%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM385+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 : n006.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 02:24:03 PM UTC 2026
% Result : Theorem 3.69s 1.27s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 30 unt; 4 def)
% Number of atoms : 207 ( 65 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 183 ( 69 ~; 76 |; 31 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% 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 : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 84 ( 0 sgn 77 !; 7 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
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,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f29,conjecture,
! [X0,X1] :
( succ(X0) = succ(X1)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_ordinal1) ).
fof(f30,negated_conjecture,
~ ! [X0,X1] :
( succ(X0) = succ(X1)
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f44,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f53,plain,
? [X0,X1] :
( succ(X0) = succ(X1)
& X0 != X1 ),
inference(ennf_transformation,[],[f30]) ).
fof(f60,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(f61,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,[],[f60]) ).
fof(f62,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))],[f61]) ).
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(nnf_transformation,[],[f8]) ).
fof(f64,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,[],[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) ) ) )
& ( ? [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,[],[f64]) ).
fof(f66,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))],[f65]) ).
fof(f78,plain,
( succ(sK13) = succ(sK14)
& sK13 != sK14 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f53]) ).
fof(f79,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f84,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f85,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f86,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f62]) ).
fof(f90,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f125,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f126,plain,
succ(sK13) = succ(sK14),
inference(cnf_transformation,[],[f78]) ).
fof(f127,plain,
sK13 != sK14,
inference(cnf_transformation,[],[f78]) ).
fof(f135,plain,
! [X0] : in(X0,set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f125,f85]) ).
fof(f136,plain,
set_union2(sK13,singleton(sK13)) = set_union2(sK14,singleton(sK14)),
inference(definition_unfolding,[],[f126,f85,f85]) ).
fof(f139,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f86]) ).
fof(f142,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f90]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f84]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f139]) ).
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,[],[f142]) ).
tcf(c_92,plain,
! [X0: $i] : in(X0,set_union2(X0,singleton(X0))),
inference(cnf_transformation,[],[f135]) ).
tcf(c_93,negated_conjecture,
sK13 != sK14,
inference(cnf_transformation,[],[f127]) ).
tcf(c_94,negated_conjecture,
set_union2(sK13,singleton(sK13)) = set_union2(sK14,singleton(sK14)),
inference(cnf_transformation,[],[f136]) ).
tcf(c_588,definition,
iPr_def_10 = singleton(sK13),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_589,definition,
iPr_def_11 = set_union2(sK13,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_590,definition,
iPr_def_12 = singleton(sK14),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_591,definition,
iPr_def_13 = set_union2(sK14,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_592,negated_conjecture,
iPr_def_11 = iPr_def_13,
inference(demodulation,[status(thm)],[c_94,c_590,c_591,c_588,c_589]) ).
tcf(c_593,negated_conjecture,
sK13 != sK14,
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_908,plain,
in(sK13,set_union2(sK13,iPr_def_10)),
inference(superposition,[status(thm)],[c_588,c_92]) ).
tcf(c_909,plain,
in(sK14,set_union2(sK14,iPr_def_12)),
inference(superposition,[status(thm)],[c_590,c_92]) ).
tcf(c_910,plain,
in(sK14,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_909,c_591,c_592]) ).
tcf(c_911,plain,
in(sK13,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_908,c_589]) ).
tcf(c_914,plain,
set_union2(iPr_def_10,sK13) = iPr_def_11,
inference(demodulation,[status(thm)],[c_589,c_52]) ).
tcf(c_915,plain,
set_union2(sK14,iPr_def_12) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_591,c_592]) ).
tcf(c_916,plain,
set_union2(iPr_def_12,sK14) = iPr_def_11,
inference(demodulation,[status(thm)],[c_915,c_52]) ).
tcf(c_985,plain,
! [X0: $i] :
( ( X0 = sK13 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_588,c_56]) ).
tcf(c_986,plain,
! [X0: $i] :
( ( X0 = sK14 )
| ~ in(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_590,c_56]) ).
tcf(c_1087,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| in(X0,sK13)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_914,c_62]) ).
tcf(c_1088,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| in(X0,sK14)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_916,c_62]) ).
tcf(c_1139,plain,
( in(sK13,iPr_def_12)
| in(sK13,sK14) ),
inference(superposition,[status(thm)],[c_911,c_1088]) ).
tcf(c_1481,plain,
( in(sK13,iPr_def_12)
| ~ in(sK14,sK13) ),
inference(superposition,[status(thm)],[c_1139,c_49]) ).
tcf(c_5170,plain,
( in(sK14,iPr_def_10)
| in(sK14,sK13) ),
inference(superposition,[status(thm)],[c_910,c_1087]) ).
tcf(c_5595,plain,
( in(sK14,iPr_def_10)
| in(sK13,iPr_def_12) ),
inference(superposition,[status(thm)],[c_5170,c_1481]) ).
tcf(c_5666,plain,
( in(sK13,iPr_def_12)
| ( sK13 = sK14 ) ),
inference(superposition,[status(thm)],[c_5595,c_985]) ).
tcf(c_5668,plain,
in(sK13,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_5666,c_593]) ).
tcf(c_5672,plain,
sK13 = sK14,
inference(superposition,[status(thm)],[c_5668,c_986]) ).
tcf(c_5674,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5672,c_593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM385+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n006.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 03:49:26 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.69/1.27 % SZS status Started for theBenchmark.p
% 3.69/1.27 % SZS status Theorem for theBenchmark.p
% 3.69/1.27
% 3.69/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.69/1.27
% 3.69/1.27 % ------ iProver source info
% 3.69/1.27
% 3.69/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.69/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.69/1.27 % git: non_committed_changes: false
% 3.69/1.27
% 3.69/1.27 % ------ Parsing...
% 3.69/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.69/1.27
% 3.69/1.27 % ------ 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 %
% 3.69/1.27
% 3.69/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.69/1.27
% 3.69/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.69/1.27 % ------ Proving...
% 3.69/1.27 % ------ Problem Properties
% 3.69/1.27
% 3.69/1.27 %
% 3.69/1.27 % clauses 34
% 3.69/1.27 % conjectures 2
% 3.69/1.27 % EPR 12
% 3.69/1.27 % Horn 30
% 3.69/1.27 % unary 18
% 3.69/1.27 % binary 9
% 3.69/1.27 % lits 58
% 3.69/1.27 % lits eq 19
% 3.69/1.27 % fd_pure 0
% 3.69/1.27 % fd_pseudo 0
% 3.69/1.27 % fd_cond 1
% 3.69/1.27 % fd_pseudo_cond 6
% 3.69/1.27 % AC symbols 0
% 3.69/1.27
% 3.69/1.27 % ------ Schedule dynamic 5 is on
% 3.69/1.27
% 3.69/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.69/1.27
% 3.69/1.27
% 3.69/1.27 % ------
% 3.69/1.27 % Current options:
% 3.69/1.27 % ------
% 3.69/1.27
% 3.69/1.27
% 3.69/1.27 %
% 3.69/1.27
% 3.69/1.27 % ------ Proving...
% 3.69/1.27 %
% 3.69/1.27
% 3.69/1.27 % SZS status Theorem for theBenchmark.p
% 3.69/1.27
% 3.69/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.69/1.28
% 3.69/1.28
%------------------------------------------------------------------------------