%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM561+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 : 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 02:26:01 PM UTC 2026
% Result : Theorem 1.56s 1.29s
% Output : CNFRefutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 15 unt; 0 def)
% Number of atoms : 147 ( 33 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 187 ( 77 ~; 74 |; 28 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 72 ( 0 sgn 61 !; 11 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(f64,axiom,
! [X0] :
( aFunction0(X0)
=> aSet0(szDzozmdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSet) ).
fof(f68,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aSubsetOf0(X1,szDzozmdt0(X0))
=> ! [X2] :
( X2 = sdtlcdtrc0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& aSet0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSImg) ).
fof(f69,axiom,
aFunction0(xF),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2911) ).
fof(f70,axiom,
aElementOf0(xx,szDzozmdt0(xF)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2911_02) ).
fof(f71,conjecture,
aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f72,negated_conjecture,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(negated_conjecture,[status(cth)],[f71]) ).
fof(f73,plain,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(flattening,[],[f72]) ).
fof(f80,plain,
! [X0] :
( ~ aFunction0(X0)
| aSet0(szDzozmdt0(X0)) ),
inference(ennf_transformation,[],[f64]) ).
fof(f81,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( X2 = sdtlcdtrc0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& aSet0(X2) ) ) ) ),
inference(ennf_transformation,[],[f68]) ).
fof(f86,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f90,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( ( sdtlcdtrc0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& ( ~ aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X2)
| X2 = sdtlcdtrc0(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f91,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( ( sdtlcdtrc0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& ( ~ aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X2)
| X2 = sdtlcdtrc0(X0,X1) ) ) ) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( ( sdtlcdtrc0(X0,X1) != X2
| ( ! [X6] :
( ( ~ aElementOf0(X6,X2)
| ? [X8] :
( sdtlpdtrp0(X0,X8) = X6
& aElementOf0(X8,X1) ) )
& ( ! [X7] :
( sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1) )
| aElementOf0(X6,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ? [X5] :
( sdtlpdtrp0(X0,X5) = X3
& aElementOf0(X5,X1) ) )
& ( ~ aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X2)
| X2 = sdtlcdtrc0(X0,X1) ) ) ) ),
inference(rectify,[],[f91]) ).
fof(f93,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( ( sdtlcdtrc0(X0,X1) != X2
| ( ! [X6] :
( ( ~ aElementOf0(X6,X2)
| ( sdtlpdtrp0(X0,sK2(X0,X1,X6)) = X6
& aElementOf0(sK2(X0,X1,X6),X1) ) )
& ( ! [X7] :
( sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1) )
| aElementOf0(X6,X2) ) )
& aSet0(X2) ) )
& ( ( ( aElementOf0(sK0(X0,X1,X2),X2)
| ( sK0(X0,X1,X2) = sdtlpdtrp0(X0,sK1(X0,X1,X2))
& aElementOf0(sK1(X0,X1,X2),X1) ) )
& ( ~ aElementOf0(sK0(X0,X1,X2),X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != sK0(X0,X1,X2)
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X2)
| X2 = sdtlcdtrc0(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f92]) ).
fof(f98,plain,
aFunction0(xF),
inference(cnf_transformation,[],[f69]) ).
fof(f99,plain,
aElementOf0(xx,szDzozmdt0(xF)),
inference(cnf_transformation,[],[f70]) ).
fof(f100,plain,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(cnf_transformation,[],[f73]) ).
fof(f101,plain,
! [X0] :
( ~ aFunction0(X0)
| aSet0(szDzozmdt0(X0)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f104,plain,
! [X2,X0,X1,X6,X7] :
( ~ aFunction0(X0)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| sdtlcdtrc0(X0,X1) != X2
| sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1)
| aElementOf0(X6,X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f111,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f118,plain,
! [X2,X0,X1,X7] :
( ~ aFunction0(X0)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| sdtlcdtrc0(X0,X1) != X2
| ~ aElementOf0(X7,X1)
| aElementOf0(sdtlpdtrp0(X0,X7),X2) ),
inference(equality_resolution,[],[f104]) ).
fof(f119,plain,
! [X0,X1,X7] :
( ~ aFunction0(X0)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aElementOf0(X7,X1)
| aElementOf0(sdtlpdtrp0(X0,X7),sdtlcdtrc0(X0,X1)) ),
inference(equality_resolution,[],[f118]) ).
tcf(c_49,plain,
aFunction0(xF),
inference(cnf_transformation,[],[f98]) ).
tcf(c_50,plain,
aElementOf0(xx,szDzozmdt0(xF)),
inference(cnf_transformation,[],[f99]) ).
tcf(c_51,negated_conjecture,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(cnf_transformation,[],[f100]) ).
tcf(c_52,plain,
! [X0: $i] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,X0))
| ~ aFunction0(X1)
| ~ aElementOf0(X2,X0)
| ~ aSubsetOf0(X0,szDzozmdt0(X1)) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_62,plain,
! [X0: $i] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_378,plain,
! [X0: $i] :
( aSet0(szDzozmdt0(X0))
| ( X0 != xF ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_52]) ).
tcf(c_379,plain,
aSet0(szDzozmdt0(xF)),
inference(unflattening,[status(thm)],[c_378]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtlpdtrp0(X0,X2),sdtlcdtrc0(X0,X1))
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ( X0 != xF ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_57]) ).
tcf(c_408,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtlpdtrp0(xF,X1),sdtlcdtrc0(xF,X0))
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,szDzozmdt0(xF)) ),
inference(unflattening,[status(thm)],[c_407]) ).
tcf(c_1135,plain,
( ~ aElementOf0(xx,szDzozmdt0(xF))
| ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF)) ),
inference(superposition,[status(thm)],[c_408,c_51]) ).
tcf(c_1136,plain,
~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF)),
inference(forward_subsumption_resolution,[status(thm)],[c_1135,c_50]) ).
tcf(c_1137,plain,
~ aSet0(szDzozmdt0(xF)),
inference(superposition,[status(thm)],[c_62,c_1136]) ).
tcf(c_1138,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1137,c_379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM561+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 04:37:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 1.56/1.29 % SZS status Started for theBenchmark.p
% 1.56/1.29 % SZS status Theorem for theBenchmark.p
% 1.56/1.29
% 1.56/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.56/1.29
% 1.56/1.29 % ------ iProver source info
% 1.56/1.29
% 1.56/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.56/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.56/1.29 % git: non_committed_changes: false
% 1.56/1.29
% 1.56/1.29 % ------ Parsing...
% 1.56/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.56/1.29
% 1.56/1.29 % ------ 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 %
% 1.56/1.29
% 1.56/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.56/1.29
% 1.56/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.56/1.29 % ------ Proving...
% 1.56/1.29 % ------ Problem Properties
% 1.56/1.29
% 1.56/1.29 %
% 1.56/1.29 % clauses 17
% 1.56/1.29 % conjectures 1
% 1.56/1.29 % EPR 5
% 1.56/1.29 % Horn 14
% 1.56/1.29 % unary 3
% 1.56/1.29 % binary 2
% 1.56/1.29 % lits 55
% 1.56/1.29 % lits eq 7
% 1.56/1.29 % fd_pure 0
% 1.56/1.29 % fd_pseudo 0
% 1.56/1.29 % fd_cond 0
% 1.56/1.29 % fd_pseudo_cond 4
% 1.56/1.29 % AC symbols 0
% 1.56/1.29
% 1.56/1.29 % ------ Schedule dynamic 5 is on
% 1.56/1.29
% 1.56/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.56/1.29
% 1.56/1.29
% 1.56/1.29 % ------
% 1.56/1.29 % Current options:
% 1.56/1.29 % ------
% 1.56/1.29
% 1.56/1.29
% 1.56/1.29 %
% 1.56/1.29
% 1.56/1.29 % ------ Proving...
% 1.56/1.29 %
% 1.56/1.29
% 1.56/1.29 % SZS status Theorem for theBenchmark.p
% 1.56/1.29
% 1.56/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.56/1.29
% 1.56/1.29
%------------------------------------------------------------------------------