%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET798+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 : n006.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 81.26s 10.73s
% Output : Proof 81.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 65 ( 47 unt; 0 def)
% Number of atoms : 128 ( 39 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 99 ( 36 ~; 25 |; 27 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 107 ( 4 sgn 43 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_bound) ).
fof(f14_nnf,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| lower_bound(M,R,E) )
& ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
| ~ lower_bound(M,R,E) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [M,R,E,X] :
( ( ( ~ apply(R,M,sk12(R,E,M))
& member(sk12(R,E,M),E) )
| lower_bound(M,R,E) )
& ( apply(R,M,X)
| ~ member(X,E)
| ~ lower_bound(M,R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12])],[f14_nnf]) ).
cnf(c103,plain,
( ~ apply(X0,X2,sk12(X0,X1,X2))
| lower_bound(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t109,plain,
ifeq(apply(X1,X2,sk12(X1,X3,X2)),true,lower_bound(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c103]) ).
cnf(t1200,plain,
ifeq(apply(X1,X2,sk12(X1,X3,X2)),true,lower_bound(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t109]) ).
cnf(c101,plain,
( apply(X0,X2,X3)
| ~ member(X3,X1)
| ~ lower_bound(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t145,plain,
ifeq(lower_bound(X1,X2,X3),true,ifeq(member(X4,X3),true,apply(X2,X1,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c101]) ).
cnf(t1370,plain,
ifeq(lower_bound(X1,X2,X3),true,ifeq(member(X4,X3),true,apply(X2,X1,X4),true),true) = true,
inference(orient,[status(thm)],[t145]) ).
fof(f21,conjecture,
! [R,E] :
( order(R,E)
=> ! [X,Y] :
( ( subset(X,Y)
& subset(Y,E)
& subset(X,E) )
=> ! [M] :
( lower_bound(M,R,Y)
=> lower_bound(M,R,X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV10) ).
fof(f21_neg,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [X,Y] :
( ( subset(X,Y)
& subset(Y,E)
& subset(X,E) )
=> ! [M] :
( lower_bound(M,R,Y)
=> lower_bound(M,R,X) ) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f21_nnf,plain,
? [R,E] :
( ? [X,Y] :
( ? [M] :
( ~ lower_bound(M,R,X)
& lower_bound(M,R,Y) )
& subset(X,Y)
& subset(Y,E)
& subset(X,E) )
& order(R,E) ),
inference(nnf_transformation,[status(thm)],[f21_neg]) ).
fof(f21_sk,plain,
( ~ lower_bound(sk23,sk19,sk21)
& lower_bound(sk23,sk19,sk22)
& subset(sk21,sk22)
& subset(sk22,sk20)
& subset(sk21,sk20)
& order(sk19,sk20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk19,sk20,sk21,sk22,sk23])],[f21_nnf]) ).
cnf(c138,plain,
lower_bound(sk23,sk19,sk22),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t13,plain,
lower_bound(sk23,sk19,sk22) = true,
inference(equality_encoding,[status(esa)],[c138]) ).
cnf(t1727,plain,
lower_bound(sk23,sk19,sk22) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t1729,plain,
true = ifeq(true,true,ifeq(member(X1,sk22),true,apply(sk19,sk23,X1),true),true),
inference(cp,[status(thm)],[t1370,t1727]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t13582,plain,
true = ifeq(member(X1,sk22),true,apply(sk19,sk23,X1),true),
inference(step,[status(thm)],[t1729,t258]) ).
cnf(t13063,plain,
ifeq(member(X1,sk22),true,apply(sk19,sk23,X1),true) = true,
inference(orient,[status(thm)],[t13582]) ).
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(t127,plain,
ifeq(subset(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t1393,plain,
ifeq(subset(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(orient,[status(thm)],[t127]) ).
cnf(c137,plain,
subset(sk21,sk22),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t10,plain,
subset(sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c137]) ).
cnf(t1735,plain,
subset(sk21,sk22) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t1740,plain,
true = ifeq(true,true,ifeq(member(X1,sk21),true,member(X1,sk22),true),true),
inference(cp,[status(thm)],[t1393,t1735]) ).
cnf(t13387,plain,
true = ifeq(member(X1,sk21),true,member(X1,sk22),true),
inference(step,[status(thm)],[t1740,t258]) ).
cnf(t7359,plain,
ifeq(member(X1,sk21),true,member(X1,sk22),true) = true,
inference(orient,[status(thm)],[t13387]) ).
cnf(c102,plain,
( member(sk12(X0,X1,X2),X1)
| lower_bound(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t94,plain,
or(lower_bound(X1,X2,X3),member(sk12(X2,X3,X1),X3)) = true,
inference(equality_encoding,[status(esa)],[c102]) ).
cnf(t485,plain,
or(lower_bound(X1,X2,X3),member(sk12(X2,X3,X1),X3)) = true,
inference(orient,[status(thm)],[t94]) ).
cnf(c139,plain,
~ lower_bound(sk23,sk19,sk21),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t12,plain,
lower_bound(sk23,sk19,sk21) = false,
inference(equality_encoding,[status(esa)],[c139]) ).
cnf(t1931,plain,
lower_bound(sk23,sk19,sk21) = false,
inference(orient,[status(thm)],[t12]) ).
cnf(t1935,plain,
true = or(false,member(sk12(sk19,sk21,sk23),sk21)),
inference(cp,[status(thm)],[t485,t1931]) ).
cnf(t6,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t257,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t13211,plain,
true = member(sk12(sk19,sk21,sk23),sk21),
inference(step,[status(thm)],[t1935,t257]) ).
cnf(t2724,plain,
member(sk12(sk19,sk21,sk23),sk21) = true,
inference(orient,[status(thm)],[t13211]) ).
cnf(t7360,plain,
true = ifeq(true,true,member(sk12(sk19,sk21,sk23),sk22),true),
inference(cp,[status(thm)],[t7359,t2724]) ).
cnf(t13388,plain,
true = member(sk12(sk19,sk21,sk23),sk22),
inference(step,[status(thm)],[t7360,t258]) ).
cnf(t7361,plain,
member(sk12(sk19,sk21,sk23),sk22) = true,
inference(orient,[status(thm)],[t13388]) ).
cnf(t13064,plain,
true = ifeq(true,true,apply(sk19,sk23,sk12(sk19,sk21,sk23)),true),
inference(cp,[status(thm)],[t13063,t7361]) ).
cnf(t13583,plain,
true = apply(sk19,sk23,sk12(sk19,sk21,sk23)),
inference(step,[status(thm)],[t13064,t258]) ).
cnf(t13065,plain,
apply(sk19,sk23,sk12(sk19,sk21,sk23)) = true,
inference(orient,[status(thm)],[t13583]) ).
cnf(t13068,plain,
true = ifeq(true,true,lower_bound(sk23,sk19,sk21),true),
inference(cp,[status(thm)],[t1200,t13065]) ).
cnf(t13584,plain,
true = lower_bound(sk23,sk19,sk21),
inference(step,[status(thm)],[t13068,t258]) ).
cnf(t13585,plain,
true = false,
inference(step,[status(thm)],[t13584,t1931]) ).
cnf(t13081,plain,
false = true,
inference(orient,[status(thm)],[t13585]) ).
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,c139]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t13081]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET798+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.40 % Computer : n006.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Thu Sep 24 11:58:56 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 81.26/10.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 81.26/10.73 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------