%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU131+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 02:51:01 PM UTC 2026
% Result : Theorem 5.28s 6.13s
% Output : Proof 5.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 10 unt; 0 def)
% Number of atoms : 130 ( 32 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 136 ( 48 ~; 61 |; 21 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 68 ( 6 sgn 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,conjecture,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(f6_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [A,B] :
( ( subset(A,B)
& set_difference(A,B) != empty_set )
| ( ~ subset(A,B)
& set_difference(A,B) = empty_set ) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( ( subset(sk2,sk3)
& set_difference(sk2,sk3) != empty_set )
| ( ~ subset(sk2,sk3)
& set_difference(sk2,sk3) = empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f6_nnf]) ).
cnf(c17,plain,
( subset(sk2,sk3)
| set_difference(sk2,sk3) = empty_set ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f2,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f2_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ~ in(D,B)
& in(D,A)
& ~ in(D,C) )
| ( ( in(D,B)
| ~ in(D,A) )
& in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [C,A,B,D] :
( ( ( ~ in(sk1(A,B,C),B)
& in(sk1(A,B,C),A)
& ~ in(sk1(A,B,C),C) )
| ( ( in(sk1(A,B,C),B)
| ~ in(sk1(A,B,C),A) )
& in(sk1(A,B,C),C) )
| C = set_difference(A,B) )
& ( ( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f2_nnf]) ).
cnf(c6,plain,
( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p55,plain,
( in(X1,sk3)
| ~ in(X1,sk2)
| in(X1,X0)
| X0 != empty_set
| subset(sk2,sk3) ),
inference(superposition,[status(thm)],[c17,c6]) ).
cnf(p59,plain,
( in(X0,sk3)
| ~ in(X0,sk2)
| in(X0,empty_set)
| subset(sk2,sk3) ),
inference(equality_resolution,[status(thm)],[p55]) ).
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f1_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk0(A,B),B)
& in(sk0(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c2,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p60,plain,
( subset(sk2,X0)
| in(sk0(sk2,X0),sk3)
| in(sk0(sk2,X0),empty_set)
| subset(sk2,sk3) ),
inference(resolution,[status(thm)],[p59,c2]) ).
cnf(p61,plain,
( in(sk0(sk2,sk3),sk3)
| in(sk0(sk2,sk3),empty_set)
| subset(sk2,sk3) ),
inference(factoring,[status(thm)],[p60]) ).
cnf(c3,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p67,plain,
( subset(sk2,sk3)
| in(sk0(sk2,sk3),empty_set)
| subset(sk2,sk3) ),
inference(resolution,[status(thm)],[p61,c3]) ).
cnf(p81,plain,
( in(sk0(sk2,sk3),empty_set)
| subset(sk2,sk3) ),
inference(factoring,[status(thm)],[p67]) ).
fof(f11,axiom,
! [A] : set_difference(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(f11_nnf,plain,
! [A] : set_difference(A,empty_set) = A,
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] : set_difference(A,empty_set) = A,
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c27,plain,
set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(c5,plain,
( ~ in(X3,X1)
| ~ in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p43,plain,
( ~ in(X2,X0)
| X0 != set_difference(X1,X0) ),
inference(factoring,[status(thm)],[c5]) ).
cnf(p49,plain,
( ~ in(X1,empty_set)
| empty_set != X0 ),
inference(superposition,[status(thm)],[c27,p43]) ).
cnf(p51,plain,
~ in(X0,empty_set),
inference(equality_resolution,[status(thm)],[p49]) ).
cnf(p84,plain,
subset(sk2,sk3),
inference(resolution,[status(thm)],[p81,p51]) ).
cnf(c1,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p86,plain,
( in(X0,sk3)
| ~ in(X0,sk2) ),
inference(resolution,[status(thm)],[p84,c1]) ).
cnf(c8,plain,
( in(sk1(X0,X1,X2),X0)
| in(sk1(X0,X1,X2),X2)
| X2 = set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p90,plain,
( in(sk1(sk2,X0,X1),X1)
| X1 = set_difference(sk2,X0)
| in(sk1(sk2,X0,X1),sk3) ),
inference(resolution,[status(thm)],[p86,c8]) ).
cnf(p118,plain,
( empty_set = set_difference(sk2,X0)
| in(sk1(sk2,X0,empty_set),sk3) ),
inference(resolution,[status(thm)],[p90,p51]) ).
cnf(c9,plain,
( ~ in(sk1(X0,X1,X2),X1)
| in(sk1(X0,X1,X2),X2)
| X2 = set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p134,plain,
( in(sk1(sk2,sk3,empty_set),empty_set)
| empty_set = set_difference(sk2,sk3)
| empty_set = set_difference(sk2,sk3) ),
inference(resolution,[status(thm)],[p118,c9]) ).
cnf(p271,plain,
( in(sk1(sk2,sk3,empty_set),empty_set)
| empty_set = set_difference(sk2,sk3) ),
inference(factoring,[status(thm)],[p134]) ).
cnf(p289,plain,
empty_set = set_difference(sk2,sk3),
inference(resolution,[status(thm)],[p271,p51]) ).
cnf(c18,plain,
( set_difference(sk2,sk3) != empty_set
| ~ subset(sk2,sk3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p85,plain,
set_difference(sk2,sk3) != empty_set,
inference(resolution,[status(thm)],[p84,c18]) ).
cnf(p290,plain,
empty_set != empty_set,
inference(superposition,[status(thm)],[p289,p85]) ).
cnf(p301,plain,
$false,
inference(equality_resolution,[status(thm)],[p290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU131+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.36 % Computer : n004.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Thu Sep 24 12:51:27 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.28/6.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.28/6.13 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------