%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM560+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 : n014.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 02:26:01 PM UTC 2026
% Result : Theorem 4.19s 11.30s
% Output : CNFRefutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 12 unt; 0 def)
% Number of atoms : 232 ( 35 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 303 ( 121 ~; 124 |; 46 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 97 ( 0 sgn 91 !; 6 ?; 26 :)
% 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(f64,axiom,
! [X0] :
( aFunction0(X0)
=> aSet0(szDzozmdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSet) ).
fof(f66,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aFunction0(X0) )
=> ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPtt) ).
fof(f67,axiom,
( aElement0(xy)
& aFunction0(xF) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2693) ).
fof(f68,conjecture,
aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f69,negated_conjecture,
~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
inference(negated_conjecture,[status(cth)],[f68]) ).
fof(f70,plain,
~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
inference(flattening,[],[f69]) ).
fof(f76,plain,
! [X0] :
( ~ aFunction0(X0)
| aSet0(szDzozmdt0(X0)) ),
inference(ennf_transformation,[],[f64]) ).
fof(f84,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f66]) ).
fof(f86,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f85]) ).
fof(f88,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,[],[f84]) ).
fof(f89,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,[],[f88]) ).
fof(f90,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,[],[f89]) ).
fof(f91,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK0(X0,X1),X1)
& ~ aElementOf0(sK0(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( ( sdtlbdtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0))
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( ~ aElementOf0(X3,X2)
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0)) ) )
| ~ aSet0(X2)
| X2 = sdtlbdtrb0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f86]) ).
fof(f93,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( ( sdtlbdtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0))
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( ~ aElementOf0(X3,X2)
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0)) ) )
| ~ aSet0(X2)
| X2 = sdtlbdtrb0(X0,X1) ) ) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( ( sdtlbdtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sdtlpdtrp0(X0,X4) = X1
& aElementOf0(X4,szDzozmdt0(X0)) ) )
& ( sdtlpdtrp0(X0,X4) != X1
| ~ aElementOf0(X4,szDzozmdt0(X0))
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( ~ aElementOf0(X3,X2)
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0)) ) )
| ~ aSet0(X2)
| X2 = sdtlbdtrb0(X0,X1) ) ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( ( sdtlbdtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sdtlpdtrp0(X0,X4) = X1
& aElementOf0(X4,szDzozmdt0(X0)) ) )
& ( sdtlpdtrp0(X0,X4) != X1
| ~ aElementOf0(X4,szDzozmdt0(X0))
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ( ( aElementOf0(sK1(X0,X1,X2),X2)
| ( sdtlpdtrp0(X0,sK1(X0,X1,X2)) = X1
& aElementOf0(sK1(X0,X1,X2),szDzozmdt0(X0)) ) )
& ( ~ aElementOf0(sK1(X0,X1,X2),X2)
| sdtlpdtrp0(X0,sK1(X0,X1,X2)) != X1
| ~ aElementOf0(sK1(X0,X1,X2),szDzozmdt0(X0)) ) )
| ~ aSet0(X2)
| X2 = sdtlbdtrb0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f94]) ).
fof(f96,plain,
aElement0(xy),
inference(cnf_transformation,[],[f67]) ).
fof(f97,plain,
aFunction0(xF),
inference(cnf_transformation,[],[f67]) ).
fof(f98,plain,
~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
inference(cnf_transformation,[],[f70]) ).
fof(f100,plain,
! [X0] :
( ~ aFunction0(X0)
| aSet0(szDzozmdt0(X0)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f107,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aElementOf0(sK0(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f108,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(sK0(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f110,plain,
! [X2,X0,X1,X4] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| sdtlbdtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| aElementOf0(X4,szDzozmdt0(X0)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| sdtlbdtrb0(X0,X1) != X2
| aSet0(X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f117,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| aSet0(sdtlbdtrb0(X0,X1)) ),
inference(equality_resolution,[],[f112]) ).
fof(f120,plain,
! [X0,X1,X4] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ~ aElementOf0(X4,sdtlbdtrb0(X0,X1))
| aElementOf0(X4,szDzozmdt0(X0)) ),
inference(equality_resolution,[],[f110]) ).
tcf(c_49,plain,
aFunction0(xF),
inference(cnf_transformation,[],[f97]) ).
tcf(c_50,plain,
aElement0(xy),
inference(cnf_transformation,[],[f96]) ).
tcf(c_51,negated_conjecture,
~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
inference(cnf_transformation,[],[f98]) ).
tcf(c_53,plain,
! [X0: $i] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X0,X1)
| aElementOf0(sK0(X1,X0),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( aSet0(sdtlbdtrb0(X0,X1))
| ~ aElement0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,szDzozmdt0(X1))
| ~ aElement0(X2)
| ~ aFunction0(X1)
| ~ aElementOf0(X0,sdtlbdtrb0(X1,X2)) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_417,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X1,szDzozmdt0(X0))
| ~ aElement0(X2)
| ~ aElementOf0(X1,sdtlbdtrb0(X0,X2))
| ( X0 != xF ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_67]) ).
tcf(c_418,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,szDzozmdt0(xF))
| ~ aElement0(X1)
| ~ aElementOf0(X0,sdtlbdtrb0(xF,X1)) ),
inference(unflattening,[status(thm)],[c_417]) ).
tcf(c_429,plain,
! [X0: $i,X1: $i] :
( aSet0(sdtlbdtrb0(X0,X1))
| ~ aElement0(X1)
| ( X0 != xF ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_65]) ).
tcf(c_430,plain,
! [X0: $i] :
( aSet0(sdtlbdtrb0(xF,X0))
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_429]) ).
tcf(c_495,plain,
! [X0: $i] :
( aSet0(szDzozmdt0(X0))
| ( X0 != xF ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_53]) ).
tcf(c_496,plain,
aSet0(szDzozmdt0(xF)),
inference(unflattening,[status(thm)],[c_495]) ).
tcf(c_1882,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(sdtlbdtrb0(xF,X0),X1)
| aElementOf0(sK0(X1,sdtlbdtrb0(xF,X0)),szDzozmdt0(xF))
| ~ aSet0(X1)
| ~ aElement0(X0)
| ~ aSet0(sdtlbdtrb0(xF,X0)) ),
inference(superposition,[status(thm)],[c_59,c_418]) ).
tcf(c_1957,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(sdtlbdtrb0(xF,X0),X1)
| aElementOf0(sK0(X1,sdtlbdtrb0(xF,X0)),szDzozmdt0(xF))
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1882,c_430,c_1882]) ).
tcf(c_1969,plain,
! [X0: $i] :
( aSubsetOf0(sdtlbdtrb0(xF,X0),szDzozmdt0(xF))
| ~ aElement0(X0)
| ~ aSet0(szDzozmdt0(xF))
| ~ aSet0(sdtlbdtrb0(xF,X0)) ),
inference(superposition,[status(thm)],[c_1957,c_58]) ).
tcf(c_1976,plain,
! [X0: $i] :
( aSubsetOf0(sdtlbdtrb0(xF,X0),szDzozmdt0(xF))
| ~ aElement0(X0)
| ~ aSet0(sdtlbdtrb0(xF,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1969,c_496]) ).
tcf(c_1987,plain,
! [X0: $i] :
( aSubsetOf0(sdtlbdtrb0(xF,X0),szDzozmdt0(xF))
| ~ aElement0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1976,c_430,c_1976]) ).
tcf(c_1994,plain,
~ aElement0(xy),
inference(superposition,[status(thm)],[c_1987,c_51]) ).
tcf(c_1999,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1994,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM560+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/10.39 % Computer : n014.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Thu Sep 24 04:37:44 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/10.43 Running first-order theorem proving
% 0.16/10.43 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
% 0.16/10.44
% 0.16/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/10.44
% 0.16/10.44 % Detected problem language: tptp
% 0.16/10.45 % Proving...
% 4.19/11.30 % SZS status Started for theBenchmark.p
% 4.19/11.30 % SZS status Theorem for theBenchmark.p
% 4.19/11.30
% 4.19/11.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.19/11.30
% 4.19/11.30 % ------ iProver source info
% 4.19/11.30
% 4.19/11.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.19/11.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.19/11.30 % git: non_committed_changes: false
% 4.19/11.30
% 4.19/11.30 % ------ Parsing...
% 4.19/11.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.19/11.30
% 4.19/11.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 4.19/11.30
% 4.19/11.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.19/11.30
% 4.19/11.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.19/11.30 % ------ Proving...
% 4.19/11.30 % ------ Problem Properties
% 4.19/11.30
% 4.19/11.30 %
% 4.19/11.30 % clauses 19
% 4.19/11.30 % conjectures 1
% 4.19/11.30 % EPR 7
% 4.19/11.30 % Horn 16
% 4.19/11.30 % unary 3
% 4.19/11.30 % binary 4
% 4.19/11.30 % lits 60
% 4.19/11.30 % lits eq 7
% 4.19/11.30 % fd_pure 0
% 4.19/11.30 % fd_pseudo 0
% 4.19/11.30 % fd_cond 0
% 4.19/11.30 % fd_pseudo_cond 4
% 4.19/11.30 % AC symbols 0
% 4.19/11.30
% 4.19/11.30 % ------ Schedule dynamic 5 is on
% 4.19/11.30
% 4.19/11.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.19/11.30
% 4.19/11.30
% 4.19/11.30 % ------
% 4.19/11.30 % Current options:
% 4.19/11.30 % ------
% 4.19/11.30
% 4.19/11.30
% 4.19/11.30 %
% 4.19/11.30
% 4.19/11.30 % ------ Proving...
% 4.19/11.30 %
% 4.19/11.30
% 4.19/11.30 % SZS status Theorem for theBenchmark.p
% 4.19/11.30
% 4.19/11.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.19/11.30
% 4.19/11.30
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