%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM571+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 : Fri Sep 25 02:26:03 PM UTC 2026
% Result : Theorem 0.60s 0.96s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 78 ( 26 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 64 ( 16 ~; 20 |; 25 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn 3 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
fof(f75,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(f81,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(f84,axiom,
( xi != sz00
=> ( isCountable0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& ? [X0] :
( szszuzczcdt0(X0) = xi
& aElementOf0(X0,szNzAzT0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3702_02) ).
fof(f85,conjecture,
( isCountable0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f86,negated_conjecture,
~ ( isCountable0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(negated_conjecture,[status(cth)],[f85]) ).
fof(f195,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(ennf_transformation,[],[f81]) ).
fof(f196,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(flattening,[],[f195]) ).
fof(f199,plain,
( sz00 = xi
| ( isCountable0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& ? [X0] :
( szszuzczcdt0(X0) = xi
& aElementOf0(X0,szNzAzT0) ) ) ),
inference(ennf_transformation,[],[f84]) ).
fof(f200,plain,
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f267,plain,
( sz00 = xi
| ( isCountable0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& xi = szszuzczcdt0(sK25)
& aElementOf0(sK25,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(X0,sK25)],[f199]) ).
fof(f414,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f75]) ).
fof(f415,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f75]) ).
fof(f429,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f196]) ).
fof(f435,plain,
( sz00 = xi
| isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(cnf_transformation,[],[f267]) ).
fof(f436,plain,
( sz00 = xi
| aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f437,plain,
( sz00 = xi
| xi = szszuzczcdt0(sK25) ),
inference(cnf_transformation,[],[f267]) ).
fof(f438,plain,
( sz00 = xi
| aElementOf0(sK25,szNzAzT0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f439,plain,
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_195,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f415]) ).
tcf(c_196,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f414]) ).
tcf(c_210,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(cnf_transformation,[],[f429]) ).
tcf(c_216,plain,
( aElementOf0(sK25,szNzAzT0)
| ( sz00 = xi ) ),
inference(cnf_transformation,[],[f438]) ).
tcf(c_217,plain,
( ( sz00 = xi )
| ( szszuzczcdt0(sK25) = xi ) ),
inference(cnf_transformation,[],[f437]) ).
tcf(c_218,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ( sz00 = xi ) ),
inference(cnf_transformation,[],[f436]) ).
tcf(c_219,plain,
( isCountable0(sdtlpdtrp0(xN,xi))
| ( sz00 = xi ) ),
inference(cnf_transformation,[],[f435]) ).
tcf(c_220,negated_conjecture,
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(cnf_transformation,[],[f439]) ).
tcf(c_342,plain,
sz00 = xi,
inference(global_subsumption_just,[status(thm)],[c_216,c_219,c_218,c_220]) ).
tcf(c_350,plain,
sz00 = xi,
inference(global_subsumption_just,[status(thm)],[c_217,c_342]) ).
tcf(c_1685,plain,
( ~ isCountable0(xS)
| ~ aSubsetOf0(xS,szNzAzT0) ),
inference(light_normalisation,[status(thm)],[c_220,c_210,c_350]) ).
tcf(c_1686,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1685,c_196,c_195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM571+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Thu Sep 24 04:40:35 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.33 Running first-order theorem proving
% 0.04/0.33 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.34 % Proving...
% 0.60/0.96 % SZS status Started for theBenchmark.p
% 0.60/0.96 % SZS status Theorem for theBenchmark.p
% 0.60/0.96
% 0.60/0.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.60/0.96
% 0.60/0.96 % ------ iProver source info
% 0.60/0.96
% 0.60/0.96 % git: date: 2026-07-19 20:42:38 +0200
% 0.60/0.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.60/0.96 % git: non_committed_changes: false
% 0.60/0.96
% 0.60/0.96 % ------ Parsing...
% 0.60/0.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.60/0.96
% 0.60/0.96 % ------ Preprocessing...%
% 0.60/0.96
% 0.60/0.96 % SZS status Theorem for theBenchmark.p
% 0.60/0.96
% 0.60/0.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.60/0.97
% 0.60/0.97
%------------------------------------------------------------------------------