%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET019+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 : n002.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 02:41:31 PM UTC 2026
% Result : Theorem 8.19s 1.68s
% Output : Proof 8.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 17 unt; 0 def)
% Number of atoms : 64 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 62 ( 27 ~; 15 |; 16 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 32 ( 2 sgn 22 !; 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]) ).
cnf(hi5,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X1,X0),true,equal_set(X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
fof(f11,conjecture,
! [A,B] :
( ( subset(B,A)
& subset(A,B) )
=> equal_set(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI02) ).
fof(f11_neg,negated_conjecture,
~ ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
=> equal_set(A,B) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [A,B] :
( ~ equal_set(A,B)
& subset(B,A)
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
( ~ equal_set(sk3,sk4)
& subset(sk4,sk3)
& subset(sk3,sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f11_nnf]) ).
cnf(c29,plain,
subset(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi27,negated_conjecture,
subset(sk3,sk4) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(c30,plain,
subset(sk4,sk3),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi28,negated_conjecture,
subset(sk4,sk3) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(h20,plain,
equal_set(sk3,sk4) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi27,hi28]) ).
cnf(c31,plain,
~ equal_set(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi31,negated_conjecture,
ifeq(equal_set(sk3,sk4),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi31,h20]) ).
cnf(t198,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]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14,c16,c31]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t198]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET019+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n002.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 09:15:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.19/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.19/1.68 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------