%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM610+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 : n001.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 4.29s 6.29s
% Output : CNFRefutation 4.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 15 unt; 0 def)
% Number of atoms : 135 ( 2 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 171 ( 75 ~; 70 |; 20 &)
% ( 2 <=>; 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 52 !; 3 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aSet0(X2)
& aSet0(X1)
& aSet0(X0) )
=> ( ( aSubsetOf0(X1,X2)
& aSubsetOf0(X0,X1) )
=> aSubsetOf0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).
fof(f96,axiom,
( isCountable0(xO)
& aSet0(xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4908) ).
fof(f100,axiom,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).
fof(f104,axiom,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& aSet0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(f107,axiom,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5195) ).
fof(f108,conjecture,
aSubsetOf0(xP,xO),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f109,negated_conjecture,
~ aSubsetOf0(xP,xO),
inference(negated_conjecture,[status(cth)],[f108]) ).
fof(f117,plain,
~ aSubsetOf0(xP,xO),
inference(flattening,[],[f109]) ).
fof(f124,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2) ),
inference(flattening,[],[f130]) ).
fof(f251,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f124]) ).
fof(f252,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(flattening,[],[f251]) ).
fof(f253,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(rectify,[],[f252]) ).
fof(f254,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK5(X0,X1),X1)
& ~ aElementOf0(sK5(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f253]) ).
fof(f318,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f254]) ).
fof(f324,plain,
! [X2,X0,X1] :
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2) ),
inference(cnf_transformation,[],[f131]) ).
fof(f504,plain,
aSet0(xO),
inference(cnf_transformation,[],[f96]) ).
fof(f511,plain,
aSubsetOf0(xQ,xO),
inference(cnf_transformation,[],[f100]) ).
fof(f516,plain,
aSet0(xP),
inference(cnf_transformation,[],[f104]) ).
fof(f519,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[],[f107]) ).
fof(f520,plain,
~ aSubsetOf0(xP,xO),
inference(cnf_transformation,[],[f117]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f318]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X2,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f324]) ).
tcf(c_242,plain,
aSet0(xO),
inference(cnf_transformation,[],[f504]) ).
tcf(c_249,plain,
aSubsetOf0(xQ,xO),
inference(cnf_transformation,[],[f511]) ).
tcf(c_254,plain,
aSet0(xP),
inference(cnf_transformation,[],[f516]) ).
tcf(c_258,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[],[f519]) ).
tcf(c_259,negated_conjecture,
~ aSubsetOf0(xP,xO),
inference(cnf_transformation,[],[f520]) ).
tcf(c_322,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_58,c_63]) ).
tcf(c_323,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(renaming,[status(thm)],[c_322]) ).
tcf(c_408,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_323]) ).
tcf(c_409,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(renaming,[status(thm)],[c_408]) ).
tcf(c_421,plain,
! [X0: $i] :
( aSubsetOf0(X0,xO)
| ~ aSet0(xO)
| ~ aSet0(X0)
| ~ aSubsetOf0(X0,xQ) ),
inference(superposition,[status(thm)],[c_249,c_409]) ).
tcf(c_485,plain,
! [X0: $i] :
( aSubsetOf0(X0,xO)
| ~ aSubsetOf0(X0,xQ)
| ~ aSet0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_421,c_242,c_421]) ).
tcf(c_486,plain,
! [X0: $i] :
( aSubsetOf0(X0,xO)
| ~ aSet0(X0)
| ~ aSubsetOf0(X0,xQ) ),
inference(renaming,[status(thm)],[c_485]) ).
tcf(c_495,plain,
( aSubsetOf0(xP,xO)
| ~ aSet0(xP) ),
inference(superposition,[status(thm)],[c_258,c_486]) ).
tcf(c_496,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_495,c_259,c_254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM610+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.36 % Computer : n001.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Thu Sep 24 05:00:12 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.40 Running first-order theorem proving
% 0.15/5.40 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
% 0.15/5.41
% 0.15/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.41
% 0.15/5.41 % Detected problem language: tptp
% 0.15/5.42 % Proving...
% 4.29/6.29 % SZS status Started for theBenchmark.p
% 4.29/6.29 % SZS status Theorem for theBenchmark.p
% 4.29/6.29
% 4.29/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.29/6.29
% 4.29/6.29 % ------ iProver source info
% 4.29/6.29
% 4.29/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 4.29/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.29/6.29 % git: non_committed_changes: false
% 4.29/6.29
% 4.29/6.29 % ------ Parsing...
% 4.29/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.29/6.29 % ------ Proving...
% 4.29/6.29 % ------ Problem Properties
% 4.29/6.29
% 4.29/6.29 %
% 4.29/6.29 % clauses 211
% 4.29/6.29 % conjectures 1
% 4.29/6.29 % EPR 56
% 4.29/6.29 % Horn 172
% 4.29/6.29 % unary 48
% 4.29/6.29 % binary 35
% 4.29/6.29 % lits 682
% 4.29/6.29 % lits eq 103
% 4.29/6.29 % fd_pure 0
% 4.29/6.29 % fd_pseudo 0
% 4.29/6.29 % fd_cond 10
% 4.29/6.29 % fd_pseudo_cond 25
% 4.29/6.29 % AC symbols 0
% 4.29/6.29
% 4.29/6.29 % ------ Input Options Time Limit: Unbounded
% 4.29/6.29
% 4.29/6.29
% 4.29/6.29 % ------
% 4.29/6.29 % Current options:
% 4.29/6.29 % ------
% 4.29/6.29
% 4.29/6.29
% 4.29/6.29 %
% 4.29/6.29
% 4.29/6.29 % ------ Proving...
% 4.29/6.29 %
% 4.29/6.29
% 4.29/6.29 % ------ Proving...
% 4.29/6.29 %
% 4.29/6.29
% 4.29/6.29 % SZS status Theorem for theBenchmark.p
% 4.29/6.29
% 4.29/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.29/6.29
% 4.29/6.29
%------------------------------------------------------------------------------