%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM547+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 : n026.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 02:25:58 PM UTC 2026
% Result : Theorem 3.64s 1.28s
% Output : CNFRefutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 21 unt; 1 def)
% Number of atoms : 231 ( 50 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 280 ( 109 ~; 100 |; 58 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 86 ( 0 sgn 74 !; 12 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f57,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aSet0(X0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(f61,axiom,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).
fof(f62,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f63,axiom,
( slbdtsldtrb0(xS,xk) != slcrc0
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
fof(f65,conjecture,
? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f66,negated_conjecture,
~ ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f75,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f80,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f147,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f57]) ).
fof(f148,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f147]) ).
fof(f155,plain,
! [X0] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(ennf_transformation,[],[f66]) ).
fof(f162,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f163,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f162]) ).
fof(f164,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f163]) ).
fof(f165,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))],[f164]) ).
fof(f166,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,[],[f80]) ).
fof(f167,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,[],[f166]) ).
fof(f168,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,[],[f167]) ).
fof(f169,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))],[f168]) ).
fof(f203,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f148]) ).
fof(f204,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(flattening,[],[f203]) ).
fof(f205,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sbrdtbr0(X4) = X1
& aSubsetOf0(X4,X0) ) )
& ( sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(rectify,[],[f204]) ).
fof(f206,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sbrdtbr0(X4) = X1
& aSubsetOf0(X4,X0) ) )
& ( sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ( ( aElementOf0(sK14(X0,X1,X2),X2)
| ( sbrdtbr0(sK14(X0,X1,X2)) = X1
& aSubsetOf0(sK14(X0,X1,X2),X0) ) )
& ( ~ aElementOf0(sK14(X0,X1,X2),X2)
| sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aSubsetOf0(sK14(X0,X1,X2),X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X0,X1,X2))],[f205]) ).
fof(f210,plain,
! [X0] :
( aElementOf0(sK4(X0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f165]) ).
fof(f215,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f169]) ).
fof(f309,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| aSet0(X2) ),
inference(cnf_transformation,[],[f206]) ).
fof(f316,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f61]) ).
fof(f318,plain,
aSet0(xT),
inference(cnf_transformation,[],[f62]) ).
fof(f320,plain,
slcrc0 != slbdtsldtrb0(xS,xk),
inference(cnf_transformation,[],[f63]) ).
fof(f321,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[],[f63]) ).
fof(f323,plain,
! [X0] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f155]) ).
fof(f341,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| aSet0(slbdtsldtrb0(X0,X1)) ),
inference(equality_resolution,[],[f309]) ).
tcf(c_50,plain,
! [X0: $i] :
( aElementOf0(sK4(X0),X0)
| ( X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( aSet0(slbdtsldtrb0(X1,X0))
| ~ aSet0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f341]) ).
tcf(c_158,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f316]) ).
tcf(c_160,plain,
aSet0(xT),
inference(cnf_transformation,[],[f318]) ).
tcf(c_162,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[],[f321]) ).
tcf(c_163,plain,
slbdtsldtrb0(xS,xk) != slcrc0,
inference(cnf_transformation,[],[f320]) ).
tcf(c_165,negated_conjecture,
! [X0: $i] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f323]) ).
tcf(c_8740,definition,
iPr_def_10 = slbdtsldtrb0(xS,xk),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8741,negated_conjecture,
! [X0: $i] : ~ aElementOf0(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_165,c_8740]) ).
tcf(c_10530,plain,
slcrc0 != iPr_def_10,
inference(light_normalisation,[status(thm)],[c_163,c_8740]) ).
tcf(c_10551,plain,
aSubsetOf0(iPr_def_10,slbdtsldtrb0(xT,xk)),
inference(light_normalisation,[status(thm)],[c_162,c_8740]) ).
tcf(c_10649,plain,
( aSet0(iPr_def_10)
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(superposition,[status(thm)],[c_10551,c_58]) ).
tcf(c_10774,plain,
( ( slcrc0 = iPr_def_10 )
| ~ aSet0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_50,c_8741]) ).
tcf(c_10775,plain,
~ aSet0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_10774,c_10530]) ).
tcf(c_10797,plain,
~ aSet0(slbdtsldtrb0(xT,xk)),
inference(backward_subsumption_resolution,[status(thm)],[c_10649,c_10775]) ).
tcf(c_10937,plain,
( ~ aSet0(xT)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[status(thm)],[c_151,c_10797]) ).
tcf(c_10938,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10937,c_160,c_158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM547+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 04:36:09 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 3.64/1.28 % SZS status Started for theBenchmark.p
% 3.64/1.28 % SZS status Theorem for theBenchmark.p
% 3.64/1.28
% 3.64/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.64/1.28
% 3.64/1.28 % ------ iProver source info
% 3.64/1.28
% 3.64/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.64/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.64/1.28 % git: non_committed_changes: false
% 3.64/1.28
% 3.64/1.28 % ------ Parsing...
% 3.64/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.64/1.28
% 3.64/1.28 % ------ 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 %
% 3.64/1.28
% 3.64/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.64/1.28
% 3.64/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.64/1.28 % ------ Proving...
% 3.64/1.28 % ------ Problem Properties
% 3.64/1.28
% 3.64/1.28 %
% 3.64/1.28 % clauses 116
% 3.64/1.28 % conjectures 1
% 3.64/1.28 % EPR 35
% 3.64/1.28 % Horn 86
% 3.64/1.28 % unary 18
% 3.64/1.28 % binary 16
% 3.64/1.28 % lits 386
% 3.64/1.28 % lits eq 58
% 3.64/1.28 % fd_pure 0
% 3.64/1.28 % fd_pseudo 0
% 3.64/1.28 % fd_cond 9
% 3.64/1.28 % fd_pseudo_cond 18
% 3.64/1.28 % AC symbols 0
% 3.64/1.28
% 3.64/1.28 % ------ Schedule dynamic 5 is on
% 3.64/1.28
% 3.64/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.64/1.28
% 3.64/1.28
% 3.64/1.28 % ------
% 3.64/1.28 % Current options:
% 3.64/1.28 % ------
% 3.64/1.28
% 3.64/1.28
% 3.64/1.28 %
% 3.64/1.28
% 3.64/1.28 % ------ Proving...
% 3.64/1.28 %
% 3.64/1.28
% 3.64/1.28 % SZS status Theorem for theBenchmark.p
% 3.64/1.28
% 3.64/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.64/1.28
% 3.64/1.28
%------------------------------------------------------------------------------