%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM625+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 : n026.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 02:26:17 PM UTC 2026
% Result : Theorem 1.39s 1.76s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 63 ( 22 unt; 2 def)
% Number of atoms : 250 ( 41 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 300 ( 113 ~; 107 |; 64 &)
% ( 11 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 100 ( 0 sgn 94 !; 6 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f16,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
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(f104,axiom,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& aSet0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(f113,axiom,
aElementOf0(xx,xP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5348) ).
fof(f114,axiom,
( aElementOf0(xx,xO)
& aElementOf0(xx,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5365) ).
fof(f120,axiom,
xp = xx,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5496) ).
fof(f131,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f137,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f147,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f148,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f147]) ).
fof(f264,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f137]) ).
fof(f265,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(flattening,[],[f264]) ).
fof(f266,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(rectify,[],[f265]) ).
fof(f267,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK5(X0,X1),X1)
& ~ aElementOf0(sK5(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f266]) ).
fof(f274,plain,
! [X1,X0] :
( ~ sP3(X1,X0)
| ! [X2] :
( ( sdtmndt0(X0,X1) != X2
| sP2(X2,X0,X1) )
& ( ~ sP2(X2,X0,X1)
| X2 = sdtmndt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f258]) ).
fof(f275,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| sP2(X2,X1,X0) )
& ( ~ sP2(X2,X1,X0)
| sdtmndt0(X1,X0) = X2 ) ) ),
inference(rectify,[],[f274]) ).
fof(f323,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f331,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f267]) ).
fof(f350,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1)
| sdtmndt0(X1,X0) != X2
| sP2(X2,X1,X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f361,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP3(X1,X0) ),
inference(cnf_transformation,[],[f259]) ).
fof(f369,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f525,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f101]) ).
fof(f527,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f103]) ).
fof(f528,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f104]) ).
fof(f540,plain,
aElementOf0(xx,xP),
inference(cnf_transformation,[],[f113]) ).
fof(f542,plain,
aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[],[f114]) ).
fof(f550,plain,
xp = xx,
inference(cnf_transformation,[],[f120]) ).
fof(f551,plain,
szmzizndt0(xQ) = xx,
inference(definition_unfolding,[],[f527,f550]) ).
fof(f561,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| sP2(sdtmndt0(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f350]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f323]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f331]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f561]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( sP3(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f361]) ).
tcf(c_94,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f369]) ).
tcf(c_251,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f525]) ).
tcf(c_253,plain,
szmzizndt0(xQ) = xx,
inference(cnf_transformation,[],[f551]) ).
tcf(c_255,plain,
sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
inference(cnf_transformation,[],[f528]) ).
tcf(c_266,plain,
aElementOf0(xx,xP),
inference(cnf_transformation,[],[f540]) ).
tcf(c_267,plain,
aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[],[f542]) ).
tcf(c_513,plain,
sdtmndt0(xQ,xx) = xP,
inference(light_normalisation,[status(thm)],[c_255,c_253]) ).
tcf(c_674,plain,
( aSet0(xQ)
| ~ aSet0(szNzAzT0) ),
inference(superposition,[status(thm)],[c_251,c_58]) ).
tcf(c_716,plain,
( aElement0(xx)
| ~ aSet0(szNzAzT0) ),
inference(superposition,[status(thm)],[c_267,c_49]) ).
tcf(c_790,plain,
( sP2(xP,xQ,xx)
| ~ sP3(xx,xQ) ),
inference(superposition,[status(thm)],[c_513,c_77]) ).
tcf(c_1215,plain,
sdtmndt0(xQ,xx) = xP,
inference(light_normalisation,[status(thm)],[c_255,c_253]) ).
tcf(c_2041,plain,
( sP2(xP,xQ,xx)
| ~ sP3(xx,xQ) ),
inference(superposition,[status(thm)],[c_1215,c_77]) ).
fof(f257,definition,
! [X2,X0,X1] :
( sP2(X2,X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f258,definition,
! [X1,X0] :
( ~ sP3(X1,X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> sP2(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f259,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP3(X1,X0) ),
inference(definition_folding,[],[f148,f258,f257]) ).
fof(f276,plain,
! [X2,X0,X1] :
( ( ~ sP2(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f257]) ).
fof(f277,plain,
! [X2,X0,X1] :
( ( ~ sP2(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP2(X2,X0,X1) ) ),
inference(flattening,[],[f276]) ).
fof(f278,plain,
! [X0,X1,X2] :
( ( ~ sP2(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( X2 != X4
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& ( X2 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X0)
| ( X2 != X3
& aElementOf0(X3,X1)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X0)
| X2 = X3
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3) ) )
| ~ aSet0(X0)
| sP2(X0,X1,X2) ) ),
inference(rectify,[],[f277]) ).
fof(f279,plain,
! [X0,X1,X2] :
( ( ~ sP2(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( X2 != X4
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& ( X2 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK7(X0,X1,X2),X0)
| ( sK7(X0,X1,X2) != X2
& aElementOf0(sK7(X0,X1,X2),X1)
& aElement0(sK7(X0,X1,X2)) ) )
& ( ~ aElementOf0(sK7(X0,X1,X2),X0)
| sK7(X0,X1,X2) = X2
| ~ aElementOf0(sK7(X0,X1,X2),X1)
| ~ aElement0(sK7(X0,X1,X2)) ) )
| ~ aSet0(X0)
| sP2(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f278]) ).
fof(f352,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| X2 != X4 ),
inference(cnf_transformation,[],[f279]) ).
fof(f562,plain,
! [X0,X1,X4] :
( ~ sP2(X0,X1,X4)
| ~ aElementOf0(X4,X0) ),
inference(equality_resolution,[],[f352]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ aElementOf0(X2,X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f562]) ).
tcf(c_6206,plain,
( ~ sP3(xx,xQ)
| ~ aElementOf0(xx,xP) ),
inference(superposition,[status(thm)],[c_790,c_86]) ).
tcf(c_11819,plain,
~ sP3(xx,xQ),
inference(global_subsumption_just,[status(thm)],[c_2041,c_266,c_6206]) ).
tcf(c_11821,plain,
( ~ aSet0(xQ)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_87,c_11819]) ).
tcf(c_11822,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11821,c_716,c_674,c_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM625+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 05:01:25 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.39/1.76 % SZS status Started for theBenchmark.p
% 1.39/1.76 % SZS status Theorem for theBenchmark.p
% 1.39/1.76
% 1.39/1.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.39/1.76
% 1.39/1.76 % ------ iProver source info
% 1.39/1.76
% 1.39/1.76 % git: date: 2026-07-19 20:42:38 +0200
% 1.39/1.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.39/1.76 % git: non_committed_changes: false
% 1.39/1.76
% 1.39/1.76 % ------ Parsing...
% 1.39/1.76 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.39/1.76 % ------ Proving...
% 1.39/1.76 % ------ Problem Properties
% 1.39/1.76
% 1.39/1.76 %
% 1.39/1.76 % clauses 228
% 1.39/1.76 % conjectures 1
% 1.39/1.76 % EPR 63
% 1.39/1.76 % Horn 189
% 1.39/1.76 % unary 64
% 1.39/1.76 % binary 36
% 1.39/1.76 % lits 700
% 1.39/1.76 % lits eq 108
% 1.39/1.76 % fd_pure 0
% 1.39/1.76 % fd_pseudo 0
% 1.39/1.76 % fd_cond 10
% 1.39/1.76 % fd_pseudo_cond 25
% 1.39/1.76 % AC symbols 0
% 1.39/1.76
% 1.39/1.76 % ------ Input Options Time Limit: Unbounded
% 1.39/1.76
% 1.39/1.76
% 1.39/1.76 % ------
% 1.39/1.76 % Current options:
% 1.39/1.76 % ------
% 1.39/1.76
% 1.39/1.76
% 1.39/1.76 %
% 1.39/1.76
% 1.39/1.76 % ------ Proving...
% 1.39/1.76 %
% 1.39/1.76
% 1.39/1.76 % ------ Proving...
% 1.39/1.76 %
% 1.39/1.76
% 1.39/1.76 % ------ Proving...
% 1.39/1.76 %
% 1.39/1.76
% 1.39/1.76 % SZS status Theorem for theBenchmark.p
% 1.39/1.76
% 1.39/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.39/1.76
% 1.39/1.76
%------------------------------------------------------------------------------