%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET809+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 02:48:38 PM UTC 2026
% Result : Theorem 3.07s 1.22s
% Output : CNFRefutation 3.07s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f34ERROR: Could not build tree for root c_9378ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( member(X0,on)
<=> ( ! [X1] :
( member(X1,X0)
=> subset(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',ordinal_number) ).
fof(f13,axiom,
! [X0,X1] :
( strict_well_order(X0,X1)
<=> ( ! [X2] :
( ( ? [X3] : member(X3,X2)
& subset(X2,X1) )
=> ? [X4] : least(X4,X0,X2) )
& strict_order(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',strict_well_order) ).
fof(f15,axiom,
! [X0,X1] :
( apply(member_predicate,X0,X1)
<=> member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',rel_member) ).
fof(f20,conjecture,
! [X0] :
( member(X0,on)
=> ~ member(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV2) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> ~ member(X0,X0) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f23,plain,
? [X0] :
( member(X0,on)
& member(X0,X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f24,plain,
! [X0] :
( member(X0,on)
<=> ( ! [X1] :
( ~ member(X1,X0)
| subset(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f27,plain,
! [X0,X1] :
( strict_well_order(X0,X1)
<=> ( ! [X2] :
( ! [X3] : ~ member(X3,X2)
| ~ subset(X2,X1)
| ? [X4] : least(X4,X0,X2) )
& strict_order(X0,X1) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f28,plain,
! [X0,X1] :
( strict_well_order(X0,X1)
<=> ( ! [X2] :
( ! [X3] : ~ member(X3,X2)
| ~ subset(X2,X1)
| ? [X4] : least(X4,X0,X2) )
& strict_order(X0,X1) ) ),
inference(flattening,[],[f27]) ).
fof(f35,plain,
( member(sK1,on)
& member(sK1,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f23]) ).
fof(f36,plain,
! [X0] :
( ( ~ member(X0,on)
| ( ! [X1] :
( ~ member(X1,X0)
| subset(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) )
& ( ? [X1] :
( member(X1,X0)
& ~ subset(X1,X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0)
| member(X0,on) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f37,plain,
! [X0] :
( ( ~ member(X0,on)
| ( ! [X1] :
( ~ member(X1,X0)
| subset(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) )
& ( ? [X1] :
( member(X1,X0)
& ~ subset(X1,X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0)
| member(X0,on) ) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0] :
( ( ~ member(X0,on)
| ( ! [X2] :
( ~ member(X2,X0)
| subset(X2,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) )
& ( ? [X1] :
( member(X1,X0)
& ~ subset(X1,X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0)
| member(X0,on) ) ),
inference(rectify,[],[f37]) ).
fof(f39,plain,
! [X0] :
( ( ~ member(X0,on)
| ( ! [X2] :
( ~ member(X2,X0)
| subset(X2,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) )
& ( ( member(sK2(X0),X0)
& ~ subset(sK2(X0),X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0)
| member(X0,on) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f38]) ).
fof(f43,plain,
! [X0,X1] :
( ( ~ strict_well_order(X0,X1)
| ( ! [X2] :
( ! [X3] : ~ member(X3,X2)
| ~ subset(X2,X1)
| ? [X4] : least(X4,X0,X2) )
& strict_order(X0,X1) ) )
& ( ? [X2] :
( ? [X3] : member(X3,X2)
& subset(X2,X1)
& ! [X4] : ~ least(X4,X0,X2) )
| ~ strict_order(X0,X1)
| strict_well_order(X0,X1) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f44,plain,
! [X0,X1] :
( ( ~ strict_well_order(X0,X1)
| ( ! [X2] :
( ! [X3] : ~ member(X3,X2)
| ~ subset(X2,X1)
| ? [X4] : least(X4,X0,X2) )
& strict_order(X0,X1) ) )
& ( ? [X2] :
( ? [X3] : member(X3,X2)
& subset(X2,X1)
& ! [X4] : ~ least(X4,X0,X2) )
| ~ strict_order(X0,X1)
| strict_well_order(X0,X1) ) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ( ~ strict_well_order(X0,X1)
| ( ! [X5] :
( ! [X7] : ~ member(X7,X5)
| ~ subset(X5,X1)
| ? [X6] : least(X6,X0,X5) )
& strict_order(X0,X1) ) )
& ( ? [X2] :
( ? [X4] : member(X4,X2)
& subset(X2,X1)
& ! [X3] : ~ least(X3,X0,X2) )
| ~ strict_order(X0,X1)
| strict_well_order(X0,X1) ) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ( ~ strict_well_order(X0,X1)
| ( ! [X5] :
( ! [X7] : ~ member(X7,X5)
| ~ subset(X5,X1)
| least(sK6(X0,X5),X0,X5) )
& strict_order(X0,X1) ) )
& ( ( member(sK5(X0,X1),sK4(X0,X1))
& subset(sK4(X0,X1),X1)
& ! [X3] : ~ least(X3,X0,sK4(X0,X1)) )
| ~ strict_order(X0,X1)
| strict_well_order(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X2,sK4(X0,X1)),skolemize(X4,sK5(X0,X1)),skolemize(X6,sK6(X0,X5))],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ( ~ apply(member_predicate,X0,X1)
| member(X0,X1) )
& ( ~ member(X0,X1)
| apply(member_predicate,X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f51,plain,
! [X0,X1] :
( ( ~ strict_order(X0,X1)
| ( sP0(X0,X1)
& ! [X2,X3] :
( ~ member(X3,X1)
| ~ member(X2,X1)
| ~ apply(X0,X3,X2)
| ~ apply(X0,X2,X3) ) ) )
& ( ~ sP0(X0,X1)
| ? [X2,X3] :
( member(X3,X1)
& member(X2,X1)
& apply(X0,X3,X2)
& apply(X0,X2,X3) )
| strict_order(X0,X1) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f52,plain,
! [X0,X1] :
( ( ~ strict_order(X0,X1)
| ( sP0(X0,X1)
& ! [X2,X3] :
( ~ member(X3,X1)
| ~ member(X2,X1)
| ~ apply(X0,X3,X2)
| ~ apply(X0,X2,X3) ) ) )
& ( ~ sP0(X0,X1)
| ? [X2,X3] :
( member(X3,X1)
& member(X2,X1)
& apply(X0,X3,X2)
& apply(X0,X2,X3) )
| strict_order(X0,X1) ) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ( ~ strict_order(X0,X1)
| ( sP0(X0,X1)
& ! [X4,X5] :
( ~ member(X5,X1)
| ~ member(X4,X1)
| ~ apply(X0,X5,X4)
| ~ apply(X0,X4,X5) ) ) )
& ( ~ sP0(X0,X1)
| ? [X2,X3] :
( member(X3,X1)
& member(X2,X1)
& apply(X0,X3,X2)
& apply(X0,X2,X3) )
| strict_order(X0,X1) ) ),
inference(rectify,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ( ~ strict_order(X0,X1)
| ( sP0(X0,X1)
& ! [X4,X5] :
( ~ member(X5,X1)
| ~ member(X4,X1)
| ~ apply(X0,X5,X4)
| ~ apply(X0,X4,X5) ) ) )
& ( ~ sP0(X0,X1)
| ( member(sK11(X0,X1),X1)
& member(sK10(X0,X1),X1)
& apply(X0,sK11(X0,X1),sK10(X0,X1))
& apply(X0,sK10(X0,X1),sK11(X0,X1)) )
| strict_order(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X2,sK10(X0,X1)),skolemize(X3,sK11(X0,X1))],[f53]) ).
fof(f60,plain,
member(sK1,on),
inference(cnf_transformation,[],[f35]) ).
fof(f61,plain,
member(sK1,sK1),
inference(cnf_transformation,[],[f35]) ).
fof(f63,plain,
! [X0] :
( ~ member(X0,on)
| strict_well_order(member_predicate,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f72,plain,
! [X0,X1] :
( ~ strict_well_order(X0,X1)
| strict_order(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f77,plain,
! [X0,X1] :
( ~ member(X0,X1)
| apply(member_predicate,X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f86,plain,
! [X0,X1,X4,X5] :
( ~ strict_order(X0,X1)
| ~ member(X5,X1)
| ~ member(X4,X1)
| ~ apply(X0,X5,X4)
| ~ apply(X0,X4,X5) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_49,negated_conjecture,
member(sK1,sK1),
inference(cnf_transformation,[],[f61]) ).
tcf(c_50,negated_conjecture,
member(sK1,on),
inference(cnf_transformation,[],[f60]) ).
tcf(c_54,plain,
! [X0: $i] :
( strict_well_order(member_predicate,X0)
| ~ member(X0,on) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( strict_order(X0,X1)
| ~ strict_well_order(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( apply(member_predicate,X0,X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ strict_order(X0,X3)
| ~ member(X2,X3)
| ~ member(X1,X3)
| ~ apply(X0,X2,X1)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_3097,plain,
strict_well_order(member_predicate,sK1),
inference(superposition,[status(thm)],[c_50,c_54]) ).
tcf(c_3102,plain,
strict_order(member_predicate,sK1),
inference(superposition,[status(thm)],[c_3097,c_63]) ).
tcf(c_3432,plain,
( apply(member_predicate,sK1,sK1)
| ~ member(sK1,sK1) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_3733,plain,
! [X0: $i,X1: $i] :
( ~ member(sK1,sK1)
| ~ strict_order(X0,sK1)
| ~ member(X1,sK1)
| ~ apply(X0,sK1,X1)
| ~ apply(X0,X1,sK1) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_4077,plain,
! [X0: $i] :
( ~ member(sK1,sK1)
| ~ strict_order(X0,sK1)
| ~ apply(X0,sK1,sK1) ),
inference(instantiation,[status(thm)],[c_3733]) ).
tcf(c_9377,plain,
( ~ strict_order(member_predicate,sK1)
| ~ member(sK1,sK1)
| ~ apply(member_predicate,sK1,sK1) ),
inference(instantiation,[status(thm)],[c_4077]) ).
tcf(c_9378,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9377,c_3432,c_3102,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET809+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:05:43 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 3.07/1.22 % SZS status Started for theBenchmark.p
% 3.07/1.22 % SZS status Theorem for theBenchmark.p
% 3.07/1.22
% 3.07/1.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.07/1.22
% 3.07/1.22 % ------ iProver source info
% 3.07/1.22
% 3.07/1.22 % git: date: 2026-07-19 20:42:38 +0200
% 3.07/1.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.07/1.22 % git: non_committed_changes: false
% 3.07/1.22
% 3.07/1.22 % ------ Parsing...
% 3.07/1.22 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.07/1.22
% 3.07/1.22 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.07/1.22
% 3.07/1.22 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.07/1.22
% 3.07/1.22 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.07/1.22 % ------ Proving...
% 3.07/1.22 % ------ Problem Properties
% 3.07/1.22
% 3.07/1.22 %
% 3.07/1.22 % clauses 38
% 3.07/1.22 % conjectures 2
% 3.07/1.22 % EPR 15
% 3.07/1.22 % Horn 23
% 3.07/1.22 % unary 3
% 3.07/1.22 % binary 16
% 3.07/1.22 % lits 102
% 3.07/1.22 % lits eq 3
% 3.07/1.22 % fd_pure 0
% 3.07/1.22 % fd_pseudo 0
% 3.07/1.22 % fd_cond 0
% 3.07/1.22 % fd_pseudo_cond 2
% 3.07/1.22 % AC symbols 0
% 3.07/1.22
% 3.07/1.22 % ------ Schedule dynamic 5 is on
% 3.07/1.22
% 3.07/1.22 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.07/1.22
% 3.07/1.22
% 3.07/1.22 % ------
% 3.07/1.22 % Current options:
% 3.07/1.22 % ------
% 3.07/1.22
% 3.07/1.22
% 3.07/1.22 %
% 3.07/1.22
% 3.07/1.22 % ------ Proving...
% 3.07/1.22 %
% 3.07/1.22
% 3.07/1.22 % SZS status Theorem for theBenchmark.p
% 3.07/1.22
% 3.07/1.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.07/1.22
% 3.07/1.22
%------------------------------------------------------------------------------