%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET063+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 02:41:53 PM UTC 2026
% Result : Theorem 6.55s 1.32s
% Output : Proof 6.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 20 unt; 0 def)
% Number of atoms : 58 ( 20 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 13 |; 9 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 31 ( 4 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f3_nnf,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c7,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi6,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X1,X0),true,X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f0,axiom,
! [B] : subset(empty_set,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_subset) ).
fof(f0_nnf,plain,
! [B] : subset(empty_set,B),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B] : subset(empty_set,B),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
subset(empty_set,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
subset(empty_set,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f6,conjecture,
! [B] :
( subset(B,empty_set)
=> B = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_of_empty_set_is_empty_set) ).
fof(f6_neg,negated_conjecture,
~ ! [B] :
( subset(B,empty_set)
=> B = empty_set ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [B] :
( B != empty_set
& subset(B,empty_set) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( sk2 != empty_set
& subset(sk2,empty_set) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f6_nnf]) ).
cnf(c11,plain,
subset(sk2,empty_set),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi9,negated_conjecture,
subset(sk2,empty_set) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h8,plain,
empty_set = sk2,
inference(hyper_resolution,[status(thm)],[hi6,hi0,hi9]) ).
cnf(c12,plain,
sk2 != empty_set,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi12,negated_conjecture,
ifeq(sk2,empty_set,false,true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t1,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi12,h8]) ).
cnf(t74,plain,
false = true,
inference(orient,[status(thm)],[t1]) ).
fof(f1,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f1_nnf,plain,
! [B] : ~ member(B,empty_set),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B] : ~ member(B,empty_set),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f5,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
fof(f5_nnf,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [B,C] :
( ( member(sk1(B),B)
| empty(B) )
& ( ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f5_nnf]) ).
cnf(c9,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c1,c9,c12]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t74]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET063+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 09:33:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.55/1.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.55/1.32 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------