%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM548+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 : n011.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 3.79s 1.23s
% Output : CNFRefutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 17 unt; 0 def)
% Number of atoms : 219 ( 38 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 281 ( 110 ~; 109 |; 48 &)
% ( 10 <=>; 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 81 ( 0 sgn 75 !; 6 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
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(f41,axiom,
! [X0] :
( aSet0(X0)
=> ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
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(f65,axiom,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).
fof(f66,conjecture,
isFinite0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f67,negated_conjecture,
~ isFinite0(xQ),
inference(negated_conjecture,[status(cth)],[f66]) ).
fof(f68,plain,
~ isFinite0(xQ),
inference(flattening,[],[f67]) ).
fof(f92,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f97,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(f98,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,[],[f97]) ).
fof(f122,plain,
! [X0] :
( ~ aSet0(X0)
| ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f161,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,[],[f92]) ).
fof(f162,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,[],[f161]) ).
fof(f163,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,[],[f162]) ).
fof(f164,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK6(X0,X1),X1)
& ~ aElementOf0(sK6(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f163]) ).
fof(f165,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,[],[f98]) ).
fof(f166,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,[],[f165]) ).
fof(f167,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,[],[f166]) ).
fof(f168,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(sK7(X0,X1,X2),X2)
| ( sbrdtbr0(sK7(X0,X1,X2)) = X1
& aSubsetOf0(sK7(X0,X1,X2),X0) ) )
& ( ~ aElementOf0(sK7(X0,X1,X2),X2)
| sbrdtbr0(sK7(X0,X1,X2)) != X1
| ~ aSubsetOf0(sK7(X0,X1,X2),X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f167]) ).
fof(f178,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0) )
& ( ~ isFinite0(X0)
| aElementOf0(sbrdtbr0(X0),szNzAzT0) ) ) ),
inference(nnf_transformation,[],[f122]) ).
fof(f192,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f61]) ).
fof(f195,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f199,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f65]) ).
fof(f200,plain,
~ isFinite0(xQ),
inference(cnf_transformation,[],[f68]) ).
fof(f222,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f164]) ).
fof(f227,plain,
! [X2,X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| sbrdtbr0(X4) = X1 ),
inference(cnf_transformation,[],[f168]) ).
fof(f228,plain,
! [X2,X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| aSubsetOf0(X4,X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f260,plain,
! [X0] :
( ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f308,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| aSubsetOf0(X4,X0) ),
inference(equality_resolution,[],[f228]) ).
fof(f309,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| sbrdtbr0(X4) = X1 ),
inference(equality_resolution,[],[f227]) ).
tcf(c_49,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f192]) ).
tcf(c_50,plain,
aSet0(xS),
inference(cnf_transformation,[],[f195]) ).
tcf(c_56,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f199]) ).
tcf(c_57,negated_conjecture,
~ isFinite0(xQ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X0,slbdtsldtrb0(X1,X2)) ),
inference(cnf_transformation,[],[f308]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sbrdtbr0(X0) = X2 )
| ~ aSet0(X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X0,slbdtsldtrb0(X1,X2)) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_118,plain,
! [X0: $i] :
( isFinite0(X0)
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f260]) ).
tcf(c_11699,plain,
( aSubsetOf0(xQ,xS)
| ~ aSet0(xS)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[status(thm)],[c_56,c_89]) ).
tcf(c_11702,plain,
aSubsetOf0(xQ,xS),
inference(forward_subsumption_resolution,[status(thm)],[c_11699,c_50,c_49]) ).
tcf(c_11733,plain,
( aSet0(xQ)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_11702,c_80]) ).
tcf(c_11735,plain,
aSet0(xQ),
inference(forward_subsumption_resolution,[status(thm)],[c_11733,c_50]) ).
tcf(c_12831,plain,
( ( sbrdtbr0(xQ) = xk )
| ~ aSet0(xS)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[status(thm)],[c_56,c_90]) ).
tcf(c_12836,plain,
sbrdtbr0(xQ) = xk,
inference(forward_subsumption_resolution,[status(thm)],[c_12831,c_50,c_49]) ).
tcf(c_13397,plain,
( isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[status(thm)],[c_12836,c_118]) ).
tcf(c_13402,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13397,c_57,c_11735,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM548+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 % Computer : n011.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Thu Sep 24 04:34:13 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 0.13/0.45
% 0.13/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.45
% 0.13/0.45 % Detected problem language: tptp
% 0.19/0.46 % Proving...
% 3.79/1.23 % SZS status Started for theBenchmark.p
% 3.79/1.23 % SZS status Theorem for theBenchmark.p
% 3.79/1.23
% 3.79/1.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.79/1.23
% 3.79/1.23 % ------ iProver source info
% 3.79/1.23
% 3.79/1.23 % git: date: 2026-07-19 20:42:38 +0200
% 3.79/1.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.79/1.23 % git: non_committed_changes: false
% 3.79/1.23
% 3.79/1.23 % ------ Parsing...
% 3.79/1.23 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.79/1.23
% 3.79/1.23 % ------ 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 %
% 3.79/1.23
% 3.79/1.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.79/1.23
% 3.79/1.23 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.79/1.23 % ------ Proving...
% 3.79/1.23 % ------ Problem Properties
% 3.79/1.23
% 3.79/1.23 %
% 3.79/1.23 % clauses 107
% 3.79/1.23 % conjectures 1
% 3.79/1.23 % EPR 35
% 3.79/1.23 % Horn 86
% 3.79/1.23 % unary 18
% 3.79/1.23 % binary 16
% 3.79/1.23 % lits 340
% 3.79/1.23 % lits eq 42
% 3.79/1.23 % fd_pure 0
% 3.79/1.23 % fd_pseudo 0
% 3.79/1.23 % fd_cond 4
% 3.79/1.23 % fd_pseudo_cond 14
% 3.79/1.23 % AC symbols 0
% 3.79/1.23
% 3.79/1.23 % ------ Schedule dynamic 5 is on
% 3.79/1.23
% 3.79/1.23 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.79/1.23
% 3.79/1.23
% 3.79/1.23 % ------
% 3.79/1.23 % Current options:
% 3.79/1.23 % ------
% 3.79/1.23
% 3.79/1.23
% 3.79/1.23 %
% 3.79/1.23
% 3.79/1.23 % ------ Proving...
% 3.79/1.23 %
% 3.79/1.23
% 3.79/1.23 % SZS status Theorem for theBenchmark.p
% 3.79/1.23
% 3.79/1.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.79/1.23
% 3.79/1.23
%------------------------------------------------------------------------------