%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM386+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 : 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 1.04s 1.37s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 63 ( 17 unt; 2 def)
% Number of atoms : 230 ( 71 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 238 ( 90 ~; 106 |; 35 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 92 ( 0 sgn 81 !; 11 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f6,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f7,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f8,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f28,conjecture,
! [X0,X1] :
( in(X0,succ(X1))
<=> ( X0 = X1
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_ordinal1) ).
fof(f29,negated_conjecture,
~ ! [X0,X1] :
( in(X0,succ(X1))
<=> ( X0 = X1
| in(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f52,plain,
? [X0,X1] :
( in(X0,succ(X1))
<~> ( X0 = X1
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f59,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f60,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X0) )
& ( ~ in(sK1(X0,X1,X2),X2)
| ( ~ in(sK1(X0,X1,X2),X1)
& ~ in(sK1(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f64]) ).
fof(f77,plain,
? [X0,X1] :
( ( in(X0,succ(X1))
| X0 = X1
| in(X0,X1) )
& ( ~ in(X0,succ(X1))
| ( X0 != X1
& ~ in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f78,plain,
? [X0,X1] :
( ( in(X0,succ(X1))
| X0 = X1
| in(X0,X1) )
& ( ~ in(X0,succ(X1))
| ( X0 != X1
& ~ in(X0,X1) ) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
( ( in(sK13,succ(sK14))
| sK13 = sK14
| in(sK13,sK14) )
& ( ~ in(sK13,succ(sK14))
| ( sK13 != sK14
& ~ in(sK13,sK14) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f78]) ).
fof(f85,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f86,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f87,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f61]) ).
fof(f88,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f91,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f93,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f65]) ).
fof(f126,plain,
( in(sK13,succ(sK14))
| sK13 = sK14
| in(sK13,sK14) ),
inference(cnf_transformation,[],[f79]) ).
fof(f127,plain,
( ~ in(sK13,succ(sK14))
| sK13 != sK14 ),
inference(cnf_transformation,[],[f79]) ).
fof(f128,plain,
( ~ in(sK13,succ(sK14))
| ~ in(sK13,sK14) ),
inference(cnf_transformation,[],[f79]) ).
fof(f136,plain,
( ~ in(sK13,set_union2(sK14,singleton(sK14)))
| ~ in(sK13,sK14) ),
inference(definition_unfolding,[],[f128,f86]) ).
fof(f137,plain,
( ~ in(sK13,set_union2(sK14,singleton(sK14)))
| sK13 != sK14 ),
inference(definition_unfolding,[],[f127,f86]) ).
fof(f138,plain,
( in(sK13,set_union2(sK14,singleton(sK14)))
| sK13 = sK14
| in(sK13,sK14) ),
inference(definition_unfolding,[],[f126,f86]) ).
fof(f139,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f88]) ).
fof(f140,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f139]) ).
fof(f141,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f87]) ).
fof(f142,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f93]) ).
fof(f144,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f91]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f85]) ).
tcf(c_55,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f140]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_92,negated_conjecture,
( ~ in(sK13,sK14)
| ~ in(sK13,set_union2(sK14,singleton(sK14))) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_93,negated_conjecture,
( ~ in(sK13,set_union2(sK14,singleton(sK14)))
| ( sK13 != sK14 ) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_94,negated_conjecture,
( in(sK13,sK14)
| in(sK13,set_union2(sK14,singleton(sK14)))
| ( sK13 = sK14 ) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_214,plain,
~ in(sK13,sK14),
inference(backward_subsumption_resolution,[status(thm)],[c_92,c_60]) ).
tcf(c_416,plain,
( ( sK13 = sK14 )
| in(sK13,set_union2(sK14,singleton(sK14))) ),
inference(prop_impl_just,[status(thm)],[c_94,c_214]) ).
tcf(c_417,plain,
( in(sK13,set_union2(sK14,singleton(sK14)))
| ( sK13 = sK14 ) ),
inference(renaming,[status(thm)],[c_416]) ).
tcf(c_705,definition,
iPr_def_10 = singleton(sK14),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_706,definition,
iPr_def_11 = set_union2(sK14,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_707,plain,
~ in(sK13,sK14),
inference(demodulation,[status(thm)],[c_214]) ).
tcf(c_708,negated_conjecture,
( ~ in(sK13,iPr_def_11)
| ( sK13 != sK14 ) ),
inference(demodulation,[status(thm)],[c_93,c_705,c_706]) ).
tcf(c_1019,plain,
in(sK14,iPr_def_10),
inference(superposition,[status(thm)],[c_705,c_55]) ).
tcf(c_1026,plain,
set_union2(iPr_def_10,sK14) = iPr_def_11,
inference(demodulation,[status(thm)],[c_706,c_52]) ).
tcf(c_1060,plain,
( in(sK13,set_union2(sK14,iPr_def_10))
| ( sK13 = sK14 ) ),
inference(light_normalisation,[status(thm)],[c_417,c_705]) ).
tcf(c_1061,plain,
( in(sK13,iPr_def_11)
| ( sK13 = sK14 ) ),
inference(demodulation,[status(thm)],[c_1060,c_52,c_1026]) ).
tcf(c_1098,plain,
! [X0: $i] :
( ( X0 = sK14 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_705,c_56]) ).
tcf(c_1112,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1026,c_60]) ).
tcf(c_1146,plain,
in(sK14,iPr_def_11),
inference(superposition,[status(thm)],[c_1019,c_1112]) ).
tcf(c_1207,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| in(X0,sK14)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1026,c_62]) ).
tcf(c_2024,plain,
( in(sK13,iPr_def_10)
| in(sK13,sK14)
| ( sK13 = sK14 ) ),
inference(superposition,[status(thm)],[c_1061,c_1207]) ).
tcf(c_2030,plain,
( in(sK13,iPr_def_10)
| ( sK13 = sK14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2024,c_707]) ).
tcf(c_2096,plain,
sK13 = sK14,
inference(forward_subsumption_resolution,[status(thm)],[c_2030,c_1098]) ).
tcf(c_2099,plain,
( ~ in(sK14,iPr_def_11)
| ( sK14 != sK14 ) ),
inference(demodulation,[status(thm)],[c_708,c_2096]) ).
tcf(c_2100,plain,
~ in(sK14,iPr_def_11),
inference(equality_resolution_simp,[status(thm)],[c_2099]) ).
tcf(c_2101,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2100,c_1146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM386+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.42 % Computer : n017.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Thu Sep 24 03:45:00 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 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
% 0.16/0.48
% 0.16/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.48
% 0.16/0.48 % Detected problem language: tptp
% 0.16/0.50 % Proving...
% 1.04/1.37 % SZS status Started for theBenchmark.p
% 1.04/1.37 % SZS status Theorem for theBenchmark.p
% 1.04/1.37
% 1.04/1.37 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.04/1.37
% 1.04/1.37 % ------ iProver source info
% 1.04/1.37
% 1.04/1.37 % git: date: 2026-07-19 20:42:38 +0200
% 1.04/1.37 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.04/1.37 % git: non_committed_changes: false
% 1.04/1.37
% 1.04/1.37 % ------ Parsing...
% 1.04/1.37 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.04/1.37
% 1.04/1.37 % ------ Preprocessing... sup_sim: 0 sf_s rm: 20 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 1.04/1.37
% 1.04/1.37 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.04/1.37
% 1.04/1.37 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.04/1.37 % ------ Proving...
% 1.04/1.37 % ------ Problem Properties
% 1.04/1.37
% 1.04/1.37 %
% 1.04/1.37 % clauses 32
% 1.04/1.37 % conjectures 1
% 1.04/1.37 % EPR 12
% 1.04/1.37 % Horn 27
% 1.04/1.37 % unary 14
% 1.04/1.37 % binary 11
% 1.04/1.37 % lits 58
% 1.04/1.37 % lits eq 17
% 1.04/1.37 % fd_pure 0
% 1.04/1.37 % fd_pseudo 0
% 1.04/1.37 % fd_cond 1
% 1.04/1.37 % fd_pseudo_cond 6
% 1.04/1.37 % AC symbols 0
% 1.04/1.37
% 1.04/1.37 % ------ Schedule dynamic 5 is on
% 1.04/1.37
% 1.04/1.37 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.04/1.37
% 1.04/1.37
% 1.04/1.37 % ------
% 1.04/1.37 % Current options:
% 1.04/1.37 % ------
% 1.04/1.37
% 1.04/1.37
% 1.04/1.37 %
% 1.04/1.37
% 1.04/1.37 % ------ Proving...
% 1.04/1.37 %
% 1.04/1.37
% 1.04/1.37 % SZS status Theorem for theBenchmark.p
% 1.04/1.37
% 1.04/1.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.04/1.37
% 1.04/1.37
%------------------------------------------------------------------------------