%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET632+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 : n014.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 02:43:40 PM UTC 2026
% Result : Theorem 13.08s 2.13s
% Output : Proof 13.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 16 unt; 0 def)
% Number of atoms : 132 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 135 ( 53 ~; 46 |; 28 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 5 sgn 44 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f1_nnf,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| intersect(B,C) )
& ( ( member(sk1(B,C),C)
& member(sk1(B,C),B) )
| ~ intersect(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f1_nnf]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_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(sk2(B),B)
| empty(B) )
& ( ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f7_nnf]) ).
cnf(c15,plain,
( member(sk2(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f0,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f0_nnf,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C,D] :
( ( ( ~ member(sk0(B,C),C)
& member(sk0(B,C),B) )
| subset(B,C) )
& ( member(D,C)
| ~ member(D,B)
| ~ subset(B,C) ) ),
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]) ).
fof(f8,conjecture,
! [B,C,D] :
( ( disjoint(C,D)
& subset(B,D)
& subset(B,C) )
=> B = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th114) ).
fof(f8_neg,negated_conjecture,
~ ! [B,C,D] :
( ( disjoint(C,D)
& subset(B,D)
& subset(B,C) )
=> B = empty_set ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [B,C,D] :
( B != empty_set
& disjoint(C,D)
& subset(B,D)
& subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( sk3 != empty_set
& disjoint(sk4,sk5)
& subset(sk3,sk5)
& subset(sk3,sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5])],[f8_nnf]) ).
cnf(c16,plain,
subset(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p20,plain,
( member(X0,sk4)
| ~ member(X0,sk3) ),
inference(resolution,[status(thm)],[c0,c16]) ).
cnf(p26,plain,
( member(sk2(sk3),sk4)
| empty(sk3) ),
inference(resolution,[status(thm)],[c15,p20]) ).
cnf(p34,plain,
( empty(sk3)
| ~ member(sk2(sk3),X0)
| intersect(sk4,X0) ),
inference(resolution,[status(thm)],[c5,p26]) ).
cnf(c17,plain,
subset(sk3,sk5),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p21,plain,
( member(X0,sk5)
| ~ member(X0,sk3) ),
inference(resolution,[status(thm)],[c0,c17]) ).
cnf(p27,plain,
( member(sk2(sk3),sk5)
| empty(sk3) ),
inference(resolution,[status(thm)],[c15,p21]) ).
cnf(p38,plain,
( empty(sk3)
| empty(sk3)
| intersect(sk4,sk5) ),
inference(resolution,[status(thm)],[p34,p27]) ).
cnf(p78,plain,
( empty(sk3)
| intersect(sk4,sk5) ),
inference(factoring,[status(thm)],[p38]) ).
fof(f3,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f3_nnf,plain,
! [B,C] :
( ( intersect(B,C)
| disjoint(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C] :
( ( intersect(B,C)
| disjoint(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c7,plain,
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(c18,plain,
disjoint(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p25,plain,
~ intersect(sk4,sk5),
inference(resolution,[status(thm)],[c7,c18]) ).
cnf(p79,plain,
empty(sk3),
inference(resolution,[status(thm)],[p78,p25]) ).
cnf(c14,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p80,plain,
~ member(X0,sk3),
inference(resolution,[status(thm)],[p79,c14]) ).
cnf(c1,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p81,plain,
subset(sk3,X0),
inference(resolution,[status(thm)],[p80,c1]) ).
fof(f4,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f4_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)],[f4]) ).
fof(f4_sk,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c11,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p82,plain,
( ~ subset(X0,sk3)
| sk3 = X0 ),
inference(resolution,[status(thm)],[p81,c11]) ).
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(c6,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p24,plain,
subset(empty_set,X0),
inference(resolution,[status(thm)],[c1,c6]) ).
cnf(p83,plain,
sk3 = empty_set,
inference(resolution,[status(thm)],[p82,p24]) ).
cnf(c19,plain,
sk3 != empty_set,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p84,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p83,c19]) ).
cnf(p85,plain,
$false,
inference(equality_resolution,[status(thm)],[p84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET632+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 11:31:03 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.08/2.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.08/2.13 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------