%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM605+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 02:26:11 PM UTC 2026
% Result : Theorem 8.75s 1.90s
% Output : CNFRefutation 8.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 19 unt; 0 def)
% Number of atoms : 188 ( 70 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 231 ( 90 ~; 86 |; 43 &)
% ( 10 <=>; 2 =>; 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 63 ( 0 sgn 56 !; 7 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f57,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aSet0(X0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(f79,axiom,
xK != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3520) ).
fof(f96,axiom,
( isCountable0(xO)
& aSet0(xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4908) ).
fof(f99,axiom,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
fof(f100,conjecture,
xQ != slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f101,negated_conjecture,
~ ( xQ != slcrc0 ),
inference(negated_conjecture,[status(cth)],[f100]) ).
fof(f109,plain,
slcrc0 = xQ,
inference(flattening,[],[f101]) ).
fof(f111,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f160,plain,
! [X0] :
( ~ aSet0(X0)
| ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f184,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f57]) ).
fof(f185,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f184]) ).
fof(f239,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f111]) ).
fof(f240,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f239]) ).
fof(f241,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f240]) ).
fof(f242,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))],[f241]) ).
fof(f262,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( sz00 != sbrdtbr0(X0)
| X0 = slcrc0 )
& ( slcrc0 != X0
| sbrdtbr0(X0) = sz00 ) ) ),
inference(nnf_transformation,[],[f160]) ).
fof(f280,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f185]) ).
fof(f281,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(flattening,[],[f280]) ).
fof(f282,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sbrdtbr0(X4) = X1
& aSubsetOf0(X4,X0) ) )
& ( sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(rectify,[],[f281]) ).
fof(f283,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sbrdtbr0(X4) = X1
& aSubsetOf0(X4,X0) ) )
& ( sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ( ( aElementOf0(sK14(X0,X1,X2),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) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X0,X1,X2))],[f282]) ).
fof(f304,plain,
! [X0] :
( slcrc0 != X0
| aSet0(X0) ),
inference(cnf_transformation,[],[f242]) ).
fof(f370,plain,
! [X0] :
( ~ aSet0(X0)
| slcrc0 != X0
| sz00 = sbrdtbr0(X0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f402,plain,
! [X2,X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| sbrdtbr0(X4) = X1 ),
inference(cnf_transformation,[],[f283]) ).
fof(f447,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f458,plain,
sz00 != xK,
inference(cnf_transformation,[],[f79]) ).
fof(f496,plain,
aSet0(xO),
inference(cnf_transformation,[],[f96]) ).
fof(f501,plain,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(cnf_transformation,[],[f99]) ).
fof(f502,plain,
slcrc0 = xQ,
inference(cnf_transformation,[],[f109]) ).
fof(f504,plain,
! [X0] :
( xQ != X0
| aSet0(X0) ),
inference(definition_unfolding,[],[f304,f502]) ).
fof(f508,plain,
! [X0] :
( ~ aSet0(X0)
| xQ != X0
| sz00 = sbrdtbr0(X0) ),
inference(definition_unfolding,[],[f370,f502]) ).
fof(f522,plain,
aSet0(xQ),
inference(equality_resolution,[],[f504]) ).
fof(f529,plain,
( ~ aSet0(xQ)
| sz00 = sbrdtbr0(xQ) ),
inference(equality_resolution,[],[f508]) ).
fof(f543,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| sbrdtbr0(X4) = X1 ),
inference(equality_resolution,[],[f402]) ).
tcf(c_51,negated_conjecture,
aSet0(xQ),
inference(cnf_transformation,[],[f522]) ).
tcf(c_116,negated_conjecture,
( ( sbrdtbr0(xQ) = sz00 )
| ~ aSet0(xQ) ),
inference(cnf_transformation,[],[f529]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sbrdtbr0(X0) = X2 )
| ~ aSet0(X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X0,slbdtsldtrb0(X1,X2)) ),
inference(cnf_transformation,[],[f543]) ).
tcf(c_194,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f447]) ).
tcf(c_205,plain,
sz00 != xK,
inference(cnf_transformation,[],[f458]) ).
tcf(c_242,plain,
aSet0(xO),
inference(cnf_transformation,[],[f496]) ).
tcf(c_248,plain,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(cnf_transformation,[],[f501]) ).
tcf(c_389,negated_conjecture,
sbrdtbr0(xQ) = sz00,
inference(global_subsumption_just,[status(thm)],[c_116,c_51,c_116]) ).
tcf(c_9264,plain,
( ( sbrdtbr0(xQ) = xK )
| ~ aSet0(xO)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(superposition,[status(thm)],[c_248,c_155]) ).
tcf(c_9272,plain,
( ( sz00 = xK )
| ~ aSet0(xO)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(demodulation,[status(thm)],[c_9264,c_389]) ).
tcf(c_9371,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9272,c_205,c_194,c_242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM605+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.43 % Computer : n009.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Thu Sep 24 04:52:44 UTC 2026
% 0.19/0.43 % CPUTime :
% 0.19/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.48 Running first-order theorem proving
% 0.19/0.48 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
% 0.19/0.50
% 0.19/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.19/0.50
% 0.19/0.50 % Detected problem language: tptp
% 0.24/0.52 % Proving...
% 8.75/1.90 % SZS status Started for theBenchmark.p
% 8.75/1.90 % SZS status Theorem for theBenchmark.p
% 8.75/1.90
% 8.75/1.90 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.75/1.90
% 8.75/1.90 % ------ iProver source info
% 8.75/1.90
% 8.75/1.90 % git: date: 2026-07-19 20:42:38 +0200
% 8.75/1.90 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.75/1.90 % git: non_committed_changes: false
% 8.75/1.90
% 8.75/1.90 % ------ Parsing...
% 8.75/1.90 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.75/1.90
% 8.75/1.90 % ------ Preprocessing... sup_sim: 0 pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 pe_s pe_e %
% 8.75/1.90
% 8.75/1.90 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 4 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 8.75/1.90
% 8.75/1.90 % ------ Preprocessing...
% 8.75/1.90 % ------ Proving...
% 8.75/1.90 % ------ Problem Properties
% 8.75/1.90
% 8.75/1.90 %
% 8.75/1.90 % clauses 203
% 8.75/1.90 % conjectures 19
% 8.75/1.90 % EPR 50
% 8.75/1.90 % Horn 160
% 8.75/1.90 % unary 37
% 8.75/1.90 % binary 40
% 8.75/1.90 % lits 672
% 8.75/1.90 % lits eq 103
% 8.75/1.90 % fd_pure 0
% 8.75/1.90 % fd_pseudo 0
% 8.75/1.90 % fd_cond 10
% 8.75/1.90 % fd_pseudo_cond 25
% 8.75/1.90 % AC symbols 0
% 8.75/1.90
% 8.75/1.90 % ------ Input Options Time Limit: Unbounded
% 8.75/1.90
% 8.75/1.90
% 8.75/1.90 % ------
% 8.75/1.90 % Current options:
% 8.75/1.90 % ------
% 8.75/1.90
% 8.75/1.90
% 8.75/1.90 %
% 8.75/1.90
% 8.75/1.90 % ------ Proving...
% 8.75/1.90 %
% 8.75/1.90
% 8.75/1.90 % SZS status Theorem for theBenchmark.p
% 8.75/1.90
% 8.75/1.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.75/1.90
% 8.75/1.90
%------------------------------------------------------------------------------