%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM390+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n003.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 02:24:04 PM UTC 2026
% Result : Theorem 2.46s 1.17s
% Output : CNFRefutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 82 ( 23 unt; 0 def)
% Number of atoms : 215 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 214 ( 81 ~; 83 |; 30 &)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 107 ( 0 sgn 99 !; 8 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f9,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f29,axiom,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ( proper_subset(X0,X1)
=> in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(f30,conjecture,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ( in(X1,X2)
& subset(X0,X1) )
=> in(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_ordinal1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ( in(X1,X2)
& subset(X0,X1) )
=> in(X0,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f33,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f37,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f42,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f52,plain,
! [X0] :
( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f58,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f59,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f60,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(flattening,[],[f59]) ).
fof(f64,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f65,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
? [X0] :
( epsilon_transitive(X0)
& ? [X1] :
( ordinal(X1)
& ? [X2] :
( ordinal(X2)
& in(X1,X2)
& subset(X0,X1)
& ~ in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f67,plain,
? [X0] :
( epsilon_transitive(X0)
& ? [X1] :
( ordinal(X1)
& ? [X2] :
( ordinal(X2)
& in(X1,X2)
& subset(X0,X1)
& ~ in(X0,X2) ) ) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f69,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f70]) ).
fof(f74,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f78,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ( in(sK0(X0),X0)
& ~ subset(sK0(X0),X0) )
| epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f78]) ).
fof(f92,plain,
( epsilon_transitive(sK13)
& ordinal(sK14)
& ordinal(sK15)
& in(sK14,sK15)
& subset(sK13,sK14)
& ~ in(sK13,sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15)],[f67]) ).
fof(f93,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f98,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f103,plain,
! [X2,X0] :
( ~ epsilon_transitive(X0)
| ~ in(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f106,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f138,plain,
! [X0,X1] :
( ~ epsilon_transitive(X0)
| ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f139,plain,
epsilon_transitive(sK13),
inference(cnf_transformation,[],[f92]) ).
fof(f140,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f92]) ).
fof(f141,plain,
ordinal(sK15),
inference(cnf_transformation,[],[f92]) ).
fof(f142,plain,
in(sK14,sK15),
inference(cnf_transformation,[],[f92]) ).
fof(f143,plain,
subset(sK13,sK14),
inference(cnf_transformation,[],[f92]) ).
fof(f144,plain,
~ in(sK13,sK15),
inference(cnf_transformation,[],[f92]) ).
fof(f145,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f147,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f151,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_52,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,X1)
| ( X0 = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_92,negated_conjecture,
~ in(sK13,sK15),
inference(cnf_transformation,[],[f144]) ).
tcf(c_93,negated_conjecture,
subset(sK13,sK14),
inference(cnf_transformation,[],[f143]) ).
tcf(c_94,negated_conjecture,
in(sK14,sK15),
inference(cnf_transformation,[],[f142]) ).
tcf(c_95,negated_conjecture,
ordinal(sK15),
inference(cnf_transformation,[],[f141]) ).
tcf(c_96,negated_conjecture,
ordinal(sK14),
inference(cnf_transformation,[],[f140]) ).
tcf(c_97,negated_conjecture,
epsilon_transitive(sK13),
inference(cnf_transformation,[],[f139]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_99]) ).
tcf(c_149,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(prop_impl_just,[status(thm)],[c_52]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_101,c_125]) ).
tcf(c_571,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ~ epsilon_transitive(X1)
| ~ proper_subset(X1,X0)
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_91,c_96]) ).
tcf(c_572,plain,
! [X0: $i] :
( in(X0,sK14)
| ~ epsilon_transitive(X0)
| ~ proper_subset(X0,sK14) ),
inference(unflattening,[status(thm)],[c_571]) ).
tcf(c_585,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( X0 != sK15 ) ),
inference(resolution_lifted,[status(thm)],[c_149,c_95]) ).
tcf(c_586,plain,
epsilon_transitive(sK15),
inference(unflattening,[status(thm)],[c_585]) ).
tcf(c_1594,plain,
epsilon_transitive(sK15),
inference(demodulation,[status(thm)],[c_586]) ).
tcf(c_1595,plain,
! [X0: $i] :
( in(X0,sK14)
| ~ epsilon_transitive(X0)
| ~ proper_subset(X0,sK14) ),
inference(demodulation,[status(thm)],[c_572]) ).
tcf(c_1597,negated_conjecture,
epsilon_transitive(sK13),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_1598,negated_conjecture,
in(sK14,sK15),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_1599,negated_conjecture,
subset(sK13,sK14),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_1600,negated_conjecture,
~ in(sK13,sK15),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_2240,plain,
~ empty(sK15),
inference(superposition,[status(thm)],[c_1598,c_104]) ).
tcf(c_2322,plain,
( subset(sK14,sK15)
| ~ epsilon_transitive(sK15) ),
inference(superposition,[status(thm)],[c_1598,c_58]) ).
tcf(c_2323,plain,
subset(sK14,sK15),
inference(forward_subsumption_resolution,[status(thm)],[c_2322,c_1594]) ).
tcf(c_2338,plain,
( proper_subset(sK13,sK14)
| ( sK13 = sK14 ) ),
inference(superposition,[status(thm)],[c_1599,c_59]) ).
tcf(c_2383,plain,
( in(sK13,sK14)
| ( sK13 = sK14 )
| ~ epsilon_transitive(sK13) ),
inference(superposition,[status(thm)],[c_2338,c_1595]) ).
tcf(c_2386,plain,
( in(sK13,sK14)
| ( sK13 = sK14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2383,c_1597]) ).
tcf(c_2394,plain,
! [X0: $i] :
( element(sK13,X0)
| ( sK13 = sK14 )
| ~ subset(sK14,X0) ),
inference(superposition,[status(thm)],[c_2386,c_243]) ).
tcf(c_2439,plain,
( element(sK13,sK15)
| ( sK13 = sK14 ) ),
inference(superposition,[status(thm)],[c_2323,c_2394]) ).
tcf(c_2508,plain,
( empty(sK15)
| in(sK13,sK15)
| ( sK13 = sK14 ) ),
inference(superposition,[status(thm)],[c_2439,c_98]) ).
tcf(c_2509,plain,
sK13 = sK14,
inference(forward_subsumption_resolution,[status(thm)],[c_2508,c_2240,c_1600]) ).
tcf(c_2521,plain,
in(sK13,sK15),
inference(demodulation,[status(thm)],[c_1598,c_2509]) ).
tcf(c_2522,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2521,c_1600]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM390+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n003.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 03:51:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.46/1.17 % SZS status Started for theBenchmark.p
% 2.46/1.17 % SZS status Theorem for theBenchmark.p
% 2.46/1.17
% 2.46/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.46/1.17
% 2.46/1.17 % ------ iProver source info
% 2.46/1.17
% 2.46/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 2.46/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.46/1.17 % git: non_committed_changes: false
% 2.46/1.17
% 2.46/1.17 % ------ Parsing...
% 2.46/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.46/1.17
% 2.46/1.17 % ------ Preprocessing... sup_sim: 0 sf_s rm: 19 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 2.46/1.17
% 2.46/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.46/1.17
% 2.46/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.46/1.17 % ------ Proving...
% 2.46/1.17 % ------ Problem Properties
% 2.46/1.17
% 2.46/1.17 %
% 2.46/1.17 % clauses 36
% 2.46/1.17 % conjectures 4
% 2.46/1.17 % EPR 31
% 2.46/1.17 % Horn 33
% 2.46/1.17 % unary 16
% 2.46/1.17 % binary 10
% 2.46/1.17 % lits 66
% 2.46/1.17 % lits eq 3
% 2.46/1.17 % fd_pure 0
% 2.46/1.17 % fd_pseudo 0
% 2.46/1.17 % fd_cond 1
% 2.46/1.17 % fd_pseudo_cond 2
% 2.46/1.17 % AC symbols 0
% 2.46/1.17
% 2.46/1.17 % ------ Schedule dynamic 5 is on
% 2.46/1.17
% 2.46/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.46/1.17
% 2.46/1.17
% 2.46/1.17 % ------
% 2.46/1.17 % Current options:
% 2.46/1.17 % ------
% 2.46/1.17
% 2.46/1.17
% 2.46/1.17 %
% 2.46/1.17
% 2.46/1.17 % ------ Proving...
% 2.46/1.17 %
% 2.46/1.17
% 2.46/1.17 % SZS status Theorem for theBenchmark.p
% 2.46/1.17
% 2.46/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.46/1.17
% 2.46/1.17
%------------------------------------------------------------------------------