%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET810+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 : n004.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 3.31s 1.20s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f36ERROR: Could not build tree for root c_734ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
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,X1] :
( ( member(X1,on)
& member(X0,on) )
=> ~ ( member(X1,X0)
& member(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV3) ).
fof(f21,negated_conjecture,
~ ! [X0,X1] :
( ( member(X1,on)
& member(X0,on) )
=> ~ ( member(X1,X0)
& member(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f25,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(f26,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(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(flattening,[],[f26]) ).
fof(f33,plain,
? [X0,X1] :
( member(X1,on)
& member(X0,on)
& member(X1,X0)
& member(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f34,plain,
? [X0,X1] :
( member(X1,on)
& member(X0,on)
& member(X1,X0)
& member(X0,X1) ),
inference(flattening,[],[f33]) ).
fof(f37,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,[],[f23]) ).
fof(f38,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,[],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK1(X0,X1),X0)
& ~ member(sK1(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f38]) ).
fof(f56,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,[],[f25]) ).
fof(f57,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,[],[f56]) ).
fof(f58,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,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ( ~ member(X0,on)
| ( ! [X2] :
( ~ member(X2,X0)
| subset(X2,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) )
& ( ( member(sK4(X0),X0)
& ~ subset(sK4(X0),X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0)
| member(X0,on) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f58]) ).
fof(f60,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,[],[f27]) ).
fof(f61,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,[],[f60]) ).
fof(f62,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,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ( ~ strict_well_order(X0,X1)
| ( ! [X5] :
( ! [X7] : ~ member(X7,X5)
| ~ subset(X5,X1)
| least(sK7(X0,X5),X0,X5) )
& strict_order(X0,X1) ) )
& ( ( member(sK6(X0,X1),sK5(X0,X1))
& subset(sK5(X0,X1),X1)
& ! [X3] : ~ least(X3,X0,sK5(X0,X1)) )
| ~ strict_order(X0,X1)
| strict_well_order(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X2,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X6,sK7(X0,X5))],[f62]) ).
fof(f68,plain,
! [X0,X1] :
( ( ~ apply(member_predicate,X0,X1)
| member(X0,X1) )
& ( ~ member(X0,X1)
| apply(member_predicate,X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f72,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,[],[f36]) ).
fof(f73,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,[],[f72]) ).
fof(f74,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,[],[f73]) ).
fof(f75,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(sK13(X0,X1),X1)
& member(sK12(X0,X1),X1)
& apply(X0,sK13(X0,X1),sK12(X0,X1))
& apply(X0,sK12(X0,X1),sK13(X0,X1)) )
| strict_order(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X2,sK12(X0,X1)),skolemize(X3,sK13(X0,X1))],[f74]) ).
fof(f79,plain,
( member(sK15,on)
& member(sK14,on)
& member(sK15,sK14)
& member(sK14,sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X1,sK15)],[f34]) ).
fof(f80,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f106,plain,
! [X2,X0] :
( ~ member(X0,on)
| ~ member(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f107,plain,
! [X0] :
( ~ member(X0,on)
| strict_well_order(member_predicate,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f112,plain,
! [X0,X1] :
( ~ strict_well_order(X0,X1)
| strict_order(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f122,plain,
! [X0,X1] :
( ~ member(X0,X1)
| apply(member_predicate,X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f131,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,[],[f75]) ).
fof(f142,plain,
member(sK15,on),
inference(cnf_transformation,[],[f79]) ).
fof(f143,plain,
member(sK14,on),
inference(cnf_transformation,[],[f79]) ).
fof(f144,plain,
member(sK15,sK14),
inference(cnf_transformation,[],[f79]) ).
fof(f145,plain,
member(sK14,sK15),
inference(cnf_transformation,[],[f79]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_78,plain,
! [X0: $i] :
( strict_well_order(member_predicate,X0)
| ~ member(X0,on) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(X1,on)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( strict_order(X0,X1)
| ~ strict_well_order(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] :
( apply(member_predicate,X0,X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_103,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,[],[f131]) ).
tcf(c_111,negated_conjecture,
member(sK14,sK15),
inference(cnf_transformation,[],[f145]) ).
tcf(c_112,negated_conjecture,
member(sK15,sK14),
inference(cnf_transformation,[],[f144]) ).
tcf(c_113,negated_conjecture,
member(sK14,on),
inference(cnf_transformation,[],[f143]) ).
tcf(c_114,negated_conjecture,
member(sK15,on),
inference(cnf_transformation,[],[f142]) ).
tcf(c_138,plain,
( subset(sK15,sK14)
| ~ member(sK14,on) ),
inference(superposition,[status(thm)],[c_112,c_79]) ).
tcf(c_177,plain,
( subset(sK15,sK14)
| ~ member(sK14,on) ),
inference(superposition,[status(thm)],[c_112,c_79]) ).
tcf(c_186,plain,
! [X0: $i] :
( member(sK14,X0)
| ~ subset(sK15,X0) ),
inference(superposition,[status(thm)],[c_111,c_51]) ).
tcf(c_208,plain,
subset(sK15,sK14),
inference(global_subsumption_just,[status(thm)],[c_177,c_113,c_138]) ).
tcf(c_239,plain,
member(sK14,sK14),
inference(superposition,[status(thm)],[c_208,c_186]) ).
tcf(c_553,plain,
strict_well_order(member_predicate,sK15),
inference(superposition,[status(thm)],[c_114,c_78]) ).
tcf(c_570,plain,
( subset(sK15,sK14)
| ~ member(sK14,on) ),
inference(superposition,[status(thm)],[c_112,c_79]) ).
tcf(c_579,plain,
! [X0: $i] :
( member(sK14,X0)
| ~ subset(sK15,X0) ),
inference(superposition,[status(thm)],[c_111,c_51]) ).
tcf(c_593,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ strict_order(member_predicate,X2)
| ~ member(X1,X2)
| ~ member(X1,X0)
| ~ member(X0,X2)
| ~ apply(member_predicate,X0,X1) ),
inference(superposition,[status(thm)],[c_90,c_103]) ).
tcf(c_595,plain,
strict_order(member_predicate,sK15),
inference(superposition,[status(thm)],[c_553,c_83]) ).
tcf(c_605,plain,
subset(sK15,sK14),
inference(global_subsumption_just,[status(thm)],[c_570,c_113,c_138]) ).
tcf(c_638,plain,
member(sK14,sK14),
inference(superposition,[status(thm)],[c_605,c_579]) ).
tcf(c_653,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ strict_order(member_predicate,X2)
| ~ member(X1,X2)
| ~ member(X1,X0)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_90,c_593]) ).
tcf(c_691,plain,
! [X0: $i] :
( ~ member(sK14,sK14)
| ~ strict_order(member_predicate,X0)
| ~ member(sK14,X0) ),
inference(superposition,[status(thm)],[c_638,c_653]) ).
tcf(c_724,plain,
! [X0: $i] :
( ~ member(sK14,X0)
| ~ strict_order(member_predicate,X0) ),
inference(global_subsumption_just,[status(thm)],[c_691,c_239,c_691]) ).
tcf(c_725,plain,
! [X0: $i] :
( ~ strict_order(member_predicate,X0)
| ~ member(sK14,X0) ),
inference(renaming,[status(thm)],[c_724]) ).
tcf(c_731,plain,
~ strict_order(member_predicate,sK15),
inference(superposition,[status(thm)],[c_111,c_725]) ).
tcf(c_734,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_595,c_731]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET810+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n004.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 12:01:26 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 3.31/1.20 % SZS status Started for theBenchmark.p
% 3.31/1.20 % SZS status Theorem for theBenchmark.p
% 3.31/1.20
% 3.31/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.31/1.20
% 3.31/1.20 % ------ iProver source info
% 3.31/1.20
% 3.31/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.31/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.31/1.20 % git: non_committed_changes: false
% 3.31/1.20
% 3.31/1.20 % ------ Parsing...
% 3.31/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.31/1.20 % ------ Proving...
% 3.31/1.20 % ------ Problem Properties
% 3.31/1.20
% 3.31/1.20 %
% 3.31/1.20 % clauses 66
% 3.31/1.20 % conjectures 4
% 3.31/1.20 % EPR 18
% 3.31/1.20 % Horn 47
% 3.31/1.20 % unary 8
% 3.31/1.20 % binary 32
% 3.31/1.20 % lits 160
% 3.31/1.20 % lits eq 5
% 3.31/1.20 % fd_pure 0
% 3.31/1.20 % fd_pseudo 0
% 3.31/1.20 % fd_cond 0
% 3.31/1.20 % fd_pseudo_cond 3
% 3.31/1.20 % AC symbols 0
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% 3.31/1.20 % ------ Input Options Time Limit: Unbounded
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% 3.31/1.20
% 3.31/1.20 % ------
% 3.31/1.20 % Current options:
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% 3.31/1.20 % ------ Proving...
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% 3.31/1.20 % ------ Proving...
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% 3.31/1.20 % ------ Proving...
% 3.31/1.20 %
% 3.31/1.20
% 3.31/1.20 % ------ Proving...
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% 3.31/1.20 % ------ Proving...
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% 3.31/1.20 % SZS status Theorem for theBenchmark.p
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% 3.31/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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