%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM609+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 : n004.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 02:26:13 PM UTC 2026
% Result : Theorem 4.28s 11.54s
% Output : CNFRefutation 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 70 ( 12 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 76 ( 23 ~; 15 |; 31 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 14 !; 1 ?; 1 :)
% Comments :
%------------------------------------------------------------------------------
fof(f104,axiom,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( X0 != szmzizndt0(xQ)
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(f107,conjecture,
( aSubsetOf0(xP,xQ)
| ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xQ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f108,negated_conjecture,
~ ( aSubsetOf0(xP,xQ)
| ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xQ) ) ),
inference(negated_conjecture,[status(cth)],[f107]) ).
fof(f130,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( szmzizndt0(xQ) != X1
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
inference(rectify,[],[f104]) ).
fof(f265,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( szmzizndt0(xQ) != X1
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
inference(ennf_transformation,[],[f130]) ).
fof(f266,plain,
( ~ aSubsetOf0(xP,xQ)
& ? [X0] :
( aElementOf0(X0,xP)
& ~ aElementOf0(X0,xQ) ) ),
inference(ennf_transformation,[],[f108]) ).
fof(f448,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X1] :
( ( ~ aElementOf0(X1,xP)
| ( szmzizndt0(xQ) != X1
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& ( szmzizndt0(xQ) = X1
| ~ aElementOf0(X1,xQ)
| ~ aElement0(X1)
| aElementOf0(X1,xP) ) )
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
inference(nnf_transformation,[],[f265]) ).
fof(f449,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X1] :
( ( ~ aElementOf0(X1,xP)
| ( szmzizndt0(xQ) != X1
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& ( szmzizndt0(xQ) = X1
| ~ aElementOf0(X1,xQ)
| ~ aElement0(X1)
| aElementOf0(X1,xP) ) )
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
inference(flattening,[],[f448]) ).
fof(f451,plain,
( ~ aSubsetOf0(xP,xQ)
& aElementOf0(sK73,xP)
& ~ aElementOf0(sK73,xQ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(X0,sK73)],[f266]) ).
fof(f864,plain,
! [X1] :
( ~ aElementOf0(X1,xP)
| aElementOf0(X1,xQ) ),
inference(cnf_transformation,[],[f449]) ).
fof(f873,plain,
aElementOf0(sK73,xP),
inference(cnf_transformation,[],[f451]) ).
fof(f874,plain,
~ aElementOf0(sK73,xQ),
inference(cnf_transformation,[],[f451]) ).
tcf(c_463,plain,
! [X0: $i] :
( aElementOf0(X0,xQ)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f864]) ).
tcf(c_469,negated_conjecture,
~ aElementOf0(sK73,xQ),
inference(cnf_transformation,[],[f874]) ).
tcf(c_470,negated_conjecture,
aElementOf0(sK73,xP),
inference(cnf_transformation,[],[f873]) ).
tcf(c_528,plain,
aElementOf0(sK73,xQ),
inference(superposition,[status(thm)],[c_470,c_463]) ).
tcf(c_529,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_469,c_528]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM609+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/10.61 % Computer : n004.cluster.edu
% 0.12/10.61 % Model : x86_64 x86_64
% 0.12/10.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.61 % Memory : 8046.5625MB
% 0.12/10.61 % OS : Linux 6.8.0-71-generic
% 0.12/10.61 % CPULimit : 300
% 0.12/10.61 % WCLimit : 300
% 0.12/10.61 % DateTime : Thu Sep 24 04:53:52 UTC 2026
% 0.12/10.61 % CPUTime :
% 0.12/10.61 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/10.65 Running first-order theorem proving
% 0.12/10.65 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
% 0.12/10.66
% 0.12/10.66 % ======== iProver multi-core TPTP/SMT =========
% 0.12/10.66
% 0.12/10.67 % Detected problem language: tptp
% 0.12/10.68 % Proving...
% 4.28/11.54 % SZS status Started for theBenchmark.p
% 4.28/11.54 % SZS status Theorem for theBenchmark.p
% 4.28/11.54
% 4.28/11.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.28/11.54
% 4.28/11.54 % ------ iProver source info
% 4.28/11.54
% 4.28/11.54 % git: date: 2026-07-19 20:42:38 +0200
% 4.28/11.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.28/11.54 % git: non_committed_changes: false
% 4.28/11.54
% 4.28/11.54 % ------ Parsing...
% 4.28/11.54 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.28/11.54 % ------ Proving...
% 4.28/11.54 % ------ Problem Properties
% 4.28/11.54
% 4.28/11.54 %
% 4.28/11.54 % clauses 423
% 4.28/11.54 % conjectures 3
% 4.28/11.54 % EPR 85
% 4.28/11.54 % Horn 338
% 4.28/11.54 % unary 61
% 4.28/11.54 % binary 125
% 4.28/11.54 % lits 1311
% 4.28/11.54 % lits eq 171
% 4.28/11.54 % fd_pure 0
% 4.28/11.54 % fd_pseudo 0
% 4.28/11.54 % fd_cond 11
% 4.28/11.54 % fd_pseudo_cond 47
% 4.28/11.54 % AC symbols 0
% 4.28/11.54
% 4.28/11.54 % ------ Input Options Time Limit: Unbounded
% 4.28/11.54
% 4.28/11.54
% 4.28/11.54 % ------
% 4.28/11.54 % Current options:
% 4.28/11.54 % ------
% 4.28/11.54
% 4.28/11.54
% 4.28/11.54 %
% 4.28/11.54
% 4.28/11.54 % ------ Proving...
% 4.28/11.54 %
% 4.28/11.54
% 4.28/11.54 % SZS status Theorem for theBenchmark.p
% 4.28/11.54
% 4.28/11.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.28/11.54
% 4.28/11.54
%------------------------------------------------------------------------------