X0),xQ)
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| szmzizndt0(X0) = szmzizndt0(xQ)
| X0 = slcrc0 ),
inference(renaming,[status(thm)],[c_21857]) ).
cnf(c_21864,plain,
( ~ aElementOf0(szmzizndt0(X0),xQ)
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| szmzizndt0(X0) = xp
| X0 = slcrc0 ),
inference(light_normalisation,[status(thm)],[c_21858,c_253]) ).
cnf(c_21878,plain,
( ~ aElementOf0(xp,sdtlpdtrp0(xN,xm))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(xx,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xm)) = xp
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(superposition,[status(thm)],[c_271,c_21864]) ).
cnf(c_21904,plain,
( ~ aElementOf0(szmzizndt0(X0),sdtlpdtrp0(xN,xm))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| sdtlpdtrp0(xN,xm) = slcrc0
| szmzizndt0(X0) = xx
| X0 = slcrc0 ),
inference(light_normalisation,[status(thm)],[c_19737,c_271]) ).
cnf(c_21921,plain,
( ~ aElementOf0(xp,sdtlpdtrp0(xN,xm))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(xx,xQ)
| ~ aSubsetOf0(xQ,szNzAzT0)
| sdtlpdtrp0(xN,xm) = slcrc0
| szmzizndt0(xQ) = xx
| slcrc0 = xQ ),
inference(superposition,[status(thm)],[c_253,c_21904]) ).
cnf(c_30340,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,xm)) = xp
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(global_subsumption_just,[status(thm)],[c_21878,c_18904]) ).
cnf(c_30345,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| sdtlpdtrp0(xN,xm) = slcrc0
| xp = xx ),
inference(light_normalisation,[status(thm)],[c_30340,c_271]) ).
cnf(c_30349,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(forward_subsumption_resolution,[status(thm)],[c_30345,c_276]) ).
cnf(c_30354,plain,
( ~ aElementOf0(xm,szNzAzT0)
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(superposition,[status(thm)],[c_214,c_30349]) ).
cnf(c_30415,plain,
sdtlpdtrp0(xN,xm) = slcrc0,
inference(global_subsumption_just,[status(thm)],[c_21921,c_270,c_30354]) ).
cnf(c_30467,plain,
( ~ aElementOf0(xm,szNzAzT0)
| isCountable0(slcrc0) ),
inference(superposition,[status(thm)],[c_30415,c_213]) ).
cnf(c_30482,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_30467,c_55,c_270,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM623+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 18:24:04 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.83/1.66 % SZS status Started for theBenchmark.p
% 7.83/1.66 % SZS status Theorem for theBenchmark.p
% 7.83/1.66
% 7.83/1.66 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.83/1.66
% 7.83/1.66 ------ iProver source info
% 7.83/1.66
% 7.83/1.66 git: date: 2023-05-31 18:12:56 +0000
% 7.83/1.66 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.83/1.66 git: non_committed_changes: false
% 7.83/1.66 git: last_make_outside_of_git: false
% 7.83/1.66
% 7.83/1.66 ------ Parsing...
% 7.83/1.66 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.83/1.66
% 7.83/1.66 ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 7.83/1.66
% 7.83/1.66 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.83/1.66
% 7.83/1.66 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.83/1.66 ------ Proving...
% 7.83/1.66 ------ Problem Properties
% 7.83/1.66
% 7.83/1.66
% 7.83/1.66 clauses 223
% 7.83/1.66 conjectures 1
% 7.83/1.66 EPR 59
% 7.83/1.66 Horn 184
% 7.83/1.66 unary 65
% 7.83/1.66 binary 32
% 7.83/1.66 lits 678
% 7.83/1.66 lits eq 112
% 7.83/1.66 fd_pure 0
% 7.83/1.66 fd_pseudo 0
% 7.83/1.66 fd_cond 10
% 7.83/1.66 fd_pseudo_cond 25
% 7.83/1.66 AC symbols 0
% 7.83/1.66
% 7.83/1.66 ------ Input Options Time Limit: Unbounded
% 7.83/1.66
% 7.83/1.66
% 7.83/1.66 ------
% 7.83/1.66 Current options:
% 7.83/1.66 ------
% 7.83/1.66
% 7.83/1.66
% 7.83/1.66
% 7.83/1.66
% 7.83/1.66 ------ Proving...
% 7.83/1.66
% 7.83/1.66
% 7.83/1.66 ------ Proving...
% 7.83/1.66
% 7.83/1.66
% 7.83/1.66 ------ Proving...
% 7.83/1.66
% 7.83/1.66
% 7.83/1.66 % SZS status Theorem for theBenchmark.p
% 7.83/1.66
% 7.83/1.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.83/1.66
% 8.01/1.67
%------------------------------------------------------------------------------