%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : PRO011+4 : 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 : n001.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 02:31:36 PM UTC 2026
% Result : Theorem 2.55s 1.50s
% Output : CNFRefutation 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 8 unt; 1 def)
% Number of atoms : 193 ( 10 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 207 ( 68 ~; 71 |; 59 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn 102 !; 23 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1,X2] :
( ( occurrence_of(X0,X2)
& occurrence_of(X0,X1) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( leaf_occ(X1,X0)
& occurrence_of(X0,X2) )
=> ~ ? [X3] : min_precedes(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
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/sandbox2/benchmark/theBenchmark.p',sos_32) ).
fof(f45,axiom,
tptp1 != tptp2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_44) ).
fof(f46,conjecture,
! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2] :
( ( occurrence_of(X2,tptp2)
=> ~ ? [X4] :
( min_precedes(X1,X4,tptp0)
& subactivity_occurrence(X4,X0)
& occurrence_of(X4,tptp1) ) )
& ( occurrence_of(X2,tptp1)
=> ~ ? [X3] :
( min_precedes(X1,X3,tptp0)
& subactivity_occurrence(X3,X0)
& occurrence_of(X3,tptp2) ) )
& leaf_occ(X2,X0) ) ),
file('/export/starexec/sandbox2/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)
& subactivity_occurrence(X4,X0)
& occurrence_of(X4,tptp1) ) )
& ( occurrence_of(X2,tptp1)
=> ~ ? [X3] :
( min_precedes(X1,X3,tptp0)
& subactivity_occurrence(X3,X0)
& occurrence_of(X3,tptp2) ) )
& leaf_occ(X2,X0) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1)
| X1 = X2 ),
inference(ennf_transformation,[],[f9]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1)
| X1 = X2 ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,X2)
| ! [X3] : ~ min_precedes(X1,X3,X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,X2)
| ! [X3] : ~ min_precedes(X1,X3,X2) ),
inference(flattening,[],[f69]) ).
fof(f96,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(f97,plain,
? [X0] :
( occurrence_of(X0,tptp0)
& ! [X1,X2] :
( ( occurrence_of(X2,tptp2)
& ? [X4] :
( min_precedes(X1,X4,tptp0)
& subactivity_occurrence(X4,X0)
& occurrence_of(X4,tptp1) ) )
| ( occurrence_of(X2,tptp1)
& ? [X3] :
( min_precedes(X1,X3,tptp0)
& subactivity_occurrence(X3,X0)
& occurrence_of(X3,tptp2) ) )
| ~ leaf_occ(X2,X0) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f124,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| ( leaf_occ(sK15(X0),X0)
& next_subocc(sK14(X0),sK15(X0),tptp0)
& ( occurrence_of(sK15(X0),tptp2)
| occurrence_of(sK15(X0),tptp1) )
& next_subocc(sK13(X0),sK14(X0),tptp0)
& occurrence_of(sK14(X0),tptp4)
& root_occ(sK13(X0),X0)
& occurrence_of(sK13(X0),tptp3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X1,sK13(X0)),skolemize(X2,sK14(X0)),skolemize(X3,sK15(X0))],[f96]) ).
fof(f128,plain,
( occurrence_of(sK17,tptp0)
& ! [X1,X2] :
( sP0(sK17,X1,X2)
| ( occurrence_of(X2,tptp1)
& min_precedes(X1,sK18(X1),tptp0)
& subactivity_occurrence(sK18(X1),sK17)
& occurrence_of(sK18(X1),tptp2) )
| ~ leaf_occ(X2,sK17) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18]),skolemize(X0,sK17),skolemize(X3,sK18(X1))],[f99]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1)
| X1 = X2 ),
inference(cnf_transformation,[],[f68]) ).
fof(f142,plain,
! [X2,X3,X0,X1] :
( ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,X2)
| ~ min_precedes(X1,X3,X2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f184,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| leaf_occ(sK15(X0),X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f201,plain,
tptp1 != tptp2,
inference(cnf_transformation,[],[f45]) ).
fof(f206,plain,
occurrence_of(sK17,tptp0),
inference(cnf_transformation,[],[f128]) ).
fof(f207,plain,
! [X2,X1] :
( sP0(sK17,X1,X2)
| occurrence_of(X2,tptp1)
| ~ leaf_occ(X2,sK17) ),
inference(cnf_transformation,[],[f128]) ).
fof(f208,plain,
! [X2,X1] :
( sP0(sK17,X1,X2)
| min_precedes(X1,sK18(X1),tptp0)
| ~ leaf_occ(X2,sK17) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_62,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]) ).
tcf(c_110,plain,
! [X0: $i] :
( leaf_occ(sK15(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_121,plain,
tptp1 != tptp2,
inference(cnf_transformation,[],[f201]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i] :
( sP0(sK17,X1,X0)
| min_precedes(X1,sK18(X1),tptp0)
| ~ leaf_occ(X0,sK17) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_129,negated_conjecture,
! [X0: $i,X1: $i] :
( occurrence_of(X0,tptp1)
| sP0(sK17,X1,X0)
| ~ leaf_occ(X0,sK17) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_130,negated_conjecture,
occurrence_of(sK17,tptp0),
inference(cnf_transformation,[],[f206]) ).
tcf(c_4573,negated_conjecture,
occurrence_of(sK17,tptp0),
inference(demodulation,[status(thm)],[c_130]) ).
tcf(c_4574,negated_conjecture,
! [X0: $i,X1: $i] :
( occurrence_of(X0,tptp1)
| sP0(sK17,X1,X0)
| ~ leaf_occ(X0,sK17) ),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_4575,negated_conjecture,
! [X0: $i,X1: $i] :
( sP0(sK17,X1,X0)
| min_precedes(X1,sK18(X1),tptp0)
| ~ leaf_occ(X0,sK17) ),
inference(demodulation,[status(thm)],[c_128]) ).
tcf(c_6509,plain,
! [X0: $i] :
( ( tptp1 = tptp2 )
| ~ occurrence_of(X0,tptp2)
| ~ occurrence_of(X0,tptp1) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_7526,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(sK17,X0,X2)
| ~ leaf_occ(X2,sK17)
| ~ occurrence_of(X1,tptp0)
| ~ leaf_occ(X0,X1) ),
inference(superposition,[status(thm)],[c_4575,c_62]) ).
tcf(c_8094,plain,
( ( tptp1 = tptp2 )
| ~ occurrence_of(sK15(sK17),tptp2)
| ~ occurrence_of(sK15(sK17),tptp1) ),
inference(instantiation,[status(thm)],[c_6509]) ).
fof(f98,definition,
! [X0,X1,X2] :
( ~ sP0(X0,X1,X2)
| ( occurrence_of(X2,tptp2)
& ? [X4] :
( min_precedes(X1,X4,tptp0)
& subactivity_occurrence(X4,X0)
& occurrence_of(X4,tptp1) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f99,plain,
? [X0] :
( occurrence_of(X0,tptp0)
& ! [X1,X2] :
( sP0(X0,X1,X2)
| ( occurrence_of(X2,tptp1)
& ? [X3] :
( min_precedes(X1,X3,tptp0)
& subactivity_occurrence(X3,X0)
& occurrence_of(X3,tptp2) ) )
| ~ leaf_occ(X2,X0) ) ),
inference(definition_folding,[],[f97,f98]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ~ sP0(X0,X1,X2)
| ( occurrence_of(X2,tptp2)
& ? [X4] :
( min_precedes(X1,X4,tptp0)
& subactivity_occurrence(X4,X0)
& occurrence_of(X4,tptp1) ) ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ~ sP0(X0,X1,X2)
| ( occurrence_of(X2,tptp2)
& ? [X3] :
( min_precedes(X1,X3,tptp0)
& subactivity_occurrence(X3,X0)
& occurrence_of(X3,tptp1) ) ) ),
inference(rectify,[],[f125]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ~ sP0(X0,X1,X2)
| ( occurrence_of(X2,tptp2)
& min_precedes(X1,sK16(X0,X1),tptp0)
& subactivity_occurrence(sK16(X0,X1),X0)
& occurrence_of(sK16(X0,X1),tptp1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X3,sK16(X0,X1))],[f126]) ).
fof(f202,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| occurrence_of(X2,tptp2) ),
inference(cnf_transformation,[],[f127]) ).
fof(f203,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| min_precedes(X1,sK16(X0,X1),tptp0) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i] :
( min_precedes(X1,sK16(X0,X1),tptp0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i] :
( occurrence_of(X2,tptp2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_5774,plain,
! [X0: $i,X1: $i] :
( occurrence_of(X0,tptp2)
| min_precedes(X1,sK18(X1),tptp0)
| ~ leaf_occ(X0,sK17) ),
inference(superposition,[status(thm)],[c_4575,c_125]) ).
tcf(c_5872,plain,
! [X0: $i] :
( occurrence_of(sK15(sK17),tptp2)
| min_precedes(X0,sK18(X0),tptp0)
| ~ occurrence_of(sK17,tptp0) ),
inference(superposition,[status(thm)],[c_110,c_5774]) ).
tcf(c_5873,plain,
! [X0: $i] :
( occurrence_of(sK15(sK17),tptp2)
| min_precedes(X0,sK18(X0),tptp0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5872,c_4573]) ).
tcf(c_7076,plain,
! [X0: $i,X1: $i] :
( occurrence_of(X0,tptp1)
| min_precedes(X1,sK16(sK17,X1),tptp0)
| ~ leaf_occ(X0,sK17) ),
inference(superposition,[status(thm)],[c_4574,c_124]) ).
tcf(c_7337,plain,
! [X0: $i] :
( occurrence_of(sK15(sK17),tptp1)
| min_precedes(X0,sK16(sK17,X0),tptp0)
| ~ occurrence_of(sK17,tptp0) ),
inference(superposition,[status(thm)],[c_110,c_7076]) ).
tcf(c_7338,plain,
! [X0: $i] :
( occurrence_of(sK15(sK17),tptp1)
| min_precedes(X0,sK16(sK17,X0),tptp0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7337,c_4573]) ).
tcf(c_7531,plain,
! [X0: $i,X1: $i] :
( occurrence_of(sK15(sK17),tptp2)
| ~ occurrence_of(X1,tptp0)
| ~ leaf_occ(X0,X1) ),
inference(superposition,[status(thm)],[c_5873,c_62]) ).
tcf(c_7533,plain,
! [X0: $i,X1: $i] :
( occurrence_of(sK15(sK17),tptp1)
| ~ occurrence_of(X1,tptp0)
| ~ leaf_occ(X0,X1) ),
inference(superposition,[status(thm)],[c_7338,c_62]) ).
tcf(c_8110,plain,
! [X0: $i,X1: $i] :
( ~ occurrence_of(X1,tptp0)
| ~ leaf_occ(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_7526,c_121,c_7533,c_7531,c_8094]) ).
tcf(c_8117,plain,
! [X0: $i] : ~ occurrence_of(X0,tptp0),
inference(backward_subsumption_resolution,[status(thm)],[c_110,c_8110]) ).
tcf(c_8118,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_4573,c_8117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO011+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.58 % Computer : n001.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Thu Sep 24 06:34:54 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.59 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.61 Running first-order theorem proving
% 0.11/0.62 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
% 0.11/0.63
% 0.11/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.63
% 0.14/0.63 % Detected problem language: tptp
% 0.14/0.64 % Proving...
% 2.55/1.50 % SZS status Started for theBenchmark.p
% 2.55/1.50 % SZS status Theorem for theBenchmark.p
% 2.55/1.50
% 2.55/1.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.55/1.50
% 2.55/1.50 % ------ iProver source info
% 2.55/1.50
% 2.55/1.50 % git: date: 2026-07-19 20:42:38 +0200
% 2.55/1.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.55/1.50 % git: non_committed_changes: false
% 2.55/1.50
% 2.55/1.50 % ------ Parsing...
% 2.55/1.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.55/1.50
% 2.55/1.50 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.55/1.50
% 2.55/1.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.55/1.50
% 2.55/1.50 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.55/1.50 % ------ Proving...
% 2.55/1.50 % ------ Problem Properties
% 2.55/1.50
% 2.55/1.50 %
% 2.55/1.50 % clauses 81
% 2.55/1.50 % conjectures 5
% 2.55/1.50 % EPR 47
% 2.55/1.50 % Horn 63
% 2.55/1.50 % unary 12
% 2.55/1.50 % binary 38
% 2.55/1.50 % lits 200
% 2.55/1.50 % lits eq 12
% 2.55/1.50 % fd_pure 0
% 2.55/1.50 % fd_pseudo 0
% 2.55/1.50 % fd_cond 0
% 2.55/1.50 % fd_pseudo_cond 6
% 2.55/1.50 % AC symbols 0
% 2.55/1.50
% 2.55/1.50 % ------ Schedule dynamic 5 is on
% 2.55/1.50
% 2.55/1.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.55/1.50
% 2.55/1.50
% 2.55/1.50 % ------
% 2.55/1.50 % Current options:
% 2.55/1.50 % ------
% 2.55/1.50
% 2.55/1.50
% 2.55/1.50 %
% 2.55/1.50
% 2.55/1.50 % ------ Proving...
% 2.55/1.50 %
% 2.55/1.50
% 2.55/1.50 % SZS status Theorem for theBenchmark.p
% 2.55/1.50
% 2.55/1.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.21/1.50
% 4.21/1.50
%------------------------------------------------------------------------------