%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM412+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 : n010.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 02:24:11 PM UTC 2026
% Result : Theorem 3.39s 1.28s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 13 unt; 1 def)
% Number of atoms : 152 ( 2 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 168 ( 74 ~; 68 |; 14 &)
% ( 3 <=>; 9 =>; 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 : 9 ( 7 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 78 !; 3 ?; 35 :)
% 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/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(f9,axiom,
! [X0,X1] :
( ( ordinal(X1)
& transfinite_sequence(X0)
& function(X0)
& relation(X0) )
=> transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_ordinal1) ).
fof(f11,axiom,
! [X0,X1] :
( transfinite_sequence_of(X1,X0)
=> ( transfinite_sequence(X1)
& function(X1)
& relation(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(f42,axiom,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( transfinite_sequence_of(X2,X0)
=> transfinite_sequence_of(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_ordinal1) ).
fof(f43,conjecture,
! [X0,X1] :
( transfinite_sequence_of(X1,X0)
=> ! [X2] :
( ordinal(X2)
=> transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_ordinal1) ).
fof(f44,negated_conjecture,
~ ! [X0,X1] :
( transfinite_sequence_of(X1,X0)
=> ! [X2] :
( ordinal(X2)
=> transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f66,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(f67,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0)
| transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f69,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0)
| transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0)) ),
inference(flattening,[],[f68]) ).
fof(f71,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| ( transfinite_sequence(X1)
& function(X1)
& relation(X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f84,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ! [X2] :
( ~ transfinite_sequence_of(X2,X0)
| transfinite_sequence_of(X2,X1) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f85,plain,
? [X0,X1] :
( transfinite_sequence_of(X1,X0)
& ? [X2] :
( ordinal(X2)
& ~ transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f92,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,[],[f67]) ).
fof(f110,plain,
( transfinite_sequence_of(sK17,sK16)
& ordinal(sK18)
& ~ transfinite_sequence_of(tseq_dom_restriction(sK17,sK18),sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18)],[f85]) ).
fof(f122,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ transfinite_sequence_of(X1,X0)
| subset(relation_rng(X1),X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f124,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0)
| transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f126,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| transfinite_sequence(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f127,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| function(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f128,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| relation(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f193,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ transfinite_sequence_of(X2,X0)
| transfinite_sequence_of(X2,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f194,plain,
transfinite_sequence_of(sK17,sK16),
inference(cnf_transformation,[],[f110]) ).
fof(f195,plain,
ordinal(sK18),
inference(cnf_transformation,[],[f110]) ).
fof(f196,plain,
~ transfinite_sequence_of(tseq_dom_restriction(sK17,sK18),sK16),
inference(cnf_transformation,[],[f110]) ).
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,[],[f122]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0))
| ~ transfinite_sequence(X0)
| ~ relation(X0)
| ~ ordinal(X1)
| ~ function(X0) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( relation(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( function(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( transfinite_sequence(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i] :
( transfinite_sequence_of(X0,X2)
| ~ subset(X1,X2)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_130,negated_conjecture,
~ transfinite_sequence_of(tseq_dom_restriction(sK17,sK18),sK16),
inference(cnf_transformation,[],[f196]) ).
tcf(c_131,negated_conjecture,
ordinal(sK18),
inference(cnf_transformation,[],[f195]) ).
tcf(c_132,negated_conjecture,
transfinite_sequence_of(sK17,sK16),
inference(cnf_transformation,[],[f194]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(X0),X1)
| ~ transfinite_sequence_of(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_59,c_64,c_63,c_62,c_59]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i] :
( transfinite_sequence(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_64]) ).
tcf(c_895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( transfinite_sequence_of(tseq_dom_restriction(X1,X3),relation_rng(X1))
| ~ relation(X1)
| ~ ordinal(X3)
| ~ function(X1)
| ~ transfinite_sequence_of(X0,X2)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_217,c_60]) ).
tcf(c_896,plain,
! [X0: $i,X1: $i,X2: $i] :
( transfinite_sequence_of(tseq_dom_restriction(X0,X2),relation_rng(X0))
| ~ relation(X0)
| ~ ordinal(X2)
| ~ function(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(unflattening,[status(thm)],[c_895]) ).
tcf(c_898,plain,
! [X0: $i,X1: $i,X2: $i] :
( transfinite_sequence_of(tseq_dom_restriction(X0,X2),relation_rng(X0))
| ~ transfinite_sequence_of(X0,X1)
| ~ ordinal(X2) ),
inference(global_subsumption_just,[status(thm)],[c_896,c_63,c_62,c_896]) ).
tcf(c_899,plain,
! [X0: $i,X1: $i,X2: $i] :
( transfinite_sequence_of(tseq_dom_restriction(X0,X2),relation_rng(X0))
| ~ ordinal(X2)
| ~ transfinite_sequence_of(X0,X1) ),
inference(renaming,[status(thm)],[c_898]) ).
tcf(c_2392,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(X0),X1)
| ~ transfinite_sequence_of(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_162]) ).
tcf(c_3266,definition,
iPr_def_10 = tseq_dom_restriction(sK17,sK18),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3267,negated_conjecture,
transfinite_sequence_of(sK17,sK16),
inference(demodulation,[status(thm)],[c_132]) ).
tcf(c_3268,negated_conjecture,
ordinal(sK18),
inference(demodulation,[status(thm)],[c_131]) ).
tcf(c_3269,negated_conjecture,
~ transfinite_sequence_of(iPr_def_10,sK16),
inference(demodulation,[status(thm)],[c_130,c_3266]) ).
tcf(c_4082,plain,
! [X0: $i] :
( transfinite_sequence_of(tseq_dom_restriction(sK17,X0),relation_rng(sK17))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_3267,c_899]) ).
tcf(c_4377,plain,
( transfinite_sequence_of(iPr_def_10,relation_rng(sK17))
| ~ ordinal(sK18) ),
inference(superposition,[status(thm)],[c_3266,c_4082]) ).
tcf(c_4378,plain,
transfinite_sequence_of(iPr_def_10,relation_rng(sK17)),
inference(forward_subsumption_resolution,[status(thm)],[c_4377,c_3268]) ).
tcf(c_5370,plain,
! [X0: $i] :
( transfinite_sequence_of(iPr_def_10,X0)
| ~ subset(relation_rng(sK17),X0) ),
inference(superposition,[status(thm)],[c_4378,c_129]) ).
tcf(c_5786,plain,
! [X0: $i] :
( transfinite_sequence_of(iPr_def_10,X0)
| ~ transfinite_sequence_of(sK17,X0) ),
inference(superposition,[status(thm)],[c_2392,c_5370]) ).
tcf(c_5891,plain,
transfinite_sequence_of(iPr_def_10,sK16),
inference(superposition,[status(thm)],[c_3267,c_5786]) ).
tcf(c_5892,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5891,c_3269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM412+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 03:52:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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...
% 3.39/1.28 % SZS status Started for theBenchmark.p
% 3.39/1.28 % SZS status Theorem for theBenchmark.p
% 3.39/1.28
% 3.39/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.39/1.28
% 3.39/1.28 % ------ iProver source info
% 3.39/1.28
% 3.39/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.39/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.39/1.28 % git: non_committed_changes: false
% 3.39/1.28
% 3.39/1.28 % ------ Parsing...
% 3.39/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.39/1.28
% 3.39/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 17 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e %
% 3.39/1.28
% 3.39/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.39/1.28
% 3.39/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.39/1.28 % ------ Proving...
% 3.39/1.28 % ------ Problem Properties
% 3.39/1.28
% 3.39/1.28 %
% 3.39/1.28 % clauses 55
% 3.39/1.28 % conjectures 3
% 3.39/1.28 % EPR 39
% 3.39/1.28 % Horn 54
% 3.39/1.28 % unary 30
% 3.39/1.28 % binary 16
% 3.39/1.28 % lits 89
% 3.39/1.28 % lits eq 5
% 3.39/1.28 % fd_pure 0
% 3.39/1.28 % fd_pseudo 0
% 3.39/1.28 % fd_cond 1
% 3.39/1.28 % fd_pseudo_cond 1
% 3.39/1.28 % AC symbols 0
% 3.39/1.28
% 3.39/1.28 % ------ Schedule dynamic 5 is on
% 3.39/1.28
% 3.39/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.39/1.28
% 3.39/1.28
% 3.39/1.28 % ------
% 3.39/1.28 % Current options:
% 3.39/1.28 % ------
% 3.39/1.28
% 3.39/1.28
% 3.39/1.28 %
% 3.39/1.28
% 3.39/1.28 % ------ Proving...
% 3.39/1.28 %
% 3.39/1.28
% 3.39/1.28 % SZS status Theorem for theBenchmark.p
% 3.39/1.28
% 3.39/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.39/1.29
% 3.39/1.29
%------------------------------------------------------------------------------