%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM411+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 : n009.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 02:24:10 PM UTC 2026
% Result : Theorem 2.24s 1.28s
% Output : CNFRefutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 15 unt; 0 def)
% Number of atoms : 139 ( 1 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 156 ( 70 ~; 64 |; 12 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 87 ( 1 sgn 84 !; 3 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1] :
( ( transfinite_sequence(X1)
& function(X1)
& relation(X1) )
=> ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(f9,axiom,
! [X0,X1] :
( transfinite_sequence_of(X1,X0)
=> ( transfinite_sequence(X1)
& function(X1)
& relation(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(f33,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f35,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f38,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( transfinite_sequence_of(X2,X0)
=> transfinite_sequence_of(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_ordinal1) ).
fof(f39,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( transfinite_sequence_of(X2,X0)
=> transfinite_sequence_of(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f45,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f33]) ).
fof(f65,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f66,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| ( transfinite_sequence(X1)
& function(X1)
& relation(X1) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f35]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f72]) ).
fof(f76,plain,
? [X0,X1] :
( subset(X0,X1)
& ? [X2] :
( transfinite_sequence_of(X2,X0)
& ~ transfinite_sequence_of(X2,X1) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f83,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ( ( ~ transfinite_sequence_of(X1,X0)
| subset(relation_rng(X1),X0) )
& ( ~ subset(relation_rng(X1),X0)
| transfinite_sequence_of(X1,X0) ) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f101,plain,
( subset(sK16,sK17)
& transfinite_sequence_of(sK18,sK16)
& ~ transfinite_sequence_of(sK18,sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18)],[f76]) ).
fof(f113,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ transfinite_sequence_of(X1,X0)
| subset(relation_rng(X1),X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f114,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_rng(X1),X0)
| transfinite_sequence_of(X1,X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f115,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| transfinite_sequence(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f116,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| function(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f117,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| relation(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f168,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f45]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f174,plain,
subset(sK16,sK17),
inference(cnf_transformation,[],[f101]) ).
fof(f175,plain,
transfinite_sequence_of(sK18,sK16),
inference(cnf_transformation,[],[f101]) ).
fof(f176,plain,
~ transfinite_sequence_of(sK18,sK17),
inference(cnf_transformation,[],[f101]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( transfinite_sequence_of(X0,X1)
| ~ transfinite_sequence(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ subset(relation_rng(X0),X1) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(X0),X1)
| ~ transfinite_sequence(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( relation(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( function(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( transfinite_sequence(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_113,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f168]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_119,negated_conjecture,
~ transfinite_sequence_of(sK18,sK17),
inference(cnf_transformation,[],[f176]) ).
tcf(c_120,negated_conjecture,
transfinite_sequence_of(sK18,sK16),
inference(cnf_transformation,[],[f175]) ).
tcf(c_121,negated_conjecture,
subset(sK16,sK17),
inference(cnf_transformation,[],[f174]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(X0),X1)
| ~ transfinite_sequence_of(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_59,c_62,c_61,c_60,c_59]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i] :
( function(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( relation(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i] :
( transfinite_sequence(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_62]) ).
tcf(c_662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( transfinite_sequence_of(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence_of(X0,X3)
| ~ subset(relation_rng(X1),X2)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_193,c_58]) ).
tcf(c_663,plain,
! [X0: $i,X1: $i,X2: $i] :
( transfinite_sequence_of(X0,X1)
| ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence_of(X0,X2)
| ~ subset(relation_rng(X0),X1) ),
inference(unflattening,[status(thm)],[c_662]) ).
tcf(c_674,plain,
! [X0: $i,X1: $i,X2: $i] :
( transfinite_sequence_of(X0,X1)
| ~ transfinite_sequence_of(X0,X2)
| ~ subset(relation_rng(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_663,c_189,c_187]) ).
tcf(c_895,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(X0),X1)
| ~ transfinite_sequence_of(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_140]) ).
tcf(c_1317,negated_conjecture,
subset(sK16,sK17),
inference(demodulation,[status(thm)],[c_121]) ).
tcf(c_1318,negated_conjecture,
transfinite_sequence_of(sK18,sK16),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_1319,negated_conjecture,
~ transfinite_sequence_of(sK18,sK17),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_1943,plain,
! [X0: $i,X1: $i] :
( transfinite_sequence_of(X0,relation_rng(X0))
| ~ transfinite_sequence_of(X0,X1) ),
inference(superposition,[status(thm)],[c_113,c_674]) ).
tcf(c_2008,plain,
transfinite_sequence_of(sK18,relation_rng(sK18)),
inference(superposition,[status(thm)],[c_1318,c_1943]) ).
tcf(c_2095,plain,
! [X0: $i] :
( subset(X0,sK17)
| ~ subset(X0,sK16) ),
inference(superposition,[status(thm)],[c_1317,c_115]) ).
tcf(c_2118,plain,
! [X0: $i] :
( subset(relation_rng(X0),sK17)
| ~ transfinite_sequence_of(X0,sK16) ),
inference(superposition,[status(thm)],[c_895,c_2095]) ).
tcf(c_2137,plain,
! [X0: $i,X1: $i] :
( transfinite_sequence_of(X0,sK17)
| ~ transfinite_sequence_of(X0,sK16)
| ~ transfinite_sequence_of(X0,X1) ),
inference(superposition,[status(thm)],[c_2118,c_674]) ).
tcf(c_2179,plain,
( transfinite_sequence_of(sK18,sK17)
| ~ transfinite_sequence_of(sK18,sK16) ),
inference(superposition,[status(thm)],[c_2008,c_2137]) ).
tcf(c_2181,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2179,c_1319,c_1318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM411+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 03:51:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 2.24/1.28 % SZS status Started for theBenchmark.p
% 2.24/1.28 % SZS status Theorem for theBenchmark.p
% 2.24/1.28
% 2.24/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.24/1.28
% 2.24/1.28 % ------ iProver source info
% 2.24/1.28
% 2.24/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.24/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.24/1.28 % git: non_committed_changes: false
% 2.24/1.28
% 2.24/1.28 % ------ Parsing...
% 2.24/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.24/1.28
% 2.24/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 22 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe_e %
% 2.24/1.28
% 2.24/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.24/1.28
% 2.24/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.24/1.28 % ------ Proving...
% 2.24/1.28 % ------ Problem Properties
% 2.24/1.28
% 2.24/1.28 %
% 2.24/1.28 % clauses 37
% 2.24/1.28 % conjectures 3
% 2.24/1.28 % EPR 21
% 2.24/1.28 % Horn 36
% 2.24/1.28 % unary 15
% 2.24/1.28 % binary 15
% 2.24/1.28 % lits 66
% 2.24/1.28 % lits eq 2
% 2.24/1.28 % fd_pure 0
% 2.24/1.28 % fd_pseudo 0
% 2.24/1.28 % fd_cond 1
% 2.24/1.28 % fd_pseudo_cond 1
% 2.24/1.28 % AC symbols 0
% 2.24/1.28
% 2.24/1.28 % ------ Schedule dynamic 5 is on
% 2.24/1.28
% 2.24/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.24/1.28
% 2.24/1.28
% 2.24/1.28 % ------
% 2.24/1.28 % Current options:
% 2.24/1.28 % ------
% 2.24/1.28
% 2.24/1.28
% 2.24/1.28 %
% 2.24/1.28
% 2.24/1.28 % ------ Proving...
% 2.24/1.28 %
% 2.24/1.28
% 2.24/1.28 % SZS status Theorem for theBenchmark.p
% 2.24/1.28
% 2.24/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.24/1.28
% 2.24/1.28
%------------------------------------------------------------------------------