%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET811+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 : n013.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 35.67s 5.80s
% Output : CNFRefutation 35.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 10 unt; 0 def)
% Number of atoms : 202 ( 2 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 228 ( 90 ~; 86 |; 38 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 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; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 120 ( 0 sgn 113 !; 7 ?; 35 :)
% 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(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
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(f15,axiom,
! [X0,X1] :
( apply(member_predicate,X0,X1)
<=> member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',rel_member) ).
fof(f18,axiom,
! [X0,X1,X2,X3] :
( member(X3,initial_segment(X0,X1,X2))
<=> ( apply(X1,X3,X0)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',initial_segment) ).
fof(f20,conjecture,
! [X0] :
( member(X0,on)
=> ! [X1] :
( member(X1,X0)
=> equal_set(X1,initial_segment(X1,member_predicate,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV5) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> ! [X1] :
( member(X1,X0)
=> equal_set(X1,initial_segment(X1,member_predicate,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f23,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f24,plain,
? [X0] :
( member(X0,on)
& ? [X1] :
( member(X1,X0)
& ~ equal_set(X1,initial_segment(X1,member_predicate,X0)) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(flattening,[],[f25]) ).
fof(f27,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(f28,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f38,plain,
( member(sK1,on)
& member(sK2,sK1)
& ~ equal_set(sK2,initial_segment(sK2,member_predicate,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f24]) ).
fof(f39,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,[],[f27]) ).
fof(f40,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,[],[f39]) ).
fof(f41,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,[],[f40]) ).
fof(f42,plain,
! [X0] :
( ( ~ member(X0,on)
| ( ! [X2] :
( ~ member(X2,X0)
| subset(X2,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) )
& ( ( member(sK3(X0),X0)
& ~ subset(sK3(X0),X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0)
| member(X0,on) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ( ~ apply(member_predicate,X0,X1)
| member(X0,X1) )
& ( ~ member(X0,X1)
| apply(member_predicate,X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( ( ~ member(X3,initial_segment(X0,X1,X2))
| ( apply(X1,X3,X0)
& member(X3,X2) ) )
& ( ~ apply(X1,X3,X0)
| ~ member(X3,X2)
| member(X3,initial_segment(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ( ~ member(X3,initial_segment(X0,X1,X2))
| ( apply(X1,X3,X0)
& member(X3,X2) ) )
& ( ~ apply(X1,X3,X0)
| ~ member(X3,X2)
| member(X3,initial_segment(X0,X1,X2)) ) ),
inference(flattening,[],[f44]) ).
fof(f46,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,[],[f28]) ).
fof(f47,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,[],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK4(X0,X1),X0)
& ~ member(sK4(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f47]) ).
fof(f65,plain,
member(sK1,on),
inference(cnf_transformation,[],[f38]) ).
fof(f66,plain,
member(sK2,sK1),
inference(cnf_transformation,[],[f38]) ).
fof(f67,plain,
~ equal_set(sK2,initial_segment(sK2,member_predicate,sK1)),
inference(cnf_transformation,[],[f38]) ).
fof(f68,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f69,plain,
! [X2,X0] :
( ~ member(X0,on)
| ~ member(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f74,plain,
! [X0,X1] :
( ~ apply(member_predicate,X0,X1)
| member(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f75,plain,
! [X0,X1] :
( ~ member(X0,X1)
| apply(member_predicate,X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,initial_segment(X0,X1,X2))
| apply(X1,X3,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ apply(X1,X3,X0)
| ~ member(X3,X2)
| member(X3,initial_segment(X0,X1,X2)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f79,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f80,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f81,plain,
! [X0,X1] :
( ~ member(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_49,negated_conjecture,
~ equal_set(sK2,initial_segment(sK2,member_predicate,sK1)),
inference(cnf_transformation,[],[f67]) ).
tcf(c_50,negated_conjecture,
member(sK2,sK1),
inference(cnf_transformation,[],[f66]) ).
tcf(c_51,negated_conjecture,
member(sK1,on),
inference(cnf_transformation,[],[f65]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(X1,on)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( apply(member_predicate,X0,X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ apply(member_predicate,X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,initial_segment(X2,X0,X3))
| ~ member(X1,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X2,X0,X1)
| ~ member(X0,initial_segment(X1,X2,X3)) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_728,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| ( X1 != sK2 )
| ( initial_segment(sK2,member_predicate,sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_52]) ).
tcf(c_729,plain,
( ~ subset(sK2,initial_segment(sK2,member_predicate,sK1))
| ~ subset(initial_segment(sK2,member_predicate,sK1),sK2) ),
inference(unflattening,[status(thm)],[c_728]) ).
tcf(c_2212,plain,
( ~ subset(sK2,initial_segment(sK2,member_predicate,sK1))
| ~ subset(initial_segment(sK2,member_predicate,sK1),sK2) ),
inference(prop_impl_just,[status(thm)],[c_729]) ).
tcf(c_5123,plain,
( subset(sK2,sK1)
| ~ member(sK1,on) ),
inference(superposition,[status(thm)],[c_50,c_57]) ).
tcf(c_5133,plain,
subset(sK2,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_5123,c_51]) ).
tcf(c_5345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(initial_segment(X1,X0,X2),X3)
| apply(X0,sK4(initial_segment(X1,X0,X2),X3),X1) ),
inference(superposition,[status(thm)],[c_64,c_62]) ).
tcf(c_6510,plain,
( subset(sK2,initial_segment(sK2,member_predicate,sK1))
| member(sK4(sK2,initial_segment(sK2,member_predicate,sK1)),sK2) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_6511,plain,
( subset(sK2,initial_segment(sK2,member_predicate,sK1))
| ~ member(sK4(sK2,initial_segment(sK2,member_predicate,sK1)),initial_segment(sK2,member_predicate,sK1)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_15969,plain,
( apply(member_predicate,sK4(sK2,initial_segment(sK2,member_predicate,sK1)),sK2)
| ~ member(sK4(sK2,initial_segment(sK2,member_predicate,sK1)),sK2) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_22030,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(initial_segment(X0,member_predicate,X1),X2)
| member(sK4(initial_segment(X0,member_predicate,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_5345,c_59]) ).
tcf(c_22064,plain,
! [X0: $i,X1: $i] : subset(initial_segment(X0,member_predicate,X1),X0),
inference(superposition,[status(thm)],[c_22030,c_63]) ).
tcf(c_22092,plain,
~ subset(sK2,initial_segment(sK2,member_predicate,sK1)),
inference(backward_subsumption_resolution,[status(thm)],[c_2212,c_22064]) ).
tcf(c_44442,plain,
( member(sK4(sK2,initial_segment(sK2,member_predicate,sK1)),initial_segment(sK2,member_predicate,sK1))
| ~ member(sK4(sK2,initial_segment(sK2,member_predicate,sK1)),sK1)
| ~ apply(member_predicate,sK4(sK2,initial_segment(sK2,member_predicate,sK1)),sK2) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_159129,plain,
! [X0: $i] :
( member(sK4(sK2,initial_segment(sK2,member_predicate,sK1)),X0)
| ~ subset(sK2,X0)
| ~ member(sK4(sK2,initial_segment(sK2,member_predicate,sK1)),sK2) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_160549,plain,
( member(sK4(sK2,initial_segment(sK2,member_predicate,sK1)),sK1)
| ~ subset(sK2,sK1)
| ~ member(sK4(sK2,initial_segment(sK2,member_predicate,sK1)),sK2) ),
inference(instantiation,[status(thm)],[c_159129]) ).
tcf(c_160552,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_160549,c_44442,c_22092,c_15969,c_6510,c_6511,c_5133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET811+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 12:01:08 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 Running first-order theorem proving
% 0.12/0.37 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
% 0.12/0.38
% 0.12/0.38 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.38
% 0.12/0.38 % Detected problem language: tptp
% 0.12/0.40 % Proving...
% 35.67/5.80 % SZS status Started for theBenchmark.p
% 35.67/5.80 % SZS status Theorem for theBenchmark.p
% 35.67/5.80
% 35.67/5.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 35.67/5.80
% 35.67/5.80 % ------ iProver source info
% 35.67/5.80
% 35.67/5.80 % git: date: 2026-07-19 20:42:38 +0200
% 35.67/5.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 35.67/5.80 % git: non_committed_changes: false
% 35.67/5.80
% 35.67/5.80 % ------ Parsing...
% 35.67/5.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 35.67/5.80
% 35.67/5.80 % ------ 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 %
% 35.67/5.80
% 35.67/5.80 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 35.67/5.80
% 35.67/5.80 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 35.67/5.80 % ------ Proving...
% 35.67/5.80 % ------ Problem Properties
% 35.67/5.80
% 35.67/5.80 %
% 35.67/5.80 % clauses 42
% 35.67/5.80 % conjectures 2
% 35.67/5.80 % EPR 15
% 35.67/5.80 % Horn 27
% 35.67/5.80 % unary 3
% 35.67/5.80 % binary 19
% 35.67/5.80 % lits 111
% 35.67/5.80 % lits eq 3
% 35.67/5.80 % fd_pure 0
% 35.67/5.80 % fd_pseudo 0
% 35.67/5.80 % fd_cond 0
% 35.67/5.80 % fd_pseudo_cond 2
% 35.67/5.80 % AC symbols 0
% 35.67/5.80
% 35.67/5.80 % ------ Schedule dynamic 5 is on
% 35.67/5.80
% 35.67/5.80 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 35.67/5.80
% 35.67/5.80
% 35.67/5.80 % ------
% 35.67/5.80 % Current options:
% 35.67/5.80 % ------
% 35.67/5.80
% 35.67/5.80
% 35.67/5.80 %
% 35.67/5.80
% 35.67/5.80 % ------ Proving...
% 35.67/5.80 %
% 35.67/5.80
% 35.67/5.80 % SZS status Theorem for theBenchmark.p
% 35.67/5.80
% 35.67/5.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 35.67/5.80
% 35.67/5.80
%------------------------------------------------------------------------------