%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET604+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 : n026.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 02:43:34 PM UTC 2026
% Result : Theorem 6.73s 1.33s
% Output : Proof 6.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 22 unt; 0 def)
% Number of atoms : 63 ( 19 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 60 ( 31 ~; 17 |; 9 &)
% ( 3 <=>; 0 =>; 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; 4 con; 0-4 aty)
% Number of variables : 44 ( 6 sgn 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_empty_set) ).
fof(f1_nnf,plain,
! [B,C] :
( ( ~ subset(B,C)
| difference(B,C) = empty_set )
& ( subset(B,C)
| difference(B,C) != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C] :
( ( ~ subset(B,C)
| difference(B,C) = empty_set )
& ( subset(B,C)
| difference(B,C) != empty_set ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c2,plain,
( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi2,axiom,
ifeq(subset(X0,X1),true,difference(X0,X1),empty_set) = empty_set,
inference(equality_encoding,[status(esa)],[c2]) ).
fof(f0,axiom,
! [B] : subset(empty_set,B),
file('/export/starexec/sandbox2/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]) ).
cnf(h4,plain,
difference(empty_set,V0) = empty_set,
inference(hyper_resolution,[status(thm)],[hi2,hi0]) ).
fof(f8,conjecture,
! [B] : difference(empty_set,B) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_no_difference_with_empty_set) ).
fof(f8_neg,negated_conjecture,
~ ! [B] : difference(empty_set,B) = empty_set,
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [B] : difference(empty_set,B) != empty_set,
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
difference(empty_set,sk2) != empty_set,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f8_nnf]) ).
cnf(c16,plain,
difference(empty_set,sk2) != empty_set,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi16,negated_conjecture,
ifeq(difference(empty_set,sk2),empty_set,false,true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi16,h4]) ).
cnf(t105,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f2,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f2_nnf,plain,
! [B] : ~ member(B,empty_set),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B] : ~ member(B,empty_set),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f3,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f3_nnf,plain,
! [B,C,D] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [D,B,C] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f7,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
fof(f7_nnf,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [B,C] :
( ( member(sk1(B),B)
| empty(B) )
& ( ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f7_nnf]) ).
cnf(c14,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c5,c14,c16]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t105]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET604+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 11:27:55 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.73/1.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.73/1.33 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------