%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM623+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n009.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 02:26:16 PM UTC 2026
% Result : Theorem 8.77s 1.95s
% Output : CNFRefutation 8.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 72 ( 26 unt; 0 def)
% Number of atoms : 219 ( 85 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 256 ( 109 ~; 121 |; 20 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 42 !; 4 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f9,axiom,
! [X0] :
( ( isCountable0(X0)
& aSet0(X0) )
=> X0 != slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(f49,axiom,
! [X0,X1] :
( ( X1 != slcrc0
& X0 != slcrc0
& aSubsetOf0(X1,szNzAzT0)
& aSubsetOf0(X0,szNzAzT0) )
=> ( ( aElementOf0(szmzizndt0(X1),X0)
& aElementOf0(szmzizndt0(X0),X1) )
=> szmzizndt0(X0) = szmzizndt0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMinMin) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).
fof(f100,axiom,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).
fof(f101,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).
fof(f103,axiom,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
fof(f115,axiom,
( xx = sdtlpdtrp0(xe,xm)
& aElementOf0(xm,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5389) ).
fof(f116,axiom,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5401) ).
fof(f119,axiom,
( aElementOf0(xx,xQ)
& aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5481) ).
fof(f120,conjecture,
xp = xx,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f121,negated_conjecture,
xp != xx,
inference(negated_conjecture,[status(cth)],[f120]) ).
fof(f129,plain,
xp != xx,
inference(flattening,[],[f121]) ).
fof(f131,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f134,plain,
! [X0] :
( ~ isCountable0(X0)
| ~ aSet0(X0)
| X0 != slcrc0 ),
inference(ennf_transformation,[],[f9]) ).
fof(f135,plain,
! [X0] :
( ~ isCountable0(X0)
| ~ aSet0(X0)
| X0 != slcrc0 ),
inference(flattening,[],[f134]) ).
fof(f193,plain,
! [X0,X1] :
( slcrc0 = X1
| slcrc0 = X0
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(szmzizndt0(X1),X0)
| ~ aElementOf0(szmzizndt0(X0),X1)
| szmzizndt0(X0) = szmzizndt0(X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f194,plain,
! [X0,X1] :
( slcrc0 = X1
| slcrc0 = X0
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(szmzizndt0(X1),X0)
| ~ aElementOf0(szmzizndt0(X0),X1)
| szmzizndt0(X0) = szmzizndt0(X1) ),
inference(flattening,[],[f193]) ).
fof(f233,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ) ),
inference(ennf_transformation,[],[f82]) ).
fof(f259,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f131]) ).
fof(f260,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f259]) ).
fof(f261,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f260]) ).
fof(f262,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( aElementOf0(sK4(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f261]) ).
fof(f324,plain,
! [X0] :
( slcrc0 != X0
| aSet0(X0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f328,plain,
! [X0] :
( ~ isCountable0(X0)
| ~ aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f135]) ).
fof(f404,plain,
! [X0,X1] :
( slcrc0 = X1
| slcrc0 = X0
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(szmzizndt0(X1),X0)
| ~ aElementOf0(szmzizndt0(X0),X1)
| szmzizndt0(X0) = szmzizndt0(X1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f486,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f233]) ).
fof(f487,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f233]) ).
fof(f522,plain,
slcrc0 != xQ,
inference(cnf_transformation,[],[f100]) ).
fof(f524,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f101]) ).
fof(f526,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f103]) ).
fof(f543,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f115]) ).
fof(f544,plain,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f116]) ).
fof(f547,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f119]) ).
fof(f548,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f119]) ).
fof(f549,plain,
xp != xx,
inference(cnf_transformation,[],[f129]) ).
fof(f550,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f324]) ).
fof(f552,plain,
( ~ isCountable0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(equality_resolution,[],[f328]) ).
tcf(c_51,plain,
aSet0(slcrc0),
inference(cnf_transformation,[],[f550]) ).
tcf(c_55,plain,
( ~ isCountable0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(cnf_transformation,[],[f552]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] :
( ( X1 = slcrc0 )
| ( X0 = slcrc0 )
| ( szmzizndt0(X0) = szmzizndt0(X1) )
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(szmzizndt0(X1),X0)
| ~ aElementOf0(szmzizndt0(X0),X1) ),
inference(cnf_transformation,[],[f404]) ).
tcf(c_213,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f487]) ).
tcf(c_214,plain,
! [X0: $i] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f486]) ).
tcf(c_250,plain,
slcrc0 != xQ,
inference(cnf_transformation,[],[f522]) ).
tcf(c_251,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f524]) ).
tcf(c_253,plain,
szmzizndt0(xQ) = xp,
inference(cnf_transformation,[],[f526]) ).
tcf(c_269,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f543]) ).
tcf(c_271,plain,
szmzizndt0(sdtlpdtrp0(xN,xm)) = xx,
inference(cnf_transformation,[],[f544]) ).
tcf(c_274,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f548]) ).
tcf(c_275,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f547]) ).
tcf(c_276,negated_conjecture,
xp != xx,
inference(cnf_transformation,[],[f549]) ).
tcf(c_374,plain,
! [X0: $i] :
( ( slcrc0 = xQ )
| ( X0 = slcrc0 )
| ( szmzizndt0(X0) = szmzizndt0(xQ) )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(szmzizndt0(X0),xQ) ),
inference(superposition,[status(thm)],[c_253,c_131]) ).
tcf(c_438,plain,
! [X0: $i] :
( ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(szmzizndt0(X0),xQ)
| ( szmzizndt0(X0) = szmzizndt0(xQ) )
| ( X0 = slcrc0 ) ),
inference(global_subsumption_just,[status(thm)],[c_374,c_251,c_250,c_374]) ).
tcf(c_439,plain,
! [X0: $i] :
( ( X0 = slcrc0 )
| ( szmzizndt0(X0) = szmzizndt0(xQ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(szmzizndt0(X0),xQ) ),
inference(renaming,[status(thm)],[c_438]) ).
tcf(c_446,plain,
! [X0: $i] :
( ( X0 = slcrc0 )
| ( szmzizndt0(X0) = xp )
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(szmzizndt0(X0),xQ) ),
inference(light_normalisation,[status(thm)],[c_439,c_253]) ).
tcf(c_459,plain,
( ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = xp )
| ~ aElementOf0(xx,xQ)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(superposition,[status(thm)],[c_271,c_446]) ).
tcf(c_617,plain,
( ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = xp )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_459,c_275,c_274,c_459]) ).
tcf(c_1257,plain,
! [X0: $i] :
( ( slcrc0 = xQ )
| ( X0 = slcrc0 )
| ( szmzizndt0(X0) = szmzizndt0(xQ) )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(szmzizndt0(X0),xQ) ),
inference(superposition,[status(thm)],[c_253,c_131]) ).
tcf(c_1258,plain,
! [X0: $i] :
( ( X0 = slcrc0 )
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(X0) )
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szmzizndt0(X0),sdtlpdtrp0(xN,xm)) ),
inference(superposition,[status(thm)],[c_271,c_131]) ).
tcf(c_2713,plain,
! [X0: $i] :
( ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(szmzizndt0(X0),xQ)
| ( szmzizndt0(X0) = szmzizndt0(xQ) )
| ( X0 = slcrc0 ) ),
inference(global_subsumption_just,[status(thm)],[c_1257,c_439]) ).
tcf(c_2714,plain,
! [X0: $i] :
( ( X0 = slcrc0 )
| ( szmzizndt0(X0) = szmzizndt0(xQ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(szmzizndt0(X0),xQ) ),
inference(renaming,[status(thm)],[c_2713]) ).
tcf(c_2720,plain,
! [X0: $i] :
( ( X0 = slcrc0 )
| ( szmzizndt0(X0) = xp )
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(szmzizndt0(X0),xQ) ),
inference(light_normalisation,[status(thm)],[c_2714,c_253]) ).
tcf(c_2734,plain,
( ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = xp )
| ~ aElementOf0(xx,xQ)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(superposition,[status(thm)],[c_271,c_2720]) ).
tcf(c_2757,plain,
! [X0: $i] :
( ( X0 = slcrc0 )
| ( szmzizndt0(X0) = xx )
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szmzizndt0(X0),sdtlpdtrp0(xN,xm)) ),
inference(light_normalisation,[status(thm)],[c_1258,c_271]) ).
tcf(c_2774,plain,
( ( slcrc0 = xQ )
| ( szmzizndt0(xQ) = xx )
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ~ aElementOf0(xx,xQ)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(superposition,[status(thm)],[c_253,c_2757]) ).
tcf(c_6878,plain,
( ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(sdtlpdtrp0(xN,xm)) = xp )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_2734,c_617]) ).
tcf(c_6883,plain,
( ( xp = xx )
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(light_normalisation,[status(thm)],[c_6878,c_271]) ).
tcf(c_6887,plain,
( ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6883,c_276]) ).
tcf(c_6892,plain,
( ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ~ aElementOf0(xm,szNzAzT0) ),
inference(superposition,[status(thm)],[c_213,c_6887]) ).
tcf(c_6953,plain,
sdtlpdtrp0(xN,xm) = slcrc0,
inference(global_subsumption_just,[status(thm)],[c_2774,c_269,c_6892]) ).
tcf(c_6983,plain,
( isCountable0(slcrc0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(superposition,[status(thm)],[c_6953,c_214]) ).
tcf(c_6998,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6983,c_55,c_51,c_269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM623+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 04:57:59 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.44 Running first-order theorem proving
% 0.16/0.44 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.46
% 0.16/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.46
% 0.16/0.46 % Detected problem language: tptp
% 0.16/0.48 % Proving...
% 8.77/1.95 % SZS status Started for theBenchmark.p
% 8.77/1.95 % SZS status Theorem for theBenchmark.p
% 8.77/1.95
% 8.77/1.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.77/1.95
% 8.77/1.95 % ------ iProver source info
% 8.77/1.95
% 8.77/1.95 % git: date: 2026-07-19 20:42:38 +0200
% 8.77/1.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.77/1.95 % git: non_committed_changes: false
% 8.77/1.95
% 8.77/1.95 % ------ Parsing...
% 8.77/1.95 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 8.77/1.95 % ------ Proving...
% 8.77/1.95 % ------ Problem Properties
% 8.77/1.95
% 8.77/1.95 %
% 8.77/1.95 % clauses 228
% 8.77/1.95 % conjectures 1
% 8.77/1.95 % EPR 63
% 8.77/1.95 % Horn 189
% 8.77/1.95 % unary 65
% 8.77/1.95 % binary 35
% 8.77/1.95 % lits 699
% 8.77/1.95 % lits eq 109
% 8.77/1.95 % fd_pure 0
% 8.77/1.95 % fd_pseudo 0
% 8.77/1.95 % fd_cond 10
% 8.77/1.95 % fd_pseudo_cond 25
% 8.77/1.95 % AC symbols 0
% 8.77/1.95
% 8.77/1.95 % ------ Input Options Time Limit: Unbounded
% 8.77/1.95
% 8.77/1.95
% 8.77/1.95 % ------
% 8.77/1.95 % Current options:
% 8.77/1.95 % ------
% 8.77/1.95
% 8.77/1.95
% 8.77/1.95 %
% 8.77/1.95
% 8.77/1.95 % ------ Proving...
% 8.77/1.95 %
% 8.77/1.95
% 8.77/1.95 % ------ Proving...
% 8.77/1.95 %
% 8.77/1.95
% 8.77/1.95 % ------ Proving...
% 8.77/1.95 %
% 8.77/1.95
% 8.77/1.95 % SZS status Theorem for theBenchmark.p
% 8.77/1.95
% 8.77/1.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.77/1.95
% 8.77/1.95
%------------------------------------------------------------------------------