%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET812+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 : 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 10.78s 7.29s
% Output : CNFRefutation 10.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 9 unt; 0 def)
% Number of atoms : 191 ( 2 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 220 ( 89 ~; 83 |; 36 &)
% ( 7 <=>; 5 =>; 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 110 !; 6 ?; 41 :)
% 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(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f3,axiom,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',intersection) ).
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/sandbox2/benchmark/Axioms/SET006+4.ax',ordinal_number) ).
fof(f20,conjecture,
! [X0] :
( member(X0,on)
=> equal_set(X0,intersection(X0,power_set(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV10) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> equal_set(X0,intersection(X0,power_set(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)
& ~ equal_set(X0,intersection(X0,power_set(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)
& ~ equal_set(sK1,intersection(sK1,power_set(sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f24]) ).
fof(f39,plain,
! [X0,X1] :
( ( ~ member(X0,power_set(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( ~ member(X0,intersection(X1,X2))
| ( member(X0,X2)
& member(X0,X1) ) )
& ( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( ~ member(X0,intersection(X1,X2))
| ( member(X0,X2)
& member(X0,X1) ) )
& ( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f40]) ).
fof(f42,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(f43,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,[],[f42]) ).
fof(f44,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,[],[f43]) ).
fof(f45,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))],[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(sK3(X0,X1),X0)
& ~ member(sK3(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f47]) ).
fof(f66,plain,
member(sK1,on),
inference(cnf_transformation,[],[f38]) ).
fof(f67,plain,
~ equal_set(sK1,intersection(sK1,power_set(sK1))),
inference(cnf_transformation,[],[f38]) ).
fof(f69,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f39]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f41]) ).
fof(f73,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f74,plain,
! [X2,X0] :
( ~ member(X0,on)
| ~ member(X2,X0)
| subset(X2,X0) ),
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(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f81,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_49,negated_conjecture,
~ equal_set(sK1,intersection(sK1,power_set(sK1))),
inference(cnf_transformation,[],[f67]) ).
tcf(c_50,negated_conjecture,
member(sK1,on),
inference(cnf_transformation,[],[f66]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(X1,on)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_752,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| ( X1 != sK1 )
| ( intersection(sK1,power_set(sK1)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_56]) ).
tcf(c_753,plain,
( ~ subset(sK1,intersection(sK1,power_set(sK1)))
| ~ subset(intersection(sK1,power_set(sK1)),sK1) ),
inference(unflattening,[status(thm)],[c_752]) ).
tcf(c_2243,plain,
( ~ subset(sK1,intersection(sK1,power_set(sK1)))
| ~ subset(intersection(sK1,power_set(sK1)),sK1) ),
inference(prop_impl_just,[status(thm)],[c_753]) ).
tcf(c_5226,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(intersection(X0,X1),X2)
| member(sK3(intersection(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_63,c_54]) ).
tcf(c_5263,plain,
! [X0: $i,X1: $i] :
( subset(X0,power_set(X1))
| ~ subset(sK3(X0,power_set(X1)),X1) ),
inference(superposition,[status(thm)],[c_51,c_62]) ).
tcf(c_5264,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,intersection(X1,X2))
| ~ member(sK3(X0,intersection(X1,X2)),X2)
| ~ member(sK3(X0,intersection(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_53,c_62]) ).
tcf(c_5416,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| subset(sK3(X0,X1),X0)
| ~ member(X0,on) ),
inference(superposition,[status(thm)],[c_63,c_61]) ).
tcf(c_5467,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| member(sK3(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_63,c_64]) ).
tcf(c_6563,plain,
! [X0: $i,X1: $i] : subset(intersection(X0,X1),X0),
inference(superposition,[status(thm)],[c_5226,c_62]) ).
tcf(c_6586,plain,
~ subset(sK1,intersection(sK1,power_set(sK1))),
inference(backward_subsumption_resolution,[status(thm)],[c_2243,c_6563]) ).
tcf(c_9896,plain,
! [X0: $i] :
( subset(X0,power_set(X0))
| ~ member(X0,on) ),
inference(superposition,[status(thm)],[c_5416,c_5263]) ).
tcf(c_12825,plain,
! [X0: $i,X1: $i] :
( subset(X0,intersection(X0,X1))
| ~ member(sK3(X0,intersection(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_63,c_5264]) ).
tcf(c_22672,plain,
! [X0: $i,X1: $i] :
( subset(X0,intersection(X0,X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5467,c_12825]) ).
tcf(c_24775,plain,
~ subset(sK1,power_set(sK1)),
inference(superposition,[status(thm)],[c_22672,c_6586]) ).
tcf(c_28599,plain,
~ member(sK1,on),
inference(superposition,[status(thm)],[c_9896,c_24775]) ).
tcf(c_28600,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_28599,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET812+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.38 % Computer : n013.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Thu Sep 24 12:01:37 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 10.78/7.29 % SZS status Started for theBenchmark.p
% 10.78/7.29 % SZS status Theorem for theBenchmark.p
% 10.78/7.29
% 10.78/7.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.78/7.29
% 10.78/7.29 % ------ iProver source info
% 10.78/7.29
% 10.78/7.29 % git: date: 2026-07-19 20:42:38 +0200
% 10.78/7.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.78/7.29 % git: non_committed_changes: false
% 10.78/7.29
% 10.78/7.29 % ------ Parsing...
% 10.78/7.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.78/7.29
% 10.78/7.29 % ------ 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 %
% 10.78/7.29
% 10.78/7.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.78/7.29
% 10.78/7.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.78/7.29 % ------ Proving...
% 10.78/7.29 % ------ Problem Properties
% 10.78/7.29
% 10.78/7.29 %
% 10.78/7.29 % clauses 43
% 10.78/7.29 % conjectures 1
% 10.78/7.29 % EPR 14
% 10.78/7.29 % Horn 28
% 10.78/7.29 % unary 2
% 10.78/7.29 % binary 21
% 10.78/7.29 % lits 114
% 10.78/7.29 % lits eq 3
% 10.78/7.29 % fd_pure 0
% 10.78/7.29 % fd_pseudo 0
% 10.78/7.29 % fd_cond 0
% 10.78/7.29 % fd_pseudo_cond 2
% 10.78/7.29 % AC symbols 0
% 10.78/7.29
% 10.78/7.29 % ------ Schedule dynamic 5 is on
% 10.78/7.29
% 10.78/7.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.78/7.29
% 10.78/7.29
% 10.78/7.29 % ------
% 10.78/7.29 % Current options:
% 10.78/7.29 % ------
% 10.78/7.29
% 10.78/7.29
% 10.78/7.29 %
% 10.78/7.29
% 10.78/7.29 % ------ Proving...
% 10.78/7.29 %
% 10.78/7.29
% 10.78/7.29 % SZS status Theorem for theBenchmark.p
% 10.78/7.29
% 10.78/7.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.78/7.29
% 10.78/7.29
%------------------------------------------------------------------------------