%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM388+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 : n011.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 2.87s 1.45s
% Output : CNFRefutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 17 unt; 0 def)
% Number of atoms : 150 ( 1 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 147 ( 55 ~; 49 |; 28 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 81 ( 0 sgn 73 !; 8 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f7,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f24,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( epsilon_transitive(X2)
=> ( ( in(X0,X1)
& in(X2,X0) )
=> in(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_ordinal1) ).
fof(f25,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( epsilon_transitive(X2)
=> ( ( in(X0,X1)
& in(X2,X0) )
=> in(X2,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f27,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f28,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f29,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f32,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f43,plain,
! [X0] :
( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f49,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f50,plain,
? [X0] :
( ordinal(X0)
& ? [X1] :
( ordinal(X1)
& ? [X2] :
( epsilon_transitive(X2)
& in(X0,X1)
& in(X2,X0)
& ~ in(X2,X1) ) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f51,plain,
? [X0] :
( ordinal(X0)
& ? [X1] :
( ordinal(X1)
& ? [X2] :
( epsilon_transitive(X2)
& in(X0,X1)
& in(X2,X0)
& ~ in(X2,X1) ) ) ),
inference(flattening,[],[f50]) ).
fof(f53,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f54,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f29]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f55]) ).
fof(f59,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f61,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,[],[f49]) ).
fof(f62,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f61]) ).
fof(f63,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))],[f62]) ).
fof(f76,plain,
( ordinal(sK13)
& ordinal(sK14)
& epsilon_transitive(sK15)
& in(sK13,sK14)
& in(sK15,sK13)
& ~ in(sK15,sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15)],[f51]) ).
fof(f77,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f81,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f86,plain,
! [X2,X0] :
( ~ epsilon_transitive(X0)
| ~ in(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f118,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f76]) ).
fof(f120,plain,
in(sK13,sK14),
inference(cnf_transformation,[],[f76]) ).
fof(f121,plain,
in(sK15,sK13),
inference(cnf_transformation,[],[f76]) ).
fof(f122,plain,
~ in(sK15,sK14),
inference(cnf_transformation,[],[f76]) ).
fof(f124,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f126,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f130,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_51,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_86,negated_conjecture,
~ in(sK15,sK14),
inference(cnf_transformation,[],[f122]) ).
tcf(c_87,negated_conjecture,
in(sK15,sK13),
inference(cnf_transformation,[],[f121]) ).
tcf(c_88,negated_conjecture,
in(sK13,sK14),
inference(cnf_transformation,[],[f120]) ).
tcf(c_90,negated_conjecture,
ordinal(sK14),
inference(cnf_transformation,[],[f118]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_94]) ).
tcf(c_134,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(prop_impl_just,[status(thm)],[c_51]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_96,c_116]) ).
tcf(c_466,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_134,c_90]) ).
tcf(c_467,plain,
epsilon_transitive(sK14),
inference(unflattening,[status(thm)],[c_466]) ).
tcf(c_1218,plain,
epsilon_transitive(sK14),
inference(demodulation,[status(thm)],[c_467]) ).
tcf(c_1220,negated_conjecture,
in(sK13,sK14),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_1221,negated_conjecture,
in(sK15,sK13),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_1222,negated_conjecture,
~ in(sK15,sK14),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_1707,plain,
~ empty(sK14),
inference(superposition,[status(thm)],[c_1220,c_99]) ).
tcf(c_1775,plain,
! [X0: $i] :
( element(sK15,X0)
| ~ subset(sK13,X0) ),
inference(superposition,[status(thm)],[c_1221,c_218]) ).
tcf(c_1798,plain,
( subset(sK13,sK14)
| ~ epsilon_transitive(sK14) ),
inference(superposition,[status(thm)],[c_1220,c_57]) ).
tcf(c_1800,plain,
subset(sK13,sK14),
inference(forward_subsumption_resolution,[status(thm)],[c_1798,c_1218]) ).
tcf(c_1817,plain,
element(sK15,sK14),
inference(superposition,[status(thm)],[c_1800,c_1775]) ).
tcf(c_1818,plain,
( empty(sK14)
| in(sK15,sK14) ),
inference(superposition,[status(thm)],[c_1817,c_93]) ).
tcf(c_1819,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1818,c_1707,c_1222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM388+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.40 % Computer : n011.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Thu Sep 24 03:49:42 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.45 Running first-order theorem proving
% 0.19/0.45 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
% 0.19/0.46
% 0.19/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.19/0.46
% 0.19/0.46 % Detected problem language: tptp
% 0.19/0.48 % Proving...
% 2.87/1.45 % SZS status Started for theBenchmark.p
% 2.87/1.45 % SZS status Theorem for theBenchmark.p
% 2.87/1.45
% 2.87/1.45 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.87/1.45
% 2.87/1.45 % ------ iProver source info
% 2.87/1.45
% 2.87/1.45 % git: date: 2026-07-19 20:42:38 +0200
% 2.87/1.45 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.87/1.45 % git: non_committed_changes: false
% 2.87/1.45
% 2.87/1.45 % ------ Parsing...
% 2.87/1.45 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.87/1.45
% 2.87/1.45 % ------ Preprocessing... sup_sim: 0 sf_s rm: 19 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 %
% 2.87/1.45
% 2.87/1.45 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.87/1.45
% 2.87/1.45 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.87/1.45 % ------ Proving...
% 2.87/1.45 % ------ Problem Properties
% 2.87/1.45
% 2.87/1.45 %
% 2.87/1.45 % clauses 28
% 2.87/1.45 % conjectures 4
% 2.87/1.45 % EPR 23
% 2.87/1.45 % Horn 26
% 2.87/1.45 % unary 15
% 2.87/1.45 % binary 8
% 2.87/1.45 % lits 46
% 2.87/1.45 % lits eq 2
% 2.87/1.45 % fd_pure 0
% 2.87/1.45 % fd_pseudo 0
% 2.87/1.45 % fd_cond 1
% 2.87/1.45 % fd_pseudo_cond 1
% 2.87/1.45 % AC symbols 0
% 2.87/1.45
% 2.87/1.45 % ------ Schedule dynamic 5 is on
% 2.87/1.45
% 2.87/1.45 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.87/1.45
% 2.87/1.45
% 2.87/1.45 % ------
% 2.87/1.45 % Current options:
% 2.87/1.45 % ------
% 2.87/1.45
% 2.87/1.45
% 2.87/1.45 %
% 2.87/1.45
% 2.87/1.45 % ------ Proving...
% 2.87/1.45 %
% 2.87/1.45
% 2.87/1.45 % SZS status Theorem for theBenchmark.p
% 2.87/1.45
% 2.87/1.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.87/1.45
% 2.87/1.45
%------------------------------------------------------------------------------