%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM550+3 : 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 02:25:59 PM UTC 2026
% Result : Theorem 1.44s 6.08s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 89 ( 41 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 94 ( 38 ~; 25 |; 25 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 21 !; 7 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f62,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f65,axiom,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xS) )
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).
fof(f67,conjecture,
~ ( xQ = slcrc0
& ~ ? [X0] : aElementOf0(X0,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f68,negated_conjecture,
~ ~ ( xQ = slcrc0
& ~ ? [X0] : aElementOf0(X0,xQ) ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f76,plain,
( xQ = slcrc0
& ~ ? [X0] : aElementOf0(X0,xQ) ),
inference(flattening,[],[f68]) ).
fof(f79,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f127,plain,
! [X0] :
( ~ aSet0(X0)
| ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f161,plain,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xS) )
& aSet0(xQ) ),
inference(ennf_transformation,[],[f65]) ).
fof(f162,plain,
( xQ = slcrc0
& ! [X0] : ~ aElementOf0(X0,xQ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f169,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f79]) ).
fof(f170,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f169]) ).
fof(f171,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f170]) ).
fof(f172,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))],[f171]) ).
fof(f192,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( sz00 != sbrdtbr0(X0)
| X0 = slcrc0 )
& ( slcrc0 != X0
| sbrdtbr0(X0) = sz00 ) ) ),
inference(nnf_transformation,[],[f127]) ).
fof(f218,plain,
! [X0] :
( slcrc0 != X0
| aSet0(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f283,plain,
! [X0] :
( ~ aSet0(X0)
| slcrc0 != X0
| sz00 = sbrdtbr0(X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f326,plain,
sz00 != xk,
inference(cnf_transformation,[],[f62]) ).
fof(f358,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f161]) ).
fof(f365,plain,
slcrc0 = xQ,
inference(cnf_transformation,[],[f162]) ).
fof(f368,plain,
! [X0] :
( xQ != X0
| aSet0(X0) ),
inference(definition_unfolding,[],[f218,f365]) ).
fof(f372,plain,
! [X0] :
( ~ aSet0(X0)
| xQ != X0
| sz00 = sbrdtbr0(X0) ),
inference(definition_unfolding,[],[f283,f365]) ).
fof(f386,plain,
aSet0(xQ),
inference(equality_resolution,[],[f368]) ).
fof(f393,plain,
( ~ aSet0(xQ)
| sz00 = sbrdtbr0(xQ) ),
inference(equality_resolution,[],[f372]) ).
tcf(c_51,negated_conjecture,
aSet0(xQ),
inference(cnf_transformation,[],[f386]) ).
tcf(c_115,negated_conjecture,
( ( sbrdtbr0(xQ) = sz00 )
| ~ aSet0(xQ) ),
inference(cnf_transformation,[],[f393]) ).
tcf(c_161,plain,
sz00 != xk,
inference(cnf_transformation,[],[f326]) ).
tcf(c_193,plain,
sbrdtbr0(xQ) = xk,
inference(cnf_transformation,[],[f358]) ).
tcf(c_296,negated_conjecture,
sbrdtbr0(xQ) = sz00,
inference(global_subsumption_just,[status(thm)],[c_115,c_51,c_115]) ).
tcf(c_1198,plain,
sz00 = xk,
inference(demodulation,[status(thm)],[c_296,c_193]) ).
tcf(c_1200,plain,
xk != xk,
inference(demodulation,[status(thm)],[c_161,c_1198]) ).
tcf(c_1201,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_1200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM550+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/5.31 % Computer : n012.cluster.edu
% 0.04/5.31 % Model : x86_64 x86_64
% 0.04/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.31 % Memory : 8046.5625MB
% 0.04/5.31 % OS : Linux 6.8.0-71-generic
% 0.04/5.31 % CPULimit : 300
% 0.04/5.31 % WCLimit : 300
% 0.04/5.31 % DateTime : Thu Sep 24 04:34:25 UTC 2026
% 0.04/5.31 % CPUTime :
% 0.04/5.31 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/5.33 Running first-order theorem proving
% 0.04/5.33 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
% 0.04/5.34
% 0.04/5.34 % ======== iProver multi-core TPTP/SMT =========
% 0.04/5.34
% 0.04/5.34 % Detected problem language: tptp
% 0.04/5.35 % Proving...
% 1.44/6.08 % SZS status Started for theBenchmark.p
% 1.44/6.08 % SZS status Theorem for theBenchmark.p
% 1.44/6.08
% 1.44/6.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.44/6.08
% 1.44/6.08 % ------ iProver source info
% 1.44/6.08
% 1.44/6.08 % git: date: 2026-07-19 20:42:38 +0200
% 1.44/6.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.44/6.08 % git: non_committed_changes: false
% 1.44/6.08
% 1.44/6.08 % ------ Parsing...
% 1.44/6.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.44/6.08
% 1.44/6.08 % ------ Preprocessing...%
% 1.44/6.08
% 1.44/6.08 % SZS status Theorem for theBenchmark.p
% 1.44/6.08
% 1.44/6.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.44/6.08
% 1.44/6.08
%------------------------------------------------------------------------------