%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : PRO009+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.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 02:31:35 PM UTC 2026
% Result : Theorem 3.67s 1.29s
% Output : CNFRefutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 52 ( 5 unt; 0 def)
% Number of atoms : 201 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 257 ( 108 ~; 97 |; 46 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 105 ( 0 sgn 90 !; 15 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( min_precedes(X1,X2,X3)
& min_precedes(X0,X1,X3) )
=> min_precedes(X0,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
fof(f5,axiom,
! [X0,X1,X2] :
( next_subocc(X0,X1,X2)
<=> ( ~ ? [X3] :
( min_precedes(X3,X1,X2)
& min_precedes(X0,X3,X2) )
& min_precedes(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(f33,axiom,
! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2,X3] :
( leaf_occ(X3,X0)
& next_subocc(X2,X3,tptp0)
& ( occurrence_of(X3,tptp1)
| occurrence_of(X3,tptp2) )
& next_subocc(X1,X2,tptp0)
& occurrence_of(X2,tptp4)
& root_occ(X1,X0)
& occurrence_of(X1,tptp3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_32) ).
fof(f46,conjecture,
! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2] :
( leaf_occ(X2,X0)
& min_precedes(X1,X2,tptp0)
& ( occurrence_of(X2,tptp1)
| occurrence_of(X2,tptp2) )
& root_occ(X1,X0)
& occurrence_of(X1,tptp3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f47,negated_conjecture,
~ ! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2] :
( leaf_occ(X2,X0)
& min_precedes(X1,X2,tptp0)
& ( occurrence_of(X2,tptp1)
| occurrence_of(X2,tptp2) )
& root_occ(X1,X0)
& occurrence_of(X1,tptp3) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( ~ min_precedes(X1,X2,X3)
| ~ min_precedes(X0,X1,X3)
| min_precedes(X0,X2,X3) ),
inference(ennf_transformation,[],[f1]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( ~ min_precedes(X1,X2,X3)
| ~ min_precedes(X0,X1,X3)
| min_precedes(X0,X2,X3) ),
inference(flattening,[],[f49]) ).
fof(f57,plain,
! [X0,X1,X2] :
( next_subocc(X0,X1,X2)
<=> ( ! [X3] :
( ~ min_precedes(X3,X1,X2)
| ~ min_precedes(X0,X3,X2) )
& min_precedes(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f90,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| ? [X1,X2,X3] :
( leaf_occ(X3,X0)
& next_subocc(X2,X3,tptp0)
& ( occurrence_of(X3,tptp1)
| occurrence_of(X3,tptp2) )
& next_subocc(X1,X2,tptp0)
& occurrence_of(X2,tptp4)
& root_occ(X1,X0)
& occurrence_of(X1,tptp3) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f91,plain,
? [X0] :
( occurrence_of(X0,tptp0)
& ! [X1,X2] :
( ~ leaf_occ(X2,X0)
| ~ min_precedes(X1,X2,tptp0)
| ( ~ occurrence_of(X2,tptp1)
& ~ occurrence_of(X2,tptp2) )
| ~ root_occ(X1,X0)
| ~ occurrence_of(X1,tptp3) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( ~ next_subocc(X0,X1,X2)
| ( ! [X3] :
( ~ min_precedes(X3,X1,X2)
| ~ min_precedes(X0,X3,X2) )
& min_precedes(X0,X1,X2) ) )
& ( ? [X3] :
( min_precedes(X3,X1,X2)
& min_precedes(X0,X3,X2) )
| ~ min_precedes(X0,X1,X2)
| next_subocc(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( ~ next_subocc(X0,X1,X2)
| ( ! [X3] :
( ~ min_precedes(X3,X1,X2)
| ~ min_precedes(X0,X3,X2) )
& min_precedes(X0,X1,X2) ) )
& ( ? [X3] :
( min_precedes(X3,X1,X2)
& min_precedes(X0,X3,X2) )
| ~ min_precedes(X0,X1,X2)
| next_subocc(X0,X1,X2) ) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( ~ next_subocc(X0,X1,X2)
| ( ! [X4] :
( ~ min_precedes(X4,X1,X2)
| ~ min_precedes(X0,X4,X2) )
& min_precedes(X0,X1,X2) ) )
& ( ? [X3] :
( min_precedes(X3,X1,X2)
& min_precedes(X0,X3,X2) )
| ~ min_precedes(X0,X1,X2)
| next_subocc(X0,X1,X2) ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ( ~ next_subocc(X0,X1,X2)
| ( ! [X4] :
( ~ min_precedes(X4,X1,X2)
| ~ min_precedes(X0,X4,X2) )
& min_precedes(X0,X1,X2) ) )
& ( ( min_precedes(sK0(X0,X1,X2),X1,X2)
& min_precedes(X0,sK0(X0,X1,X2),X2) )
| ~ min_precedes(X0,X1,X2)
| next_subocc(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f94]) ).
fof(f117,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| ( leaf_occ(sK16(X0),X0)
& next_subocc(sK15(X0),sK16(X0),tptp0)
& ( occurrence_of(sK16(X0),tptp1)
| occurrence_of(sK16(X0),tptp2) )
& next_subocc(sK14(X0),sK15(X0),tptp0)
& occurrence_of(sK15(X0),tptp4)
& root_occ(sK14(X0),X0)
& occurrence_of(sK14(X0),tptp3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X1,sK14(X0)),skolemize(X2,sK15(X0)),skolemize(X3,sK16(X0))],[f90]) ).
fof(f118,plain,
( occurrence_of(sK17,tptp0)
& ! [X1,X2] :
( ~ leaf_occ(X2,sK17)
| ~ min_precedes(X1,X2,tptp0)
| ( ~ occurrence_of(X2,tptp1)
& ~ occurrence_of(X2,tptp2) )
| ~ root_occ(X1,sK17)
| ~ occurrence_of(X1,tptp3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X0,sK17)],[f91]) ).
fof(f119,plain,
! [X2,X3,X0,X1] :
( ~ min_precedes(X1,X2,X3)
| ~ min_precedes(X0,X1,X3)
| min_precedes(X0,X2,X3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ next_subocc(X0,X1,X2)
| min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f181,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| leaf_occ(sK16(X0),X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f182,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| next_subocc(sK15(X0),sK16(X0),tptp0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f183,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| occurrence_of(sK16(X0),tptp1)
| occurrence_of(sK16(X0),tptp2) ),
inference(cnf_transformation,[],[f117]) ).
fof(f184,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| next_subocc(sK14(X0),sK15(X0),tptp0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f186,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| root_occ(sK14(X0),X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f187,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| occurrence_of(sK14(X0),tptp3) ),
inference(cnf_transformation,[],[f117]) ).
fof(f200,plain,
occurrence_of(sK17,tptp0),
inference(cnf_transformation,[],[f118]) ).
fof(f201,plain,
! [X2,X1] :
( ~ leaf_occ(X2,sK17)
| ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X2,tptp1)
| ~ root_occ(X1,sK17)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[],[f118]) ).
fof(f202,plain,
! [X2,X1] :
( ~ leaf_occ(X2,sK17)
| ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X2,tptp2)
| ~ root_occ(X1,sK17)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( min_precedes(X0,X3,X2)
| ~ min_precedes(X1,X3,X2)
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( min_precedes(X0,X1,X2)
| ~ next_subocc(X0,X1,X2) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_111,plain,
! [X0: $i] :
( occurrence_of(sK14(X0),tptp3)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_112,plain,
! [X0: $i] :
( root_occ(sK14(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_114,plain,
! [X0: $i] :
( next_subocc(sK14(X0),sK15(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_115,plain,
! [X0: $i] :
( occurrence_of(sK16(X0),tptp1)
| occurrence_of(sK16(X0),tptp2)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_116,plain,
! [X0: $i] :
( next_subocc(sK15(X0),sK16(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_117,plain,
! [X0: $i] :
( leaf_occ(sK16(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_130,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ leaf_occ(X1,sK17)
| ~ root_occ(X0,sK17)
| ~ occurrence_of(X1,tptp2)
| ~ occurrence_of(X0,tptp3)
| ~ min_precedes(X0,X1,tptp0) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_131,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ leaf_occ(X1,sK17)
| ~ root_occ(X0,sK17)
| ~ occurrence_of(X1,tptp1)
| ~ occurrence_of(X0,tptp3)
| ~ min_precedes(X0,X1,tptp0) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_132,negated_conjecture,
occurrence_of(sK17,tptp0),
inference(cnf_transformation,[],[f200]) ).
tcf(c_5535,negated_conjecture,
occurrence_of(sK17,tptp0),
inference(demodulation,[status(thm)],[c_132]) ).
tcf(c_5536,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ leaf_occ(X1,sK17)
| ~ root_occ(X0,sK17)
| ~ occurrence_of(X1,tptp1)
| ~ occurrence_of(X0,tptp3)
| ~ min_precedes(X0,X1,tptp0) ),
inference(demodulation,[status(thm)],[c_131]) ).
tcf(c_5537,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ leaf_occ(X1,sK17)
| ~ root_occ(X0,sK17)
| ~ occurrence_of(X1,tptp2)
| ~ occurrence_of(X0,tptp3)
| ~ min_precedes(X0,X1,tptp0) ),
inference(demodulation,[status(thm)],[c_130]) ).
tcf(c_7099,plain,
! [X0: $i] :
( min_precedes(sK14(X0),sK15(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(superposition,[status(thm)],[c_114,c_55]) ).
tcf(c_7108,plain,
! [X0: $i] :
( min_precedes(sK15(X0),sK16(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(superposition,[status(thm)],[c_116,c_55]) ).
tcf(c_7129,plain,
! [X0: $i,X1: $i] :
( min_precedes(sK14(X0),X1,tptp0)
| ~ occurrence_of(X0,tptp0)
| ~ min_precedes(sK15(X0),X1,tptp0) ),
inference(superposition,[status(thm)],[c_7099,c_49]) ).
tcf(c_7380,plain,
( leaf_occ(sK16(sK17),sK17)
| ~ occurrence_of(sK17,tptp0) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_7647,plain,
! [X0: $i] :
( min_precedes(sK14(X0),sK16(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(superposition,[status(thm)],[c_7108,c_7129]) ).
tcf(c_8002,plain,
! [X0: $i] :
( ~ occurrence_of(X0,tptp0)
| ~ leaf_occ(sK16(X0),sK17)
| ~ root_occ(sK14(X0),sK17)
| ~ occurrence_of(sK16(X0),tptp2)
| ~ occurrence_of(sK14(X0),tptp3) ),
inference(superposition,[status(thm)],[c_7647,c_5537]) ).
tcf(c_8003,plain,
! [X0: $i] :
( ~ occurrence_of(X0,tptp0)
| ~ leaf_occ(sK16(X0),sK17)
| ~ root_occ(sK14(X0),sK17)
| ~ occurrence_of(sK16(X0),tptp1)
| ~ occurrence_of(sK14(X0),tptp3) ),
inference(superposition,[status(thm)],[c_7647,c_5536]) ).
tcf(c_8295,plain,
! [X0: $i] :
( ~ occurrence_of(X0,tptp0)
| ~ leaf_occ(sK16(X0),sK17)
| ~ root_occ(sK14(X0),sK17) ),
inference(global_subsumption_just,[status(thm)],[c_8002,c_111,c_115,c_8003,c_8002]) ).
tcf(c_8304,plain,
( ~ occurrence_of(sK17,tptp0)
| ~ leaf_occ(sK16(sK17),sK17) ),
inference(superposition,[status(thm)],[c_112,c_8295]) ).
tcf(c_8305,plain,
~ leaf_occ(sK16(sK17),sK17),
inference(forward_subsumption_resolution,[status(thm)],[c_8304,c_5535]) ).
tcf(c_8306,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8305,c_7380,c_132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 06:27:51 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 3.67/1.29 % SZS status Started for theBenchmark.p
% 3.67/1.29 % SZS status Theorem for theBenchmark.p
% 3.67/1.29
% 3.67/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.67/1.29
% 3.67/1.29 % ------ iProver source info
% 3.67/1.29
% 3.67/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 3.67/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.67/1.29 % git: non_committed_changes: false
% 3.67/1.29
% 3.67/1.29 % ------ Parsing...
% 3.67/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.67/1.29
% 3.67/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.67/1.29
% 3.67/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.67/1.29
% 3.67/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.67/1.29 % ------ Proving...
% 3.67/1.29 % ------ Problem Properties
% 3.67/1.29
% 3.67/1.29 %
% 3.67/1.29 % clauses 83
% 3.67/1.29 % conjectures 3
% 3.67/1.29 % EPR 47
% 3.67/1.29 % Horn 69
% 3.67/1.29 % unary 13
% 3.67/1.29 % binary 41
% 3.67/1.29 % lits 197
% 3.67/1.29 % lits eq 10
% 3.67/1.29 % fd_pure 0
% 3.67/1.29 % fd_pseudo 0
% 3.67/1.29 % fd_cond 0
% 3.67/1.29 % fd_pseudo_cond 4
% 3.67/1.29 % AC symbols 0
% 3.67/1.29
% 3.67/1.29 % ------ Schedule dynamic 5 is on
% 3.67/1.29
% 3.67/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.67/1.29
% 3.67/1.29
% 3.67/1.29 % ------
% 3.67/1.29 % Current options:
% 3.67/1.29 % ------
% 3.67/1.29
% 3.67/1.29
% 3.67/1.29 %
% 3.67/1.29
% 3.67/1.29 % ------ Proving...
% 3.67/1.29 %
% 3.67/1.29
% 3.67/1.29 % SZS status Theorem for theBenchmark.p
% 3.67/1.29
% 3.67/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.67/1.29
% 3.67/1.29
%------------------------------------------------------------------------------