%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET766+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 02:43:54 PM UTC 2026
% Result : Theorem 11.81s 2.21s
% Output : Proof 11.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 19 unt; 0 def)
% Number of atoms : 152 ( 11 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 178 ( 65 ~; 51 |; 51 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 91 ( 2 sgn 59 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [A,R] :
( equivalence(R,A)
<=> ( ! [X,Y,Z] :
( ( member(Z,A)
& member(Y,A)
& member(X,A) )
=> ( ( apply(R,Y,Z)
& apply(R,X,Y) )
=> apply(R,X,Z) ) )
& ! [X,Y] :
( ( member(Y,A)
& member(X,A) )
=> ( apply(R,X,Y)
=> apply(R,Y,X) ) )
& ! [X] :
( member(X,A)
=> apply(R,X,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence) ).
fof(f13_nnf,plain,
! [A,R] :
( ( ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,Y,Z)
& apply(R,X,Y)
& member(Z,A)
& member(Y,A)
& member(X,A) )
| ? [X,Y] :
( ~ apply(R,Y,X)
& apply(R,X,Y)
& member(Y,A)
& member(X,A) )
| ? [X] :
( ~ apply(R,X,X)
& member(X,A) )
| equivalence(R,A) )
& ( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,A)
| ~ member(Y,A)
| ~ member(X,A) )
& ! [X,Y] :
( apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,A)
| ~ member(X,A) )
& ! [X] :
( apply(R,X,X)
| ~ member(X,A) ) )
| ~ equivalence(R,A) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [R,A,X,Y,Z] :
( ( ( ~ apply(R,sk13(A,R),sk15(A,R))
& apply(R,sk14(A,R),sk15(A,R))
& apply(R,sk13(A,R),sk14(A,R))
& member(sk15(A,R),A)
& member(sk14(A,R),A)
& member(sk13(A,R),A) )
| ( ~ apply(R,sk12(A,R),sk11(A,R))
& apply(R,sk11(A,R),sk12(A,R))
& member(sk12(A,R),A)
& member(sk11(A,R),A) )
| ( ~ apply(R,sk10(A,R),sk10(A,R))
& member(sk10(A,R),A) )
| equivalence(R,A) )
& ( ( ( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,A)
| ~ member(Y,A)
| ~ member(X,A) )
& ( apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,A)
| ~ member(X,A) )
& ( apply(R,X,X)
| ~ member(X,A) ) )
| ~ equivalence(R,A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10,sk11,sk12,sk13,sk14,sk15])],[f13_nnf]) ).
cnf(c56,plain,
( apply(X1,X2,X2)
| ~ member(X2,X0)
| ~ equivalence(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi53,axiom,
ifeq(equivalence(X0,X1),true,ifeq(member(X2,X1),true,apply(X0,X2,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
fof(f16,conjecture,
! [E,R,A] :
( ( member(A,E)
& equivalence(R,E) )
=> member(A,equivalence_class(A,E,R)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII02) ).
fof(f16_neg,negated_conjecture,
~ ! [E,R,A] :
( ( member(A,E)
& equivalence(R,E) )
=> member(A,equivalence_class(A,E,R)) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [E,R,A] :
( ~ member(A,equivalence_class(A,E,R))
& member(A,E)
& equivalence(R,E) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( ~ member(sk22,equivalence_class(sk22,sk20,sk21))
& member(sk22,sk20)
& equivalence(sk21,sk20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22])],[f16_nnf]) ).
cnf(c124,plain,
equivalence(sk21,sk20),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi121,negated_conjecture,
equivalence(sk21,sk20) = true,
inference(equality_encoding,[status(esa)],[c124]) ).
cnf(c125,plain,
member(sk22,sk20),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi122,negated_conjecture,
member(sk22,sk20) = true,
inference(equality_encoding,[status(esa)],[c125]) ).
cnf(h18,plain,
apply(sk21,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi53,hi121,hi122]) ).
fof(f14,axiom,
! [R,E,A,X] :
( member(X,equivalence_class(A,E,R))
<=> ( apply(R,A,X)
& member(X,E) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_class) ).
fof(f14_nnf,plain,
! [R,E,A,X] :
( ( ~ apply(R,A,X)
| ~ member(X,E)
| member(X,equivalence_class(A,E,R)) )
& ( ( apply(R,A,X)
& member(X,E) )
| ~ member(X,equivalence_class(A,E,R)) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,A,E,R] :
( ( ~ apply(R,A,X)
| ~ member(X,E)
| member(X,equivalence_class(A,E,R)) )
& ( ( apply(R,A,X)
& member(X,E) )
| ~ member(X,equivalence_class(A,E,R)) ) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c109,plain,
( ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| member(X3,equivalence_class(X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi106,axiom,
ifeq(member(X0,X1),true,ifeq(apply(X2,X3,X0),true,member(X0,equivalence_class(X3,X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c109]) ).
cnf(h65,plain,
member(sk22,equivalence_class(sk22,sk20,sk21)) = true,
inference(hyper_resolution,[status(thm)],[hi106,hi122,h18]) ).
cnf(c126,plain,
~ member(sk22,equivalence_class(sk22,sk20,sk21)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi126,negated_conjecture,
ifeq(member(sk22,equivalence_class(sk22,sk20,sk21)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c126]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi126,h65]) ).
cnf(t2182,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f5,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox2/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/sandbox2/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]) ).
fof(f11,axiom,
! [A,B] :
( disjoint(A,B)
<=> ~ ? [X] :
( member(X,B)
& member(X,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint) ).
fof(f11_nnf,plain,
! [A,B] :
( ( ? [X] :
( member(X,B)
& member(X,A) )
| disjoint(A,B) )
& ( ! [X] :
( ~ member(X,B)
| ~ member(X,A) )
| ~ disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B,X] :
( ( ( member(sk3(A,B),B)
& member(sk3(A,B),A) )
| disjoint(A,B) )
& ( ~ member(X,B)
| ~ member(X,A)
| ~ disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f11_nnf]) ).
cnf(c29,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14,c16,c29,c126]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2182]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET766+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 11:53:43 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 11.81/2.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.81/2.21 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------