%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU169+1 : TPTP v9.3.1. Released v3.3.0.
% 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 02:55:44 PM UTC 2026
% Result : Theorem 2.28s 1.28s
% Output : CNFRefutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 17 unt; 1 def)
% Number of atoms : 140 ( 11 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 148 ( 55 ~; 54 |; 24 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 63 !; 7 ?; 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] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f11,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( element(X1,X0)
<=> empty(X1) ) )
& ( empty(X0)
| ( element(X1,X0)
<=> in(X1,X0) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f24,plain,
? [X0,X1] :
( element(X1,powerset(X0))
& ? [X2] :
( in(X2,X1)
& ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f29,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(f30,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,[],[f29]) ).
fof(f31,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))],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( ( ~ element(X1,X0)
| empty(X1) )
& ( ~ empty(X1)
| element(X1,X0) ) ) )
& ( empty(X0)
| ( ( ~ element(X1,X0)
| in(X1,X0) )
& ( ~ in(X1,X0)
| element(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f33,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,[],[f23]) ).
fof(f34,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,[],[f33]) ).
fof(f35,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))],[f34]) ).
fof(f37,plain,
( element(sK4,powerset(sK3))
& in(sK5,sK4)
& ~ in(sK5,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f24]) ).
fof(f42,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f48,plain,
! [X0,X1] :
( empty(X0)
| ~ element(X1,X0)
| in(X1,X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f50,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f56,plain,
element(sK4,powerset(sK3)),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
in(sK5,sK4),
inference(cnf_transformation,[],[f37]) ).
fof(f58,plain,
~ in(sK5,sK3),
inference(cnf_transformation,[],[f37]) ).
fof(f68,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f42]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_62,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f54]) ).
tcf(c_64,negated_conjecture,
~ in(sK5,sK3),
inference(cnf_transformation,[],[f58]) ).
tcf(c_65,negated_conjecture,
in(sK5,sK4),
inference(cnf_transformation,[],[f57]) ).
tcf(c_66,negated_conjecture,
element(sK4,powerset(sK3)),
inference(cnf_transformation,[],[f56]) ).
tcf(c_375,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ( X0 != sK4 )
| ( powerset(sK3) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_66]) ).
tcf(c_376,plain,
( empty(powerset(sK3))
| in(sK4,powerset(sK3)) ),
inference(unflattening,[status(thm)],[c_375]) ).
tcf(c_381,plain,
in(sK4,powerset(sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_376,c_62]) ).
tcf(c_1006,definition,
iPr_def_10 = powerset(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1007,plain,
in(sK4,iPr_def_10),
inference(demodulation,[status(thm)],[c_381,c_1006]) ).
tcf(c_1008,negated_conjecture,
in(sK5,sK4),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_1009,negated_conjecture,
~ in(sK5,sK3),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_1529,plain,
! [X0: $i] :
( subset(X0,sK3)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1006,c_53]) ).
tcf(c_1623,plain,
subset(sK4,sK3),
inference(superposition,[status(thm)],[c_1007,c_1529]) ).
tcf(c_1688,plain,
! [X0: $i] :
( in(sK5,X0)
| ~ subset(sK4,X0) ),
inference(superposition,[status(thm)],[c_1008,c_60]) ).
tcf(c_1751,plain,
in(sK5,sK3),
inference(superposition,[status(thm)],[c_1623,c_1688]) ).
tcf(c_1752,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1751,c_1009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU169+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:59:53 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.28/1.28 % SZS status Started for theBenchmark.p
% 2.28/1.28 % SZS status Theorem for theBenchmark.p
% 2.28/1.28
% 2.28/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.28/1.28
% 2.28/1.28 % ------ iProver source info
% 2.28/1.28
% 2.28/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.28/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.28/1.28 % git: non_committed_changes: false
% 2.28/1.28
% 2.28/1.28 % ------ Parsing...
% 2.28/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.28/1.28
% 2.28/1.28 % ------ 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 %
% 2.28/1.28
% 2.28/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.28/1.28
% 2.28/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.28/1.28 % ------ Proving...
% 2.28/1.28 % ------ Problem Properties
% 2.28/1.28
% 2.28/1.28 %
% 2.28/1.28 % clauses 24
% 2.28/1.28 % conjectures 2
% 2.28/1.28 % EPR 12
% 2.28/1.28 % Horn 20
% 2.28/1.28 % unary 9
% 2.28/1.28 % binary 11
% 2.28/1.28 % lits 43
% 2.28/1.28 % lits eq 5
% 2.28/1.28 % fd_pure 0
% 2.28/1.28 % fd_pseudo 0
% 2.28/1.28 % fd_cond 1
% 2.28/1.28 % fd_pseudo_cond 3
% 2.28/1.28 % AC symbols 0
% 2.28/1.28
% 2.28/1.28 % ------ Schedule dynamic 5 is on
% 2.28/1.28
% 2.28/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.28/1.28
% 2.28/1.28
% 2.28/1.28 % ------
% 2.28/1.28 % Current options:
% 2.28/1.28 % ------
% 2.28/1.28
% 2.28/1.28
% 2.28/1.28 %
% 2.28/1.28
% 2.28/1.28 % ------ Proving...
% 2.28/1.28 %
% 2.28/1.28
% 2.28/1.28 % SZS status Theorem for theBenchmark.p
% 2.28/1.28
% 2.28/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.28/1.28
% 2.28/1.28
%------------------------------------------------------------------------------