%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM414+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 02:24:11 PM UTC 2026
% Result : Theorem 2.30s 1.28s
% Output : CNFRefutation 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 16 unt; 0 def)
% Number of atoms : 127 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 149 ( 65 ~; 52 |; 21 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 50 ( 0 sgn 46 !; 4 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f10,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f31,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f38,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ proper_subset(X1,X0)
& X0 != X1
& ~ proper_subset(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_ordinal1) ).
fof(f39,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ proper_subset(X1,X0)
& X0 != X1
& ~ proper_subset(X0,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f46,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f67,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f68,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f70,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f72,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(flattening,[],[f71]) ).
fof(f80,plain,
? [X0] :
( ordinal(X0)
& ? [X1] :
( ordinal(X1)
& ~ proper_subset(X1,X0)
& X0 != X1
& ~ proper_subset(X0,X1) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f81,plain,
? [X0] :
( ordinal(X0)
& ? [X1] :
( ordinal(X1)
& ~ proper_subset(X1,X0)
& X0 != X1
& ~ proper_subset(X0,X1) ) ),
inference(flattening,[],[f80]) ).
fof(f101,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ( ~ ordinal_subset(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| ordinal_subset(X0,X1) ) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f103,plain,
( ordinal(sK15)
& ordinal(sK16)
& ~ proper_subset(sK16,sK15)
& sK15 != sK16
& ~ proper_subset(sK15,sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X0,sK15),skolemize(X1,sK16)],[f81]) ).
fof(f116,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f117,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f164,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f173,plain,
ordinal(sK15),
inference(cnf_transformation,[],[f103]) ).
fof(f174,plain,
ordinal(sK16),
inference(cnf_transformation,[],[f103]) ).
fof(f175,plain,
~ proper_subset(sK16,sK15),
inference(cnf_transformation,[],[f103]) ).
fof(f176,plain,
sK15 != sK16,
inference(cnf_transformation,[],[f103]) ).
fof(f177,plain,
~ proper_subset(sK15,sK16),
inference(cnf_transformation,[],[f103]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,X1)
| ( X0 = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_116,negated_conjecture,
~ proper_subset(sK15,sK16),
inference(cnf_transformation,[],[f177]) ).
tcf(c_117,negated_conjecture,
sK15 != sK16,
inference(cnf_transformation,[],[f176]) ).
tcf(c_118,negated_conjecture,
~ proper_subset(sK16,sK15),
inference(cnf_transformation,[],[f175]) ).
tcf(c_119,negated_conjecture,
ordinal(sK16),
inference(cnf_transformation,[],[f174]) ).
tcf(c_120,negated_conjecture,
ordinal(sK15),
inference(cnf_transformation,[],[f173]) ).
tcf(c_1446,negated_conjecture,
ordinal(sK15),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_1447,negated_conjecture,
ordinal(sK16),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_1448,negated_conjecture,
~ proper_subset(sK16,sK15),
inference(demodulation,[status(thm)],[c_118]) ).
tcf(c_1449,negated_conjecture,
sK15 != sK16,
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_1450,negated_conjecture,
~ proper_subset(sK15,sK16),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_2113,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_59,c_108]) ).
tcf(c_2281,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_2113,c_108]) ).
tcf(c_2430,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| proper_subset(X1,X0)
| ( X0 = X1 )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_2281,c_60]) ).
tcf(c_2543,plain,
! [X0: $i,X1: $i] :
( proper_subset(X1,X0)
| proper_subset(X0,X1)
| ( X0 = X1 )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_2430,c_60]) ).
tcf(c_2655,plain,
( proper_subset(sK15,sK16)
| ( sK15 = sK16 )
| ~ ordinal(sK16)
| ~ ordinal(sK15) ),
inference(superposition,[status(thm)],[c_2543,c_1448]) ).
tcf(c_2659,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2655,c_1450,c_1449,c_1447,c_1446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM414+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.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 03:52:14 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 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...
% 2.30/1.28 % SZS status Started for theBenchmark.p
% 2.30/1.28 % SZS status Theorem for theBenchmark.p
% 2.30/1.28
% 2.30/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.30/1.28
% 2.30/1.28 % ------ iProver source info
% 2.30/1.28
% 2.30/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.30/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.30/1.28 % git: non_committed_changes: false
% 2.30/1.28
% 2.30/1.28 % ------ Parsing...
% 2.30/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.30/1.28
% 2.30/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 24 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 %
% 2.30/1.28
% 2.30/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.30/1.28
% 2.30/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.30/1.28 % ------ Proving...
% 2.30/1.28 % ------ Problem Properties
% 2.30/1.28
% 2.30/1.28 %
% 2.30/1.28 % clauses 37
% 2.30/1.28 % conjectures 5
% 2.30/1.28 % EPR 34
% 2.30/1.28 % Horn 34
% 2.30/1.28 % unary 20
% 2.30/1.28 % binary 9
% 2.30/1.28 % lits 65
% 2.30/1.28 % lits eq 4
% 2.30/1.28 % fd_pure 0
% 2.30/1.28 % fd_pseudo 0
% 2.30/1.28 % fd_cond 1
% 2.30/1.28 % fd_pseudo_cond 2
% 2.30/1.28 % AC symbols 0
% 2.30/1.28
% 2.30/1.28 % ------ Schedule dynamic 5 is on
% 2.30/1.28
% 2.30/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.30/1.28
% 2.30/1.28
% 2.30/1.28 % ------
% 2.30/1.28 % Current options:
% 2.30/1.28 % ------
% 2.30/1.28
% 2.30/1.28
% 2.30/1.28 %
% 2.30/1.28
% 2.30/1.28 % ------ Proving...
% 2.30/1.28 %
% 2.30/1.28
% 2.30/1.28 % SZS status Theorem for theBenchmark.p
% 2.30/1.28
% 2.30/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.30/1.28
% 2.30/1.28
%------------------------------------------------------------------------------