%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM410+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 : n018.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 1.31s 1.28s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 14 unt; 0 def)
% Number of atoms : 111 ( 3 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 134 ( 59 ~; 47 |; 16 &)
% ( 6 <=>; 6 =>; 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 : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 30 ( 1 sgn 28 !; 2 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_ordinal1) ).
fof(f9,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(f36,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f40,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ordinal(relation_dom(X0))
=> transfinite_sequence_of(X0,relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_ordinal1) ).
fof(f41,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ordinal(relation_dom(X0))
=> transfinite_sequence_of(X0,relation_rng(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f47,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f36]) ).
fof(f67,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f68,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) ) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f70,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
inference(flattening,[],[f69]) ).
fof(f81,plain,
? [X0] :
( function(X0)
& relation(X0)
& ordinal(relation_dom(X0))
& ~ transfinite_sequence_of(X0,relation_rng(X0)) ),
inference(ennf_transformation,[],[f41]) ).
fof(f82,plain,
? [X0] :
( function(X0)
& relation(X0)
& ordinal(relation_dom(X0))
& ~ transfinite_sequence_of(X0,relation_rng(X0)) ),
inference(flattening,[],[f81]) ).
fof(f89,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ transfinite_sequence(X0)
| ordinal(relation_dom(X0)) )
& ( ~ ordinal(relation_dom(X0))
| transfinite_sequence(X0) ) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f90,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,[],[f70]) ).
fof(f108,plain,
( function(sK16)
& relation(sK16)
& ordinal(relation_dom(sK16))
& ~ transfinite_sequence_of(sK16,relation_rng(sK16)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f82]) ).
fof(f121,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ ordinal(relation_dom(X0))
| transfinite_sequence(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f123,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_rng(X1),X0)
| transfinite_sequence_of(X1,X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f180,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f47]) ).
fof(f185,plain,
function(sK16),
inference(cnf_transformation,[],[f108]) ).
fof(f186,plain,
relation(sK16),
inference(cnf_transformation,[],[f108]) ).
fof(f187,plain,
ordinal(relation_dom(sK16)),
inference(cnf_transformation,[],[f108]) ).
fof(f188,plain,
~ transfinite_sequence_of(sK16,relation_rng(sK16)),
inference(cnf_transformation,[],[f108]) ).
tcf(c_58,plain,
! [X0: $i] :
( transfinite_sequence(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ ordinal(relation_dom(X0)) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_60,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,[],[f123]) ).
tcf(c_118,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f180]) ).
tcf(c_123,negated_conjecture,
~ transfinite_sequence_of(sK16,relation_rng(sK16)),
inference(cnf_transformation,[],[f188]) ).
tcf(c_124,negated_conjecture,
ordinal(relation_dom(sK16)),
inference(cnf_transformation,[],[f187]) ).
tcf(c_125,negated_conjecture,
relation(sK16),
inference(cnf_transformation,[],[f186]) ).
tcf(c_126,negated_conjecture,
function(sK16),
inference(cnf_transformation,[],[f185]) ).
tcf(c_1006,plain,
! [X0: $i,X1: $i] :
( ~ transfinite_sequence(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ subset(relation_rng(X0),X1)
| ( X0 != sK16 )
| ( relation_rng(sK16) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_123]) ).
tcf(c_1007,plain,
( ~ transfinite_sequence(sK16)
| ~ relation(sK16)
| ~ function(sK16)
| ~ subset(relation_rng(sK16),relation_rng(sK16)) ),
inference(unflattening,[status(thm)],[c_1006]) ).
tcf(c_1008,plain,
( ~ transfinite_sequence(sK16)
| ~ subset(relation_rng(sK16),relation_rng(sK16)) ),
inference(global_subsumption_just,[status(thm)],[c_1007,c_126,c_125,c_1007]) ).
tcf(c_1014,plain,
~ transfinite_sequence(sK16),
inference(forward_subsumption_resolution,[status(thm)],[c_1008,c_118]) ).
tcf(c_1045,plain,
! [X0: $i] :
( ~ relation(X0)
| ~ function(X0)
| ~ ordinal(relation_dom(X0))
| ( X0 != sK16 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_1014]) ).
tcf(c_1046,plain,
( ~ relation(sK16)
| ~ function(sK16)
| ~ ordinal(relation_dom(sK16)) ),
inference(unflattening,[status(thm)],[c_1045]) ).
tcf(c_1047,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1046,c_124,c_125,c_126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM410+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 : n018.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 03:53:48 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...
% 1.31/1.28 % SZS status Started for theBenchmark.p
% 1.31/1.28 % SZS status Theorem for theBenchmark.p
% 1.31/1.28
% 1.31/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.31/1.28
% 1.31/1.28 % ------ iProver source info
% 1.31/1.28
% 1.31/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.31/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.31/1.28 % git: non_committed_changes: false
% 1.31/1.28
% 1.31/1.28 % ------ Parsing...
% 1.31/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.31/1.28
% 1.31/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s%
% 1.31/1.28
% 1.31/1.28 % SZS status Theorem for theBenchmark.p
% 1.31/1.28
% 1.31/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.31/1.28
% 1.31/1.28
%------------------------------------------------------------------------------