%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET799+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 : 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 02:43:58 PM UTC 2026
% Result : Theorem 14.22s 12.25s
% Output : Proof 14.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 36 unt; 0 def)
% Number of atoms : 224 ( 30 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 245 ( 82 ~; 67 |; 77 &)
% ( 5 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-4 aty)
% Number of variables : 142 ( 10 sgn 81 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [A,X,R,E] :
( least_upper_bound(A,X,R,E)
<=> ( ! [M] :
( ( upper_bound(M,R,X)
& member(M,E) )
=> apply(R,A,M) )
& upper_bound(A,R,X)
& member(A,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',least_upper_bound) ).
fof(f19_nnf,plain,
! [A,X,R,E] :
( ( ? [M] :
( ~ apply(R,A,M)
& upper_bound(M,R,X)
& member(M,E) )
| ~ upper_bound(A,R,X)
| ~ member(A,X)
| least_upper_bound(A,X,R,E) )
& ( ( ! [M] :
( apply(R,A,M)
| ~ upper_bound(M,R,X)
| ~ member(M,E) )
& upper_bound(A,R,X)
& member(A,X) )
| ~ least_upper_bound(A,X,R,E) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,X,R,E,M] :
( ( ( ~ apply(R,A,sk17(A,X,R,E))
& upper_bound(sk17(A,X,R,E),R,X)
& member(sk17(A,X,R,E),E) )
| ~ upper_bound(A,R,X)
| ~ member(A,X)
| least_upper_bound(A,X,R,E) )
& ( ( ( apply(R,A,M)
| ~ upper_bound(M,R,X)
| ~ member(M,E) )
& upper_bound(A,R,X)
& member(A,X) )
| ~ least_upper_bound(A,X,R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk17])],[f19_nnf]) ).
cnf(c122,plain,
( member(X0,X1)
| ~ least_upper_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi120,axiom,
ifeq(least_upper_bound(X0,X1,X2,X3),true,member(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c122]) ).
fof(f21,conjecture,
! [R,E] :
( order(R,E)
=> ! [X1,X2] :
( ( subset(X1,X2)
& subset(X2,E)
& subset(X1,E) )
=> ! [M1,M2] :
( ( least_upper_bound(M2,X2,R,E)
& least_upper_bound(M1,X1,R,E) )
=> apply(R,M1,M2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV11) ).
fof(f21_neg,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [X1,X2] :
( ( subset(X1,X2)
& subset(X2,E)
& subset(X1,E) )
=> ! [M1,M2] :
( ( least_upper_bound(M2,X2,R,E)
& least_upper_bound(M1,X1,R,E) )
=> apply(R,M1,M2) ) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f21_nnf,plain,
? [R,E] :
( ? [X1,X2] :
( ? [M1,M2] :
( ~ apply(R,M1,M2)
& least_upper_bound(M2,X2,R,E)
& least_upper_bound(M1,X1,R,E) )
& subset(X1,X2)
& subset(X2,E)
& subset(X1,E) )
& order(R,E) ),
inference(nnf_transformation,[status(thm)],[f21_neg]) ).
fof(f21_sk,plain,
( ~ apply(sk19,sk23,sk24)
& least_upper_bound(sk24,sk22,sk19,sk20)
& least_upper_bound(sk23,sk21,sk19,sk20)
& subset(sk21,sk22)
& subset(sk22,sk20)
& subset(sk21,sk20)
& order(sk19,sk20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk19,sk20,sk21,sk22,sk23,sk24])],[f21_nnf]) ).
cnf(c138,plain,
least_upper_bound(sk23,sk21,sk19,sk20),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi136,negated_conjecture,
least_upper_bound(sk23,sk21,sk19,sk20) = true,
inference(equality_encoding,[status(esa)],[c138]) ).
cnf(h134,plain,
member(sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi120,hi136]) ).
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(c135,plain,
subset(sk21,sk20),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi133,negated_conjecture,
subset(sk21,sk20) = true,
inference(equality_encoding,[status(esa)],[c135]) ).
cnf(h154,plain,
member(sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi133,h134]) ).
fof(f11,axiom,
! [R,E] :
( 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) )
=> X = Y ) )
& ! [X] :
( member(X,E)
=> apply(R,X,X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f11_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] :
( X != Y
& apply(R,Y,X)
& apply(R,X,Y)
& member(Y,E)
& member(X,E) )
| ? [X] :
( ~ apply(R,X,X)
& member(X,E) )
| 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] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] :
( apply(R,X,X)
| ~ member(X,E) ) )
| ~ order(R,E) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [R,E,X,Y,Z] :
( ( ( ~ apply(R,sk6(R,E),sk8(R,E))
& apply(R,sk7(R,E),sk8(R,E))
& apply(R,sk6(R,E),sk7(R,E))
& member(sk8(R,E),E)
& member(sk7(R,E),E)
& member(sk6(R,E),E) )
| ( sk4(R,E) != sk5(R,E)
& apply(R,sk5(R,E),sk4(R,E))
& apply(R,sk4(R,E),sk5(R,E))
& member(sk5(R,E),E)
& member(sk4(R,E),E) )
| ( ~ apply(R,sk3(R,E),sk3(R,E))
& member(sk3(R,E),E) )
| order(R,E) )
& ( ( ( 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) )
& ( apply(R,X,X)
| ~ member(X,E) ) )
| ~ order(R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5,sk6,sk7,sk8])],[f11_nnf]) ).
cnf(c29,plain,
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi27,axiom,
ifeq(order(X0,X1),true,ifeq(member(X2,X1),true,apply(X0,X2,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(c134,plain,
order(sk19,sk20),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi132,negated_conjecture,
order(sk19,sk20) = true,
inference(equality_encoding,[status(esa)],[c134]) ).
cnf(t18,plain,
apply(sk19,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi27,hi132,h154]) ).
cnf(t2782,plain,
apply(sk19,sk23,sk23) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(c137,plain,
subset(sk21,sk22),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi135,negated_conjecture,
subset(sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c137]) ).
cnf(h153,plain,
member(sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi135,h134]) ).
cnf(c123,plain,
( upper_bound(X0,X2,X1)
| ~ least_upper_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi121,axiom,
ifeq(least_upper_bound(X0,X1,X2,X3),true,upper_bound(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c123]) ).
cnf(c139,plain,
least_upper_bound(sk24,sk22,sk19,sk20),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi137,negated_conjecture,
least_upper_bound(sk24,sk22,sk19,sk20) = true,
inference(equality_encoding,[status(esa)],[c139]) ).
cnf(h214,plain,
upper_bound(sk24,sk19,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi121,hi137]) ).
fof(f13,axiom,
! [R,E,M] :
( upper_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,X,M) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_bound) ).
fof(f13_nnf,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,X,M)
& member(X,E) )
| upper_bound(M,R,E) )
& ( ! [X] :
( apply(R,X,M)
| ~ member(X,E) )
| ~ upper_bound(M,R,E) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [M,R,E,X] :
( ( ( ~ apply(R,sk11(R,E,M),M)
& member(sk11(R,E,M),E) )
| upper_bound(M,R,E) )
& ( apply(R,X,M)
| ~ member(X,E)
| ~ upper_bound(M,R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f13_nnf]) ).
cnf(c98,plain,
( apply(X0,X3,X2)
| ~ member(X3,X1)
| ~ upper_bound(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi96,axiom,
ifeq(upper_bound(X0,X1,X2),true,ifeq(member(X3,X2),true,apply(X1,X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c98]) ).
cnf(t20,plain,
apply(sk19,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi96,h214,h153]) ).
cnf(t2799,plain,
apply(sk19,sk23,sk24) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t27,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t27]) ).
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(c140,plain,
~ apply(sk19,sk23,sk24),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14,c16,c140]) ).
cnf(g0_0,plain,
true != ifeq(apply(sk19,sk23,sk24),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(apply(sk19,sk23,sk24),true,false,apply(sk19,sk23,sk23)),
inference(rw,[status(thm)],[g0_0,t2782]) ).
cnf(g0_2,plain,
true != ifeq(apply(sk19,sk23,sk24),apply(sk19,sk23,sk24),false,apply(sk19,sk23,sk23)),
inference(rw,[status(thm)],[g0_1,t2799]) ).
cnf(g0_3,plain,
true != false,
inference(rw,[status(thm)],[g0_2,t258]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET799+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/10.37 % Computer : n004.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Thu Sep 24 12:00:02 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.22/12.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.22/12.25 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------