%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET691+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 : n012.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 02:43:49 PM UTC 2026
% Result : Theorem 26.69s 14.30s
% Output : Proof 26.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 10 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 75 ( 31 ~; 26 |; 13 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 3 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f1_nnf,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f11,conjecture,
! [A] :
( subset(A,empty_set)
<=> equal_set(A,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI16) ).
fof(f11_neg,negated_conjecture,
~ ! [A] :
( subset(A,empty_set)
<=> equal_set(A,empty_set) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [A] :
( ( equal_set(A,empty_set)
& ~ subset(A,empty_set) )
| ( ~ equal_set(A,empty_set)
& subset(A,empty_set) ) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
( ( equal_set(sk3,empty_set)
& ~ subset(sk3,empty_set) )
| ( ~ equal_set(sk3,empty_set)
& subset(sk3,empty_set) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f11_nnf]) ).
cnf(c30,plain,
( equal_set(sk3,empty_set)
| subset(sk3,empty_set) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(c3,plain,
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p33,plain,
( subset(sk3,empty_set)
| subset(sk3,empty_set) ),
inference(resolution,[status(thm)],[c30,c3]) ).
cnf(p35,plain,
subset(sk3,empty_set),
inference(factoring,[status(thm)],[p33]) ).
fof(f0,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/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(p37,plain,
( member(X0,empty_set)
| ~ member(X0,sk3) ),
inference(resolution,[status(thm)],[p35,c0]) ).
cnf(c1,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p38,plain,
( subset(sk3,X0)
| member(sk0(sk3,X0),empty_set) ),
inference(resolution,[status(thm)],[p37,c1]) ).
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]) ).
cnf(p39,plain,
subset(sk3,X0),
inference(resolution,[status(thm)],[p38,c14]) ).
cnf(p44,plain,
( ~ subset(X0,sk3)
| equal_set(sk3,X0) ),
inference(resolution,[status(thm)],[c5,p39]) ).
cnf(p36,plain,
subset(empty_set,X0),
inference(resolution,[status(thm)],[c1,c14]) ).
cnf(p47,plain,
equal_set(sk3,empty_set),
inference(resolution,[status(thm)],[p44,p36]) ).
cnf(c31,plain,
( ~ subset(sk3,empty_set)
| ~ equal_set(sk3,empty_set) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p48,plain,
~ subset(sk3,empty_set),
inference(resolution,[status(thm)],[p47,c31]) ).
cnf(p49,plain,
$false,
inference(resolution,[status(thm)],[p48,p39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET691+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.04/10.32 % Computer : n012.cluster.edu
% 0.04/10.32 % Model : x86_64 x86_64
% 0.04/10.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/10.32 % Memory : 8046.5625MB
% 0.04/10.32 % OS : Linux 6.8.0-71-generic
% 0.04/10.32 % CPULimit : 300
% 0.04/10.32 % WCLimit : 300
% 0.04/10.32 % DateTime : Thu Sep 24 11:41:06 UTC 2026
% 0.04/10.32 % CPUTime :
% 0.04/10.32 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 26.69/14.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.69/14.30 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------