%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM550+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 : n019.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 1.93s 1.29s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 14 unt; 0 def)
% Number of atoms : 75 ( 39 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 77 ( 33 ~; 24 |; 15 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 22 ( 0 sgn 18 !; 4 ?; 0 :)
% 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(f62,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
fof(f66,axiom,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
fof(f67,conjecture,
xQ != slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f68,negated_conjecture,
~ ( xQ != slcrc0 ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f75,plain,
slcrc0 = xQ,
inference(flattening,[],[f68]) ).
fof(f78,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f126,plain,
! [X0] :
( ~ aSet0(X0)
| ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f164,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f165,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f164]) ).
fof(f166,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f165]) ).
fof(f167,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))],[f166]) ).
fof(f187,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( sz00 != sbrdtbr0(X0)
| X0 = slcrc0 )
& ( slcrc0 != X0
| sbrdtbr0(X0) = sz00 ) ) ),
inference(nnf_transformation,[],[f126]) ).
fof(f211,plain,
! [X0] :
( slcrc0 != X0
| aSet0(X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f276,plain,
! [X0] :
( ~ aSet0(X0)
| slcrc0 != X0
| sz00 = sbrdtbr0(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f319,plain,
sz00 != xk,
inference(cnf_transformation,[],[f62]) ).
fof(f326,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f329,plain,
slcrc0 = xQ,
inference(cnf_transformation,[],[f75]) ).
fof(f331,plain,
! [X0] :
( xQ != X0
| aSet0(X0) ),
inference(definition_unfolding,[],[f211,f329]) ).
fof(f335,plain,
! [X0] :
( ~ aSet0(X0)
| xQ != X0
| sz00 = sbrdtbr0(X0) ),
inference(definition_unfolding,[],[f276,f329]) ).
fof(f349,plain,
aSet0(xQ),
inference(equality_resolution,[],[f331]) ).
fof(f356,plain,
( ~ aSet0(xQ)
| sz00 = sbrdtbr0(xQ) ),
inference(equality_resolution,[],[f335]) ).
tcf(c_51,negated_conjecture,
aSet0(xQ),
inference(cnf_transformation,[],[f349]) ).
tcf(c_115,negated_conjecture,
( ( sbrdtbr0(xQ) = sz00 )
| ~ aSet0(xQ) ),
inference(cnf_transformation,[],[f356]) ).
tcf(c_161,plain,
sz00 != xk,
inference(cnf_transformation,[],[f319]) ).
tcf(c_168,plain,
sbrdtbr0(xQ) = xk,
inference(cnf_transformation,[],[f326]) ).
tcf(c_249,negated_conjecture,
sbrdtbr0(xQ) = sz00,
inference(global_subsumption_just,[status(thm)],[c_115,c_51,c_115]) ).
tcf(c_1043,plain,
sz00 = xk,
inference(light_normalisation,[status(thm)],[c_168,c_249]) ).
tcf(c_1046,plain,
sz00 != sz00,
inference(demodulation,[status(thm)],[c_161,c_1043]) ).
tcf(c_1047,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_1046]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM550+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Thu Sep 24 04:34:34 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 1.93/1.29 % SZS status Started for theBenchmark.p
% 1.93/1.29 % SZS status Theorem for theBenchmark.p
% 1.93/1.29
% 1.93/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.93/1.29
% 1.93/1.29 % ------ iProver source info
% 1.93/1.29
% 1.93/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.93/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.93/1.29 % git: non_committed_changes: false
% 1.93/1.29
% 1.93/1.29 % ------ Parsing...
% 1.93/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.93/1.29
% 1.93/1.29 % ------ Preprocessing...%
% 1.93/1.29
% 1.93/1.29 % SZS status Theorem for theBenchmark.p
% 1.93/1.29
% 1.93/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.93/1.29
% 1.93/1.29
%------------------------------------------------------------------------------