%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : PRO010+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 : 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 4.51s 1.32s
% Output : CNFRefutation 4.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 4 unt; 1 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 133 ( 40 ~; 39 |; 46 &)
% ( 0 <=>; 8 =>; 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 : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-1 aty)
% Number of variables : 80 ( 0 sgn 57 !; 23 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X0,X1,X2] :
( ( leaf_occ(X1,X0)
& occurrence_of(X0,X2) )
=> ~ ? [X3] : min_precedes(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_21) ).
fof(f33,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/sandbox/benchmark/theBenchmark.p',sos_32) ).
fof(f46,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/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f47,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)],[f46]) ).
fof(f48,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,[],[f47]) ).
fof(f49,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,[],[f33]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,X2)
| ! [X3] : ~ min_precedes(X1,X3,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,X2)
| ! [X3] : ~ min_precedes(X1,X3,X2) ),
inference(flattening,[],[f52]) ).
fof(f91,plain,
( occurrence_of(sK2,tptp0)
& ! [X1,X2] :
( sP0(X1,X2)
| ( occurrence_of(X2,tptp1)
& min_precedes(X1,sK3(X1),tptp0)
& occurrence_of(sK3(X1),tptp2) )
| ~ leaf_occ(X2,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X3,sK3(X1))],[f87]) ).
fof(f92,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| ( leaf_occ(sK6(X0),X0)
& next_subocc(sK5(X0),sK6(X0),tptp0)
& ( occurrence_of(sK6(X0),tptp2)
| occurrence_of(sK6(X0),tptp1) )
& next_subocc(sK4(X0),sK5(X0),tptp0)
& occurrence_of(sK5(X0),tptp4)
& root_occ(sK4(X0),X0)
& occurrence_of(sK4(X0),tptp3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X1,sK4(X0)),skolemize(X2,sK5(X0)),skolemize(X3,sK6(X0))],[f49]) ).
fof(f121,plain,
occurrence_of(sK2,tptp0),
inference(cnf_transformation,[],[f91]) ).
fof(f123,plain,
! [X2,X1] :
( sP0(X1,X2)
| min_precedes(X1,sK3(X1),tptp0)
| ~ leaf_occ(X2,sK2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f127,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| leaf_occ(sK6(X0),X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f142,plain,
! [X2,X3,X0,X1] :
( ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,X2)
| ~ min_precedes(X1,X3,X2) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i] :
( sP0(X1,X0)
| min_precedes(X1,sK3(X1),tptp0)
| ~ leaf_occ(X0,sK2) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_55,negated_conjecture,
occurrence_of(sK2,tptp0),
inference(cnf_transformation,[],[f121]) ).
tcf(c_64,plain,
! [X0: $i] :
( leaf_occ(sK6(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ leaf_occ(X0,X3)
| ~ occurrence_of(X3,X2)
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f142]) ).
fof(f86,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(f87,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,[],[f48,f86]) ).
fof(f88,plain,
! [X1,X2] :
( ~ sP0(X1,X2)
| ( occurrence_of(X2,tptp2)
& ? [X4] :
( min_precedes(X1,X4,tptp0)
& occurrence_of(X4,tptp1) ) ) ),
inference(nnf_transformation,[],[f86]) ).
fof(f89,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( occurrence_of(X1,tptp2)
& ? [X2] :
( min_precedes(X0,X2,tptp0)
& occurrence_of(X2,tptp1) ) ) ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( occurrence_of(X1,tptp2)
& min_precedes(X0,sK1(X0),tptp0)
& occurrence_of(sK1(X0),tptp1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0))],[f89]) ).
fof(f119,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| min_precedes(X0,sK1(X0),tptp0) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( min_precedes(X0,sK1(X0),tptp0)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_4328,plain,
! [X0: $i,X1: $i] :
( min_precedes(X1,sK3(X1),tptp0)
| min_precedes(X1,sK1(X1),tptp0)
| ~ leaf_occ(X0,sK2) ),
inference(superposition,[status(thm)],[c_53,c_50]) ).
tcf(c_4398,plain,
! [X0: $i] :
( min_precedes(X0,sK3(X0),tptp0)
| min_precedes(X0,sK1(X0),tptp0)
| ~ occurrence_of(sK2,tptp0) ),
inference(superposition,[status(thm)],[c_64,c_4328]) ).
tcf(c_4399,plain,
! [X0: $i] :
( min_precedes(X0,sK3(X0),tptp0)
| min_precedes(X0,sK1(X0),tptp0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4398,c_55]) ).
tcf(c_5023,plain,
! [X0: $i,X1: $i] :
( min_precedes(X0,sK1(X0),tptp0)
| ~ occurrence_of(X1,tptp0)
| ~ leaf_occ(X0,X1) ),
inference(superposition,[status(thm)],[c_4399,c_73]) ).
tcf(c_5254,plain,
! [X0: $i,X1: $i] :
( ~ occurrence_of(X1,tptp0)
| ~ leaf_occ(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5023,c_73]) ).
tcf(c_5261,plain,
! [X0: $i] : ~ occurrence_of(X0,tptp0),
inference(backward_subsumption_resolution,[status(thm)],[c_64,c_5254]) ).
tcf(c_5262,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_55,c_5261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 06:27:28 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 4.51/1.32 % SZS status Started for theBenchmark.p
% 4.51/1.32 % SZS status Theorem for theBenchmark.p
% 4.51/1.32
% 4.51/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.51/1.32
% 4.51/1.32 % ------ iProver source info
% 4.51/1.32
% 4.51/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 4.51/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.51/1.32 % git: non_committed_changes: false
% 4.51/1.32
% 4.51/1.32 % ------ Parsing...
% 4.51/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.51/1.32
% 4.51/1.32 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.51/1.32
% 4.51/1.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.51/1.32
% 4.51/1.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.51/1.32 % ------ Proving...
% 4.51/1.32 % ------ Problem Properties
% 4.51/1.32
% 4.51/1.32 %
% 4.51/1.32 % clauses 83
% 4.51/1.32 % conjectures 4
% 4.51/1.32 % EPR 43
% 4.51/1.32 % Horn 66
% 4.51/1.32 % unary 13
% 4.51/1.32 % binary 41
% 4.51/1.32 % lits 193
% 4.51/1.32 % lits eq 10
% 4.51/1.32 % fd_pure 0
% 4.51/1.32 % fd_pseudo 0
% 4.51/1.32 % fd_cond 0
% 4.51/1.32 % fd_pseudo_cond 4
% 4.51/1.32 % AC symbols 0
% 4.51/1.32
% 4.51/1.32 % ------ Schedule dynamic 5 is on
% 4.51/1.32
% 4.51/1.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.51/1.32
% 4.51/1.32
% 4.51/1.32 % ------
% 4.51/1.32 % Current options:
% 4.51/1.32 % ------
% 4.51/1.32
% 4.51/1.32
% 4.51/1.32 %
% 4.51/1.32
% 4.51/1.32 % ------ Proving...
% 4.51/1.32 %
% 4.51/1.32
% 4.51/1.32 % SZS status Theorem for theBenchmark.p
% 4.51/1.32
% 4.51/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.51/1.32
% 4.51/1.32
%------------------------------------------------------------------------------