%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET947+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 02:49:10 PM UTC 2026
% Result : Theorem 3.10s 1.53s
% Output : CNFRefutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 11 unt; 2 def)
% Number of atoms : 109 ( 10 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 106 ( 42 ~; 43 |; 15 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 56 !; 5 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(f8,conjecture,
! [X0] : subset(X0,powerset(union(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0] : subset(X0,powerset(union(X0))),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f13,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f14,plain,
? [X0] : ~ subset(X0,powerset(union(X0))),
inference(ennf_transformation,[],[f9]) ).
fof(f15,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| subset(X2,X0) )
& ( ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| subset(sK0(X0,X1),X0) )
& ( ~ in(sK0(X0,X1),X1)
| ~ subset(sK0(X0,X1),X0) ) )
| X1 = powerset(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK1(X0,X1),X0)
& ~ in(sK1(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f19]) ).
fof(f23,plain,
~ subset(sK4,powerset(union(sK4))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f14]) ).
fof(f26,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f36,plain,
~ subset(sK4,powerset(union(sK4))),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f26]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_61,negated_conjecture,
~ subset(sK4,powerset(union(sK4))),
inference(cnf_transformation,[],[f36]) ).
tcf(c_896,definition,
iPr_def_10 = union(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_897,definition,
iPr_def_11 = powerset(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_898,negated_conjecture,
~ subset(sK4,iPr_def_11),
inference(demodulation,[status(thm)],[c_61,c_896,c_897]) ).
tcf(c_1209,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ subset(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_897,c_52]) ).
tcf(c_1257,plain,
! [X0: $i] :
( subset(X0,iPr_def_10)
| ~ in(X0,sK4) ),
inference(superposition,[status(thm)],[c_896,c_57]) ).
tcf(c_1283,plain,
! [X0: $i] :
( subset(sK4,X0)
| subset(sK1(sK4,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_55,c_1257]) ).
tcf(c_1298,plain,
! [X0: $i] :
( subset(sK4,X0)
| in(sK1(sK4,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_1283,c_1209]) ).
tcf(c_1306,plain,
subset(sK4,iPr_def_11),
inference(superposition,[status(thm)],[c_1298,c_54]) ).
tcf(c_1308,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1306,c_898]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET947+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.46 % Computer : n007.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Thu Sep 24 12:23:23 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.22/0.52 Running first-order theorem proving
% 0.22/0.52 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
% 0.22/0.54
% 0.22/0.54 % ======== iProver multi-core TPTP/SMT =========
% 0.22/0.54
% 0.22/0.54 % Detected problem language: tptp
% 0.22/0.55 % Proving...
% 3.10/1.53 % SZS status Started for theBenchmark.p
% 3.10/1.53 % SZS status Theorem for theBenchmark.p
% 3.10/1.53
% 3.10/1.53 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.10/1.53
% 3.10/1.53 % ------ iProver source info
% 3.10/1.53
% 3.10/1.53 % git: date: 2026-07-19 20:42:38 +0200
% 3.10/1.53 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.10/1.53 % git: non_committed_changes: false
% 3.10/1.53
% 3.10/1.53 % ------ Parsing...
% 3.10/1.53 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.10/1.53
% 3.10/1.53 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.10/1.53
% 3.10/1.53 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.10/1.53
% 3.10/1.53 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.10/1.53 % ------ Proving...
% 3.10/1.53 % ------ Problem Properties
% 3.10/1.53
% 3.10/1.53 %
% 3.10/1.53 % clauses 14
% 3.10/1.53 % conjectures 1
% 3.10/1.53 % EPR 5
% 3.10/1.53 % Horn 12
% 3.10/1.53 % unary 5
% 3.10/1.53 % binary 6
% 3.10/1.53 % lits 26
% 3.10/1.53 % lits eq 5
% 3.10/1.53 % fd_pure 0
% 3.10/1.53 % fd_pseudo 0
% 3.10/1.53 % fd_cond 0
% 3.10/1.53 % fd_pseudo_cond 2
% 3.10/1.53 % AC symbols 0
% 3.10/1.53
% 3.10/1.53 % ------ Schedule dynamic 5 is on
% 3.10/1.53
% 3.10/1.53 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.10/1.53
% 3.10/1.53
% 3.10/1.53 % ------
% 3.10/1.53 % Current options:
% 3.10/1.53 % ------
% 3.10/1.53
% 3.10/1.53
% 3.10/1.53 %
% 3.10/1.53
% 3.10/1.53 % ------ Proving...
% 3.10/1.53 %
% 3.10/1.53
% 3.10/1.53 % SZS status Theorem for theBenchmark.p
% 3.10/1.53
% 3.10/1.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.10/1.53
% 3.10/1.53
%------------------------------------------------------------------------------