%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET810+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 02:43:59 PM UTC 2026
% Result : Theorem 7.25s 1.57s
% Output : Proof 7.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 27 unt; 0 def)
% Number of atoms : 207 ( 19 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 234 ( 83 ~; 70 |; 67 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-4 aty)
% Number of variables : 115 ( 2 sgn 69 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X,Y] :
( apply(member_predicate,X,Y)
<=> member(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rel_member) ).
fof(f14_nnf,plain,
! [X,Y] :
( ( ~ member(X,Y)
| apply(member_predicate,X,Y) )
& ( member(X,Y)
| ~ apply(member_predicate,X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y] :
( ( ~ member(X,Y)
| apply(member_predicate,X,Y) )
& ( member(X,Y)
| ~ apply(member_predicate,X,Y) ) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c45,plain,
( ~ member(X0,X1)
| apply(member_predicate,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi43,axiom,
ifeq(member(X0,X1),true,apply(member_predicate,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
fof(f19,conjecture,
! [A,B] :
( ( member(B,on)
& member(A,on) )
=> ~ ( member(B,A)
& member(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV3) ).
fof(f19_neg,negated_conjecture,
~ ! [A,B] :
( ( member(B,on)
& member(A,on) )
=> ~ ( member(B,A)
& member(A,B) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f19_nnf,plain,
? [A,B] :
( member(B,A)
& member(A,B)
& member(B,on)
& member(A,on) ),
inference(nnf_transformation,[status(thm)],[f19_neg]) ).
fof(f19_sk,plain,
( member(sk14,sk13)
& member(sk13,sk14)
& member(sk14,on)
& member(sk13,on) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14])],[f19_nnf]) ).
cnf(c81,plain,
member(sk14,sk13),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi78,negated_conjecture,
member(sk14,sk13) = true,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(h68,plain,
apply(member_predicate,sk14,sk13) = true,
inference(hyper_resolution,[status(thm)],[hi43,hi78]) ).
cnf(c80,plain,
member(sk13,sk14),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi77,negated_conjecture,
member(sk13,sk14) = true,
inference(equality_encoding,[status(esa)],[c80]) ).
cnf(h52,plain,
apply(member_predicate,sk13,sk14) = true,
inference(hyper_resolution,[status(thm)],[hi43,hi77]) ).
fof(f11,axiom,
! [A] :
( member(A,on)
<=> ( ! [X] :
( member(X,A)
=> subset(X,A) )
& strict_well_order(member_predicate,A)
& set(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_number) ).
fof(f11_nnf,plain,
! [A] :
( ( ? [X] :
( ~ subset(X,A)
& member(X,A) )
| ~ strict_well_order(member_predicate,A)
| ~ set(A)
| member(A,on) )
& ( ( ! [X] :
( subset(X,A)
| ~ member(X,A) )
& strict_well_order(member_predicate,A)
& set(A) )
| ~ member(A,on) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,X] :
( ( ( ~ subset(sk3(A),A)
& member(sk3(A),A) )
| ~ strict_well_order(member_predicate,A)
| ~ set(A)
| member(A,on) )
& ( ( ( subset(X,A)
| ~ member(X,A) )
& strict_well_order(member_predicate,A)
& set(A) )
| ~ member(A,on) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f11_nnf]) ).
cnf(c31,plain,
( subset(X1,X0)
| ~ member(X1,X0)
| ~ member(X0,on) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi29,axiom,
ifeq(member(X0,on),true,ifeq(member(X1,X0),true,subset(X1,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(c79,plain,
member(sk14,on),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi76,negated_conjecture,
member(sk14,on) = true,
inference(equality_encoding,[status(esa)],[c79]) ).
cnf(h54,plain,
subset(sk13,sk14) = true,
inference(hyper_resolution,[status(thm)],[hi29,hi76,hi77]) ).
fof(f0,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f0_nnf,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,X] :
( ( ( ~ member(sk0(A,B),B)
& member(sk0(A,B),A) )
| subset(A,B) )
& ( member(X,B)
| ~ member(X,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(subset(X0,X1),true,ifeq(member(X2,X0),true,member(X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h140,plain,
member(sk14,sk14) = true,
inference(hyper_resolution,[status(thm)],[hi0,h54,hi78]) ).
cnf(c30,plain,
( strict_well_order(member_predicate,X0)
| ~ member(X0,on) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi28,axiom,
ifeq(member(X0,on),true,strict_well_order(member_predicate,X0),true) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(h34,plain,
strict_well_order(member_predicate,sk14) = true,
inference(hyper_resolution,[status(thm)],[hi28,hi76]) ).
fof(f12,axiom,
! [R,E] :
( strict_well_order(R,E)
<=> ( ! [A] :
( ( ? [X] : member(X,A)
& subset(A,E) )
=> ? [Y] : least(Y,R,A) )
& strict_order(R,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strict_well_order) ).
fof(f12_nnf,plain,
! [R,E] :
( ( ? [A] :
( ! [Y] : ~ least(Y,R,A)
& ? [X] : member(X,A)
& subset(A,E) )
| ~ strict_order(R,E)
| strict_well_order(R,E) )
& ( ( ! [A] :
( ? [Y] : least(Y,R,A)
| ! [X] : ~ member(X,A)
| ~ subset(A,E) )
& strict_order(R,E) )
| ~ strict_well_order(R,E) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [R,E,A,X,Y] :
( ( ( ~ least(Y,R,sk5(R,E))
& member(sk6(R,E),sk5(R,E))
& subset(sk5(R,E),E) )
| ~ strict_order(R,E)
| strict_well_order(R,E) )
& ( ( ( least(sk4(R,E,A),R,A)
| ~ member(X,A)
| ~ subset(A,E) )
& strict_order(R,E) )
| ~ strict_well_order(R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6])],[f12_nnf]) ).
cnf(c34,plain,
( strict_order(X0,X1)
| ~ strict_well_order(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi32,axiom,
ifeq(strict_well_order(X0,X1),true,strict_order(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(h130,plain,
strict_order(member_predicate,sk14) = true,
inference(hyper_resolution,[status(thm)],[hi32,h34]) ).
fof(f15,axiom,
! [R,E] :
( strict_order(R,E)
<=> ( ! [X,Y,Z] :
( ( member(Z,E)
& member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,Z)
& apply(R,X,Y) )
=> apply(R,X,Z) ) )
& ! [X,Y] :
( ( member(Y,E)
& member(X,E) )
=> ~ ( apply(R,Y,X)
& apply(R,X,Y) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strict_order) ).
fof(f15_nnf,plain,
! [R,E] :
( ( ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,Y,Z)
& apply(R,X,Y)
& member(Z,E)
& member(Y,E)
& member(X,E) )
| ? [X,Y] :
( apply(R,Y,X)
& apply(R,X,Y)
& member(Y,E)
& member(X,E) )
| strict_order(R,E) )
& ( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X,Y] :
( ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) ) )
| ~ strict_order(R,E) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [R,E,X,Y,Z] :
( ( ( ~ apply(R,sk10(R,E),sk12(R,E))
& apply(R,sk11(R,E),sk12(R,E))
& apply(R,sk10(R,E),sk11(R,E))
& member(sk12(R,E),E)
& member(sk11(R,E),E)
& member(sk10(R,E),E) )
| ( apply(R,sk9(R,E),sk8(R,E))
& apply(R,sk8(R,E),sk9(R,E))
& member(sk9(R,E),E)
& member(sk8(R,E),E) )
| strict_order(R,E) )
& ( ( ( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ( ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) ) )
| ~ strict_order(R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9,sk10,sk11,sk12])],[f15_nnf]) ).
cnf(c46,plain,
( ~ apply(X0,X3,X2)
| ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ strict_order(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi81,axiom,
ifeq(strict_order(X0,X1),true,ifeq(member(X2,X1),true,ifeq(member(X3,X1),true,ifeq(apply(X0,X2,X3),true,ifeq(apply(X0,X3,X2),true,false,true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi81,h130,hi77,h140,h52,h68]) ).
cnf(t4394,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f5,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
fof(f5_nnf,plain,
! [X] : ~ member(X,empty_set),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : ~ member(X,empty_set),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c14,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f6,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( ~ member(B,A)
& member(B,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
fof(f6_nnf,plain,
! [B,A,E] :
( ( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [B,E,A] :
( ( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c16,plain,
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14,c16,c46]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t4394]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET810+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:04:21 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.25/1.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.25/1.57 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------