%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : PRO010+3 : TPTP v9.3.1. Released v4.0.0.
% 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 02:31:35 PM UTC 2026
% Result : Theorem 1.34s 1.49s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 9 unt; 1 def)
% Number of atoms : 142 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 139 ( 39 ~; 43 |; 46 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-1 aty)
% Number of variables : 81 ( 0 sgn 59 !; 22 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1] :
( occurrence_of(X0,X1)
=> ( arboreal(X0)
<=> atomic(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
fof(f47,axiom,
! [X0,X1,X2] :
( min_precedes(X0,X1,X2)
=> arboreal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_46) ).
fof(f50,axiom,
! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2,X3] :
( leaf_occ(X3,X0)
& next_subocc(X2,X3,tptp0)
& ( occurrence_of(X3,tptp2)
| occurrence_of(X3,tptp1) )
& next_subocc(X1,X2,tptp0)
& occurrence_of(X2,tptp4)
& root_occ(X1,X0)
& occurrence_of(X1,tptp3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_49) ).
fof(f52,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_51) ).
fof(f63,conjecture,
! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2] :
( ( occurrence_of(X2,tptp2)
=> ~ ? [X4] :
( min_precedes(X1,X4,tptp0)
& occurrence_of(X4,tptp1) ) )
& ( occurrence_of(X2,tptp1)
=> ~ ? [X3] :
( min_precedes(X1,X3,tptp0)
& occurrence_of(X3,tptp2) ) )
& leaf_occ(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f64,negated_conjecture,
~ ! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2] :
( ( occurrence_of(X2,tptp2)
=> ~ ? [X4] :
( min_precedes(X1,X4,tptp0)
& occurrence_of(X4,tptp1) ) )
& ( occurrence_of(X2,tptp1)
=> ~ ? [X3] :
( min_precedes(X1,X3,tptp0)
& occurrence_of(X3,tptp2) ) )
& leaf_occ(X2,X0) ) ),
inference(negated_conjecture,[status(cth)],[f63]) ).
fof(f75,plain,
! [X0,X1] :
( ~ occurrence_of(X0,X1)
| ( arboreal(X0)
<=> atomic(X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ min_precedes(X0,X1,X2)
| arboreal(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f136,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| ? [X1,X2,X3] :
( leaf_occ(X3,X0)
& next_subocc(X2,X3,tptp0)
& ( occurrence_of(X3,tptp2)
| occurrence_of(X3,tptp1) )
& next_subocc(X1,X2,tptp0)
& occurrence_of(X2,tptp4)
& root_occ(X1,X0)
& occurrence_of(X1,tptp3) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f137,plain,
? [X0] :
( occurrence_of(X0,tptp0)
& ! [X1,X2] :
( ( occurrence_of(X2,tptp2)
& ? [X4] :
( min_precedes(X1,X4,tptp0)
& occurrence_of(X4,tptp1) ) )
| ( occurrence_of(X2,tptp1)
& ? [X3] :
( min_precedes(X1,X3,tptp0)
& occurrence_of(X3,tptp2) ) )
| ~ leaf_occ(X2,X0) ) ),
inference(ennf_transformation,[],[f64]) ).
fof(f141,plain,
! [X0,X1] :
( ~ occurrence_of(X0,X1)
| ( ( ~ arboreal(X0)
| atomic(X1) )
& ( ~ atomic(X1)
| arboreal(X0) ) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f169,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| ( leaf_occ(sK19(X0),X0)
& next_subocc(sK18(X0),sK19(X0),tptp0)
& ( occurrence_of(sK19(X0),tptp2)
| occurrence_of(sK19(X0),tptp1) )
& next_subocc(sK17(X0),sK18(X0),tptp0)
& occurrence_of(sK18(X0),tptp4)
& root_occ(sK17(X0),X0)
& occurrence_of(sK17(X0),tptp3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X1,sK17(X0)),skolemize(X2,sK18(X0)),skolemize(X3,sK19(X0))],[f136]) ).
fof(f173,plain,
( occurrence_of(sK21,tptp0)
& ! [X1,X2] :
( sP0(X1,X2)
| ( occurrence_of(X2,tptp1)
& min_precedes(X1,sK22(X1),tptp0)
& occurrence_of(sK22(X1),tptp2) )
| ~ leaf_occ(X2,sK21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22]),skolemize(X0,sK21),skolemize(X3,sK22(X1))],[f139]) ).
fof(f183,plain,
! [X0,X1] :
( ~ occurrence_of(X0,X1)
| ~ arboreal(X0)
| atomic(X1) ),
inference(cnf_transformation,[],[f141]) ).
fof(f253,plain,
! [X2,X0,X1] :
( ~ min_precedes(X0,X1,X2)
| arboreal(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f256,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| leaf_occ(sK19(X0),X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f264,plain,
~ atomic(tptp0),
inference(cnf_transformation,[],[f52]) ).
fof(f278,plain,
occurrence_of(sK21,tptp0),
inference(cnf_transformation,[],[f173]) ).
fof(f280,plain,
! [X2,X1] :
( sP0(X1,X2)
| min_precedes(X1,sK22(X1),tptp0)
| ~ leaf_occ(X2,sK21) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( atomic(X1)
| ~ arboreal(X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i] :
( arboreal(X0)
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f253]) ).
tcf(c_137,plain,
! [X0: $i] :
( leaf_occ(sK19(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f256]) ).
tcf(c_139,plain,
~ atomic(tptp0),
inference(cnf_transformation,[],[f264]) ).
tcf(c_154,negated_conjecture,
! [X0: $i,X1: $i] :
( sP0(X1,X0)
| min_precedes(X1,sK22(X1),tptp0)
| ~ leaf_occ(X0,sK21) ),
inference(cnf_transformation,[],[f280]) ).
tcf(c_156,negated_conjecture,
occurrence_of(sK21,tptp0),
inference(cnf_transformation,[],[f278]) ).
tcf(c_4022,negated_conjecture,
occurrence_of(sK21,tptp0),
inference(demodulation,[status(thm)],[c_156]) ).
tcf(c_4024,negated_conjecture,
! [X0: $i,X1: $i] :
( sP0(X1,X0)
| min_precedes(X1,sK22(X1),tptp0)
| ~ leaf_occ(X0,sK21) ),
inference(demodulation,[status(thm)],[c_154]) ).
tcf(c_5564,plain,
! [X0: $i,X1: $i] :
( arboreal(X1)
| sP0(X1,X0)
| ~ leaf_occ(X0,sK21) ),
inference(superposition,[status(thm)],[c_4024,c_128]) ).
tcf(c_5772,plain,
! [X0: $i] :
( arboreal(X0)
| sP0(X0,sK19(sK21))
| ~ occurrence_of(sK21,tptp0) ),
inference(superposition,[status(thm)],[c_137,c_5564]) ).
tcf(c_5782,plain,
! [X0: $i] :
( arboreal(X0)
| sP0(X0,sK19(sK21)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5772,c_4022]) ).
tcf(c_5978,plain,
( atomic(tptp0)
| ~ arboreal(sK21) ),
inference(superposition,[status(thm)],[c_4022,c_59]) ).
tcf(c_5980,plain,
~ arboreal(sK21),
inference(forward_subsumption_resolution,[status(thm)],[c_5978,c_139]) ).
fof(f138,definition,
! [X1,X2] :
( ~ sP0(X1,X2)
| ( occurrence_of(X2,tptp2)
& ? [X4] :
( min_precedes(X1,X4,tptp0)
& occurrence_of(X4,tptp1) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f139,plain,
? [X0] :
( occurrence_of(X0,tptp0)
& ! [X1,X2] :
( sP0(X1,X2)
| ( occurrence_of(X2,tptp1)
& ? [X3] :
( min_precedes(X1,X3,tptp0)
& occurrence_of(X3,tptp2) ) )
| ~ leaf_occ(X2,X0) ) ),
inference(definition_folding,[],[f137,f138]) ).
fof(f170,plain,
! [X1,X2] :
( ~ sP0(X1,X2)
| ( occurrence_of(X2,tptp2)
& ? [X4] :
( min_precedes(X1,X4,tptp0)
& occurrence_of(X4,tptp1) ) ) ),
inference(nnf_transformation,[],[f138]) ).
fof(f171,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( occurrence_of(X1,tptp2)
& ? [X2] :
( min_precedes(X0,X2,tptp0)
& occurrence_of(X2,tptp1) ) ) ),
inference(rectify,[],[f170]) ).
fof(f172,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( occurrence_of(X1,tptp2)
& min_precedes(X0,sK20(X0),tptp0)
& occurrence_of(sK20(X0),tptp1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X2,sK20(X0))],[f171]) ).
fof(f276,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| min_precedes(X0,sK20(X0),tptp0) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( min_precedes(X0,sK20(X0),tptp0)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_6604,plain,
! [X0: $i] :
( arboreal(X0)
| min_precedes(X0,sK20(X0),tptp0) ),
inference(superposition,[status(thm)],[c_5782,c_151]) ).
tcf(c_6833,plain,
! [X0: $i] : arboreal(X0),
inference(forward_subsumption_resolution,[status(thm)],[c_6604,c_128]) ).
tcf(c_6834,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_5980,c_6833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : PRO010+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.42 % Computer : n011.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 06:27:12 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.49 Running first-order theorem proving
% 0.16/0.49 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
% 0.25/0.50
% 0.25/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.50
% 0.25/0.50 % Detected problem language: tptp
% 0.25/0.52 % Proving...
% 1.34/1.49 % SZS status Started for theBenchmark.p
% 1.34/1.49 % SZS status Theorem for theBenchmark.p
% 1.34/1.49
% 1.34/1.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.34/1.49
% 1.34/1.49 % ------ iProver source info
% 1.34/1.49
% 1.34/1.49 % git: date: 2026-07-19 20:42:38 +0200
% 1.34/1.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.34/1.49 % git: non_committed_changes: false
% 1.34/1.49
% 1.34/1.49 % ------ Parsing...
% 1.34/1.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.34/1.49
% 1.34/1.49 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.34/1.49
% 1.34/1.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.34/1.49
% 1.34/1.49 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.34/1.49 % ------ Proving...
% 1.34/1.49 % ------ Problem Properties
% 1.34/1.49
% 1.34/1.49 %
% 1.34/1.49 % clauses 108
% 1.34/1.49 % conjectures 4
% 1.34/1.49 % EPR 64
% 1.34/1.49 % Horn 83
% 1.34/1.49 % unary 13
% 1.34/1.49 % binary 49
% 1.34/1.49 % lits 290
% 1.34/1.49 % lits eq 18
% 1.34/1.49 % fd_pure 0
% 1.34/1.49 % fd_pseudo 0
% 1.34/1.49 % fd_cond 0
% 1.34/1.49 % fd_pseudo_cond 12
% 1.34/1.49 % AC symbols 0
% 1.34/1.49
% 1.34/1.49 % ------ Schedule dynamic 5 is on
% 1.34/1.49
% 1.34/1.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.34/1.49
% 1.34/1.49
% 1.34/1.49 % ------
% 1.34/1.49 % Current options:
% 1.34/1.49 % ------
% 1.34/1.49
% 1.34/1.49
% 1.34/1.49 %
% 1.34/1.49
% 1.34/1.49 % ------ Proving...
% 1.34/1.49 %
% 1.34/1.49
% 1.34/1.49 % SZS status Theorem for theBenchmark.p
% 1.34/1.49
% 1.34/1.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.34/1.49
% 1.34/1.49
%------------------------------------------------------------------------------