%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET798+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 : n017.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 4.31s 1.30s
% Output : CNFRefutation 4.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 103 ( 2 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 103 ( 34 ~; 31 |; 25 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-3 aty)
% Number of variables : 85 ( 0 sgn 73 !; 12 ?; 21 :)
% 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(f15,axiom,
! [X0,X1,X2] :
( lower_bound(X2,X0,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',lower_bound) ).
fof(f22,conjecture,
! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
=> ! [X4] :
( lower_bound(X4,X0,X3)
=> lower_bound(X4,X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV10) ).
fof(f23,negated_conjecture,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
=> ! [X4] :
( lower_bound(X4,X0,X3)
=> lower_bound(X4,X0,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f26,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f27,plain,
? [X0,X1] :
( order(X0,X1)
& ? [X2,X3] :
( subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1)
& ? [X4] :
( lower_bound(X4,X0,X3)
& ~ lower_bound(X4,X0,X2) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f28,plain,
? [X0,X1] :
( order(X0,X1)
& ? [X2,X3] :
( subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1)
& ? [X4] :
( lower_bound(X4,X0,X3)
& ~ lower_bound(X4,X0,X2) ) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f32,plain,
! [X0,X1,X2] :
( lower_bound(X2,X0,X1)
<=> ! [X3] :
( ~ member(X3,X1)
| apply(X0,X2,X3) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f33,plain,
( order(sK0,sK1)
& subset(sK2,sK3)
& subset(sK3,sK1)
& subset(sK2,sK1)
& lower_bound(sK4,sK0,sK3)
& ~ lower_bound(sK4,sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f28]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( ~ lower_bound(X2,X0,X1)
| ! [X3] :
( ~ member(X3,X1)
| apply(X0,X2,X3) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ apply(X0,X2,X3) )
| lower_bound(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( ~ lower_bound(X2,X0,X1)
| ! [X4] :
( ~ member(X4,X1)
| apply(X0,X2,X4) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ apply(X0,X2,X3) )
| lower_bound(X2,X0,X1) ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( ~ lower_bound(X2,X0,X1)
| ! [X4] :
( ~ member(X4,X1)
| apply(X0,X2,X4) ) )
& ( ( member(sK5(X0,X1,X2),X1)
& ~ apply(X0,X2,sK5(X0,X1,X2)) )
| lower_bound(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f35]) ).
fof(f38,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f33]) ).
fof(f41,plain,
lower_bound(sK4,sK0,sK3),
inference(cnf_transformation,[],[f33]) ).
fof(f42,plain,
~ lower_bound(sK4,sK0,sK2),
inference(cnf_transformation,[],[f33]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f47,plain,
! [X2,X0,X1,X4] :
( ~ lower_bound(X2,X0,X1)
| ~ member(X4,X1)
| apply(X0,X2,X4) ),
inference(cnf_transformation,[],[f36]) ).
fof(f48,plain,
! [X2,X0,X1] :
( member(sK5(X0,X1,X2),X1)
| lower_bound(X2,X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ apply(X0,X2,sK5(X0,X1,X2))
| lower_bound(X2,X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_49,negated_conjecture,
~ lower_bound(sK4,sK0,sK2),
inference(cnf_transformation,[],[f42]) ).
tcf(c_50,negated_conjecture,
lower_bound(sK4,sK0,sK3),
inference(cnf_transformation,[],[f41]) ).
tcf(c_53,negated_conjecture,
subset(sK2,sK3),
inference(cnf_transformation,[],[f38]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( lower_bound(X1,X0,X2)
| ~ apply(X0,X1,sK5(X0,X2,X1)) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( lower_bound(X2,X0,X1)
| member(sK5(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,X0,X3)
| ~ member(X3,X2)
| ~ lower_bound(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_55]) ).
tcf(c_208,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_207]) ).
tcf(c_755,plain,
! [X0: $i,X1: $i] :
( lower_bound(X1,X0,sK2)
| member(sK5(X0,sK2,X1),sK3) ),
inference(superposition,[status(thm)],[c_60,c_208]) ).
tcf(c_777,plain,
! [X0: $i] :
( apply(sK0,sK4,X0)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_50,c_61]) ).
tcf(c_784,plain,
! [X0: $i] :
( lower_bound(sK4,sK0,X0)
| ~ member(sK5(sK0,X0,sK4),sK3) ),
inference(superposition,[status(thm)],[c_777,c_59]) ).
tcf(c_820,plain,
lower_bound(sK4,sK0,sK2),
inference(superposition,[status(thm)],[c_755,c_784]) ).
tcf(c_821,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_820,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET798+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n017.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 11:54:01 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 4.31/1.30 % SZS status Started for theBenchmark.p
% 4.31/1.30 % SZS status Theorem for theBenchmark.p
% 4.31/1.30
% 4.31/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.31/1.30
% 4.31/1.30 % ------ iProver source info
% 4.31/1.30
% 4.31/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.31/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.31/1.30 % git: non_committed_changes: false
% 4.31/1.30
% 4.31/1.30 % ------ Parsing...
% 4.31/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.31/1.30
% 4.31/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 4.31/1.30
% 4.31/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.31/1.30
% 4.31/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.31/1.30 % ------ Proving...
% 4.31/1.30 % ------ Problem Properties
% 4.31/1.30
% 4.31/1.30 %
% 4.31/1.30 % clauses 11
% 4.31/1.30 % conjectures 2
% 4.31/1.30 % EPR 9
% 4.31/1.30 % Horn 10
% 4.31/1.30 % unary 2
% 4.31/1.30 % binary 6
% 4.31/1.30 % lits 28
% 4.31/1.30 % lits eq 1
% 4.31/1.30 % fd_pure 0
% 4.31/1.30 % fd_pseudo 0
% 4.31/1.30 % fd_cond 0
% 4.31/1.30 % fd_pseudo_cond 1
% 4.31/1.30 % AC symbols 0
% 4.31/1.30
% 4.31/1.30 % ------ Schedule dynamic 5 is on
% 4.31/1.30
% 4.31/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.31/1.30
% 4.31/1.30
% 4.31/1.30 % ------
% 4.31/1.30 % Current options:
% 4.31/1.30 % ------
% 4.31/1.30
% 4.31/1.30
% 4.31/1.30 %
% 4.31/1.30
% 4.31/1.30 % ------ Proving...
% 4.31/1.30 %
% 4.31/1.30
% 4.31/1.30 % SZS status Theorem for theBenchmark.p
% 4.31/1.30
% 4.31/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.31/1.30
% 4.31/1.30
%------------------------------------------------------------------------------