%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET583+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 02:43:30 PM UTC 2026
% Result : Theorem 6.04s 1.19s
% Output : Proof 6.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 11 unt; 0 def)
% Number of atoms : 41 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 36 ( 14 ~; 8 |; 11 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 16 ( 0 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f0_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)],[f0]) ).
fof(f0_sk,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c2,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X1,X0),true,X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
fof(f3,conjecture,
! [B,C] :
( ( subset(C,B)
& subset(B,C) )
=> B = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_extensionality) ).
fof(f3_neg,negated_conjecture,
~ ! [B,C] :
( ( subset(C,B)
& subset(B,C) )
=> B = C ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f3_nnf,plain,
? [B,C] :
( B != C
& subset(C,B)
& subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f3_neg]) ).
fof(f3_sk,plain,
( sk1 != sk2
& subset(sk2,sk1)
& subset(sk1,sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f3_nnf]) ).
cnf(c7,plain,
subset(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi7,negated_conjecture,
subset(sk1,sk2) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(c8,plain,
subset(sk2,sk1),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi8,negated_conjecture,
subset(sk2,sk1) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t0,plain,
sk2 = sk1,
inference(hyper_resolution,[status(thm)],[hi2,hi7,hi8]) ).
cnf(t58,plain,
sk1 = sk2,
inference(orient,[status(thm)],[t0]) ).
cnf(c9,plain,
sk1 != sk2,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
sk2 != sk1,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(g0_0,plain,
sk2 != sk2,
inference(rw,[status(thm)],[goal_0,t58]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET583+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 11:24:11 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.04/1.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.04/1.19 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------