%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET799+4 : 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 : n018.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 02:48:36 PM UTC 2026
% Result : Theorem 3.12s 1.48s
% Output : CNFRefutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 51 ( 17 unt; 0 def)
% Number of atoms : 164 ( 8 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 172 ( 59 ~; 51 |; 46 &)
% ( 5 <=>; 11 =>; 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 : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 135 ( 0 sgn 119 !; 16 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f14,axiom,
! [X0,X1,X2] :
( upper_bound(X2,X0,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',upper_bound) ).
fof(f20,axiom,
! [X0,X1,X2,X3] :
( least_upper_bound(X0,X1,X2,X3)
<=> ( ! [X4] :
( ( upper_bound(X4,X2,X1)
& member(X4,X3) )
=> apply(X2,X0,X4) )
& upper_bound(X0,X2,X1)
& member(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',least_upper_bound) ).
fof(f22,conjecture,
! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
=> ! [X4,X5] :
( ( least_upper_bound(X5,X3,X0,X1)
& least_upper_bound(X4,X2,X0,X1) )
=> apply(X0,X4,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV11) ).
fof(f23,negated_conjecture,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
=> ! [X4,X5] :
( ( least_upper_bound(X5,X3,X0,X1)
& least_upper_bound(X4,X2,X0,X1) )
=> apply(X0,X4,X5) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( least_upper_bound(X0,X1,X2,X3)
=> ( ! [X4] :
( ( upper_bound(X4,X2,X1)
& member(X4,X3) )
=> apply(X2,X0,X4) )
& upper_bound(X0,X2,X1)
& member(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f31,plain,
! [X0,X1,X2] :
( upper_bound(X2,X0,X1)
<=> ! [X3] :
( ~ member(X3,X1)
| apply(X0,X3,X2) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ~ least_upper_bound(X0,X1,X2,X3)
| ( ! [X4] :
( ~ upper_bound(X4,X2,X1)
| ~ member(X4,X3)
| apply(X2,X0,X4) )
& upper_bound(X0,X2,X1)
& member(X0,X1) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( ~ least_upper_bound(X0,X1,X2,X3)
| ( ! [X4] :
( ~ upper_bound(X4,X2,X1)
| ~ member(X4,X3)
| apply(X2,X0,X4) )
& upper_bound(X0,X2,X1)
& member(X0,X1) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
? [X0,X1] :
( order(X0,X1)
& ? [X2,X3] :
( subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1)
& ? [X4,X5] :
( least_upper_bound(X5,X3,X0,X1)
& least_upper_bound(X4,X2,X0,X1)
& ~ apply(X0,X4,X5) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f35,plain,
? [X0,X1] :
( order(X0,X1)
& ? [X2,X3] :
( subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1)
& ? [X4,X5] :
( least_upper_bound(X5,X3,X0,X1)
& least_upper_bound(X4,X2,X0,X1)
& ~ apply(X0,X4,X5) ) ) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f37,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f37]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( ~ upper_bound(X2,X0,X1)
| ! [X3] :
( ~ member(X3,X1)
| apply(X0,X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ apply(X0,X3,X2) )
| upper_bound(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( ~ upper_bound(X2,X0,X1)
| ! [X4] :
( ~ member(X4,X1)
| apply(X0,X4,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ apply(X0,X3,X2) )
| upper_bound(X2,X0,X1) ) ),
inference(rectify,[],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( ~ upper_bound(X2,X0,X1)
| ! [X4] :
( ~ member(X4,X1)
| apply(X0,X4,X2) ) )
& ( ( member(sK3(X0,X1,X2),X1)
& ~ apply(X0,sK3(X0,X1,X2),X2) )
| upper_bound(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f56]) ).
fof(f58,plain,
( order(sK4,sK5)
& subset(sK6,sK7)
& subset(sK7,sK5)
& subset(sK6,sK5)
& least_upper_bound(sK9,sK7,sK4,sK5)
& least_upper_bound(sK8,sK6,sK4,sK5)
& ~ apply(sK4,sK8,sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7),skolemize(X4,sK8),skolemize(X5,sK9)],[f35]) ).
fof(f59,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f88,plain,
! [X2,X0,X1,X4] :
( ~ upper_bound(X2,X0,X1)
| ~ member(X4,X1)
| apply(X0,X4,X2) ),
inference(cnf_transformation,[],[f57]) ).
fof(f92,plain,
! [X2,X3,X0,X1] :
( ~ least_upper_bound(X0,X1,X2,X3)
| upper_bound(X0,X2,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f93,plain,
! [X2,X3,X0,X1] :
( ~ least_upper_bound(X0,X1,X2,X3)
| member(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f95,plain,
subset(sK6,sK7),
inference(cnf_transformation,[],[f58]) ).
fof(f98,plain,
least_upper_bound(sK9,sK7,sK4,sK5),
inference(cnf_transformation,[],[f58]) ).
fof(f99,plain,
least_upper_bound(sK8,sK6,sK4,sK5),
inference(cnf_transformation,[],[f58]) ).
fof(f100,plain,
~ apply(sK4,sK8,sK9),
inference(cnf_transformation,[],[f58]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,X3,X0)
| ~ member(X3,X2)
| ~ upper_bound(X0,X1,X2) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X1)
| ~ least_upper_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( upper_bound(X0,X2,X1)
| ~ least_upper_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_84,negated_conjecture,
~ apply(sK4,sK8,sK9),
inference(cnf_transformation,[],[f100]) ).
tcf(c_85,negated_conjecture,
least_upper_bound(sK8,sK6,sK4,sK5),
inference(cnf_transformation,[],[f99]) ).
tcf(c_86,negated_conjecture,
least_upper_bound(sK9,sK7,sK4,sK5),
inference(cnf_transformation,[],[f98]) ).
tcf(c_89,negated_conjecture,
subset(sK6,sK7),
inference(cnf_transformation,[],[f95]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ least_upper_bound(X0,X1,X2,X3)
| member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_81]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X1)
| ~ least_upper_bound(X0,X1,X2,X3) ),
inference(renaming,[status(thm)],[c_136]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( upper_bound(X0,X2,X1)
| ~ least_upper_bound(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_82]) ).
tcf(c_634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X1)
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK6 )
| ( X0 != sK8 ) ),
inference(resolution_lifted,[status(thm)],[c_137,c_85]) ).
tcf(c_635,plain,
member(sK8,sK6),
inference(unflattening,[status(thm)],[c_634]) ).
tcf(c_651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( upper_bound(X0,X2,X1)
| ( X3 != sK5 )
| ( X2 != sK4 )
| ( X1 != sK7 )
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_168,c_86]) ).
tcf(c_652,plain,
upper_bound(sK9,sK4,sK7),
inference(unflattening,[status(thm)],[c_651]) ).
tcf(c_994,plain,
upper_bound(sK9,sK4,sK7),
inference(demodulation,[status(thm)],[c_652]) ).
tcf(c_996,plain,
member(sK8,sK6),
inference(demodulation,[status(thm)],[c_635]) ).
tcf(c_999,negated_conjecture,
subset(sK6,sK7),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_1002,negated_conjecture,
~ apply(sK4,sK8,sK9),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_2014,plain,
! [X0: $i] :
( member(sK8,X0)
| ~ subset(sK6,X0) ),
inference(superposition,[status(thm)],[c_996,c_51]) ).
tcf(c_2099,plain,
member(sK8,sK7),
inference(superposition,[status(thm)],[c_999,c_2014]) ).
tcf(c_2584,plain,
! [X0: $i] :
( apply(sK4,X0,sK9)
| ~ member(X0,sK7) ),
inference(superposition,[status(thm)],[c_994,c_80]) ).
tcf(c_2786,plain,
~ member(sK8,sK7),
inference(superposition,[status(thm)],[c_2584,c_1002]) ).
tcf(c_2791,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2786,c_2099]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET799+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.56 % Computer : n018.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.56 % CPULimit : 300
% 0.10/0.56 % WCLimit : 300
% 0.10/0.56 % DateTime : Thu Sep 24 12:02:04 UTC 2026
% 0.10/0.56 % CPUTime :
% 0.10/0.56 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.60 Running first-order theorem proving
% 0.10/0.60 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
% 0.10/0.61
% 0.10/0.61 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.61
% 0.10/0.61 % Detected problem language: tptp
% 0.15/0.63 % Proving...
% 3.12/1.48 % SZS status Started for theBenchmark.p
% 3.12/1.48 % SZS status Theorem for theBenchmark.p
% 3.12/1.48
% 3.12/1.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.12/1.48
% 3.12/1.48 % ------ iProver source info
% 3.12/1.48
% 3.12/1.48 % git: date: 2026-07-19 20:42:38 +0200
% 3.12/1.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.12/1.48 % git: non_committed_changes: false
% 3.12/1.48
% 3.12/1.48 % ------ Parsing...
% 3.12/1.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.12/1.48
% 3.12/1.48 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 3.12/1.48
% 3.12/1.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.12/1.48
% 3.12/1.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.12/1.48 % ------ Proving...
% 3.12/1.48 % ------ Problem Properties
% 3.12/1.48
% 3.12/1.48 %
% 3.12/1.48 % clauses 42
% 3.12/1.48 % conjectures 4
% 3.12/1.48 % EPR 16
% 3.12/1.48 % Horn 36
% 3.12/1.48 % unary 12
% 3.12/1.48 % binary 18
% 3.12/1.48 % lits 89
% 3.12/1.48 % lits eq 4
% 3.12/1.48 % fd_pure 0
% 3.12/1.48 % fd_pseudo 0
% 3.12/1.48 % fd_cond 0
% 3.12/1.48 % fd_pseudo_cond 3
% 3.12/1.48 % AC symbols 0
% 3.12/1.48
% 3.12/1.48 % ------ Schedule dynamic 5 is on
% 3.12/1.48
% 3.12/1.48 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.12/1.48
% 3.12/1.48
% 3.12/1.48 % ------
% 3.12/1.48 % Current options:
% 3.12/1.48 % ------
% 3.12/1.48
% 3.12/1.48
% 3.12/1.48 %
% 3.12/1.48
% 3.12/1.48 % ------ Proving...
% 3.12/1.48 %
% 3.12/1.48
% 3.12/1.48 % SZS status Theorem for theBenchmark.p
% 3.12/1.48
% 3.12/1.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.12/1.48
% 3.12/1.48
%------------------------------------------------------------------------------