%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM551+1 : 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 : n005.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 3.97s 1.30s
% Output : CNFRefutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 7 unt; 0 def)
% Number of atoms : 78 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 88 ( 39 ~; 31 |; 14 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 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 : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 32 ( 0 sgn 26 !; 6 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f66,axiom,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
fof(f67,axiom,
xQ != slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2313) ).
fof(f68,conjecture,
? [X0] :
( aElementOf0(X0,xQ)
& aElement0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f69,negated_conjecture,
~ ? [X0] :
( aElementOf0(X0,xQ)
& aElement0(X0) ),
inference(negated_conjecture,[status(cth)],[f68]) ).
fof(f77,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f78,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f158,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f165,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f166,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f165]) ).
fof(f167,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f166]) ).
fof(f168,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))],[f167]) ).
fof(f210,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f213,plain,
! [X0] :
( aElementOf0(sK4(X0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f168]) ).
fof(f329,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f330,plain,
slcrc0 != xQ,
inference(cnf_transformation,[],[f67]) ).
fof(f331,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_50,plain,
! [X0: $i] :
( aElementOf0(sK4(X0),X0)
| ( X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_166,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f329]) ).
tcf(c_169,plain,
slcrc0 != xQ,
inference(cnf_transformation,[],[f330]) ).
tcf(c_170,negated_conjecture,
! [X0: $i] :
( ~ aElement0(X0)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f331]) ).
tcf(c_8942,negated_conjecture,
! [X0: $i] :
( ~ aElement0(X0)
| ~ aElementOf0(X0,xQ) ),
inference(demodulation,[status(thm)],[c_170]) ).
tcf(c_11049,plain,
! [X0: $i] :
( aElement0(sK4(X0))
| ( X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_11057,plain,
( ( slcrc0 = xQ )
| ~ aSet0(xQ)
| ~ aElement0(sK4(xQ)) ),
inference(superposition,[status(thm)],[c_50,c_8942]) ).
tcf(c_11061,plain,
~ aElement0(sK4(xQ)),
inference(forward_subsumption_resolution,[status(thm)],[c_11057,c_169,c_166]) ).
tcf(c_11182,plain,
( ( slcrc0 = xQ )
| ~ aSet0(xQ) ),
inference(superposition,[status(thm)],[c_11049,c_11061]) ).
tcf(c_11183,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11182,c_169,c_166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM551+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n005.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Thu Sep 24 04:34:32 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 3.97/1.30 % SZS status Started for theBenchmark.p
% 3.97/1.30 % SZS status Theorem for theBenchmark.p
% 3.97/1.30
% 3.97/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.97/1.30
% 3.97/1.30 % ------ iProver source info
% 3.97/1.30
% 3.97/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.97/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.97/1.30 % git: non_committed_changes: false
% 3.97/1.30
% 3.97/1.30 % ------ Parsing...
% 3.97/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.97/1.30
% 3.97/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.97/1.30
% 3.97/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.97/1.30
% 3.97/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.97/1.30 % ------ Proving...
% 3.97/1.30 % ------ Problem Properties
% 3.97/1.30
% 3.97/1.30 %
% 3.97/1.30 % clauses 120
% 3.97/1.30 % conjectures 1
% 3.97/1.30 % EPR 38
% 3.97/1.30 % Horn 90
% 3.97/1.30 % unary 21
% 3.97/1.30 % binary 17
% 3.97/1.30 % lits 391
% 3.97/1.30 % lits eq 59
% 3.97/1.30 % fd_pure 0
% 3.97/1.30 % fd_pseudo 0
% 3.97/1.30 % fd_cond 9
% 3.97/1.30 % fd_pseudo_cond 18
% 3.97/1.30 % AC symbols 0
% 3.97/1.30
% 3.97/1.30 % ------ Schedule dynamic 5 is on
% 3.97/1.30
% 3.97/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.97/1.30
% 3.97/1.30
% 3.97/1.30 % ------
% 3.97/1.30 % Current options:
% 3.97/1.30 % ------
% 3.97/1.30
% 3.97/1.30
% 3.97/1.30 %
% 3.97/1.30
% 3.97/1.30 % ------ Proving...
% 3.97/1.30 %
% 3.97/1.30
% 3.97/1.30 % SZS status Theorem for theBenchmark.p
% 3.97/1.30
% 3.97/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.97/1.31
% 3.97/1.31
%------------------------------------------------------------------------------