%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM394+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 : n017.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 2.48s 6.30s
% Output : CNFRefutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 18 unt; 0 def)
% Number of atoms : 167 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 183 ( 72 ~; 74 |; 22 &)
% ( 5 <=>; 10 =>; 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; 2 con; 0-1 aty)
% Number of variables : 60 ( 0 sgn 54 !; 6 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f7,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(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f24,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(f28,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f29,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
| ordinal_subset(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_ordinal1) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
| ordinal_subset(X0,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f47,plain,
! [X0] :
( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f53,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f54,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f56,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f57,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(flattening,[],[f56]) ).
fof(f61,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f62,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
? [X0] :
( ordinal(X0)
& ? [X1] :
( ordinal(X1)
& ~ in(X1,X0)
& ~ ordinal_subset(X0,X1) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f64,plain,
? [X0] :
( ordinal(X0)
& ? [X1] :
( ordinal(X1)
& ~ in(X1,X0)
& ~ ordinal_subset(X0,X1) ) ),
inference(flattening,[],[f63]) ).
fof(f73,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,[],[f55]) ).
fof(f74,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f73]) ).
fof(f75,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))],[f74]) ).
fof(f88,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ( ~ ordinal_subset(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| ordinal_subset(X0,X1) ) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f89,plain,
( ordinal(sK13)
& ordinal(sK14)
& ~ in(sK14,sK13)
& ~ ordinal_subset(sK13,sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f64]) ).
fof(f94,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f99,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f100,plain,
! [X2,X0] :
( ~ epsilon_transitive(X0)
| ~ in(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f131,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ~ subset(X0,X1)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f135,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f136,plain,
ordinal(sK13),
inference(cnf_transformation,[],[f89]) ).
fof(f137,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f89]) ).
fof(f138,plain,
~ in(sK14,sK13),
inference(cnf_transformation,[],[f89]) ).
fof(f139,plain,
~ ordinal_subset(sK13,sK14),
inference(cnf_transformation,[],[f89]) ).
tcf(c_51,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_92,negated_conjecture,
~ ordinal_subset(sK13,sK14),
inference(cnf_transformation,[],[f139]) ).
tcf(c_93,negated_conjecture,
~ in(sK14,sK13),
inference(cnf_transformation,[],[f138]) ).
tcf(c_94,negated_conjecture,
ordinal(sK14),
inference(cnf_transformation,[],[f137]) ).
tcf(c_95,negated_conjecture,
ordinal(sK13),
inference(cnf_transformation,[],[f136]) ).
tcf(c_1574,negated_conjecture,
ordinal(sK13),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_1575,negated_conjecture,
ordinal(sK14),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_1576,negated_conjecture,
~ in(sK14,sK13),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_1577,negated_conjecture,
~ ordinal_subset(sK13,sK14),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_2162,plain,
epsilon_transitive(sK14),
inference(superposition,[status(thm)],[c_1575,c_51]) ).
tcf(c_2316,plain,
( ordinal_subset(sK14,sK13)
| ~ ordinal(sK14)
| ~ ordinal(sK13) ),
inference(superposition,[status(thm)],[c_55,c_1577]) ).
tcf(c_2320,plain,
ordinal_subset(sK14,sK13),
inference(forward_subsumption_resolution,[status(thm)],[c_2316,c_1575,c_1574]) ).
tcf(c_2389,plain,
( in(sK13,sK14)
| ( sK13 = sK14 )
| ~ ordinal(sK14)
| ~ ordinal(sK13) ),
inference(superposition,[status(thm)],[c_91,c_1576]) ).
tcf(c_2394,plain,
( in(sK13,sK14)
| ( sK13 = sK14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2389,c_1575,c_1574]) ).
tcf(c_2432,plain,
( subset(sK13,sK14)
| ( sK13 = sK14 )
| ~ epsilon_transitive(sK14) ),
inference(superposition,[status(thm)],[c_2394,c_58]) ).
tcf(c_2440,plain,
( subset(sK13,sK14)
| ( sK13 = sK14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2432,c_2162]) ).
tcf(c_2460,plain,
( ordinal_subset(sK13,sK14)
| ( sK13 = sK14 )
| ~ ordinal(sK14)
| ~ ordinal(sK13) ),
inference(superposition,[status(thm)],[c_2440,c_86]) ).
tcf(c_2461,plain,
sK13 = sK14,
inference(forward_subsumption_resolution,[status(thm)],[c_2460,c_1577,c_1575,c_1574]) ).
tcf(c_2463,plain,
ordinal_subset(sK13,sK13),
inference(demodulation,[status(thm)],[c_2320,c_2461]) ).
tcf(c_2465,plain,
~ ordinal_subset(sK13,sK13),
inference(demodulation,[status(thm)],[c_1577,c_2461]) ).
tcf(c_2468,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2463,c_2465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM394+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n017.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 03:45:36 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 2.48/6.30 % SZS status Started for theBenchmark.p
% 2.48/6.30 % SZS status Theorem for theBenchmark.p
% 2.48/6.30
% 2.48/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.48/6.30
% 2.48/6.30 % ------ iProver source info
% 2.48/6.30
% 2.48/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.48/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.48/6.30 % git: non_committed_changes: false
% 2.48/6.30
% 2.48/6.30 % ------ Parsing...
% 2.48/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.48/6.30
% 2.48/6.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 19 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 2.48/6.30
% 2.48/6.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.48/6.30
% 2.48/6.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.48/6.30 % ------ Proving...
% 2.48/6.30 % ------ Problem Properties
% 2.48/6.30
% 2.48/6.30 %
% 2.48/6.30 % clauses 33
% 2.48/6.30 % conjectures 4
% 2.48/6.30 % EPR 28
% 2.48/6.30 % Horn 29
% 2.48/6.30 % unary 14
% 2.48/6.30 % binary 10
% 2.48/6.30 % lits 66
% 2.48/6.30 % lits eq 3
% 2.48/6.30 % fd_pure 0
% 2.48/6.30 % fd_pseudo 0
% 2.48/6.30 % fd_cond 1
% 2.48/6.30 % fd_pseudo_cond 2
% 2.48/6.30 % AC symbols 0
% 2.48/6.30
% 2.48/6.30 % ------ Schedule dynamic 5 is on
% 2.48/6.30
% 2.48/6.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.48/6.30
% 2.48/6.30
% 2.48/6.30 % ------
% 2.48/6.30 % Current options:
% 2.48/6.30 % ------
% 2.48/6.30
% 2.48/6.30
% 2.48/6.30 %
% 2.48/6.30
% 2.48/6.30 % ------ Proving...
% 2.48/6.30 %
% 2.48/6.30
% 2.48/6.30 % SZS status Theorem for theBenchmark.p
% 2.48/6.30
% 2.48/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.48/6.30
% 2.48/6.30
%------------------------------------------------------------------------------