%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET994+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 02:44:25 PM UTC 2026
% Result : Theorem 21.08s 3.16s
% Output : Proof 21.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 24 unt; 0 def)
% Number of atoms : 163 ( 63 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 158 ( 56 ~; 58 |; 32 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 4 sgn 34 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f29,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f29_nnf,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c47,plain,
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
fof(f21,axiom,
empty(n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',spc0_boole) ).
fof(f21_nnf,plain,
empty(n0),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c37,plain,
empty(n0),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(p1356,plain,
n0 = empty_set,
inference(resolution,[status(thm)],[c47,c37]) ).
fof(f19,axiom,
! [A] :
? [B] :
( ! [C] :
( in(C,A)
=> apply(B,C) = n0 )
& relation_dom(B) = A
& function(B)
& relation(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e4_14__funct_1) ).
fof(f19_nnf,plain,
! [A] :
? [B] :
( ! [C] :
( apply(B,C) = n0
| ~ in(C,A) )
& relation_dom(B) = A
& function(B)
& relation(B) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,C] :
( ( apply(sk9(A),C) = n0
| ~ in(C,A) )
& relation_dom(sk9(A)) = A
& function(sk9(A))
& relation(sk9(A)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f19_nnf]) ).
cnf(c32,plain,
( apply(sk9(X0),X2) = n0
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p1357,plain,
( apply(sk9(X1),X0) = empty_set
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[p1356,c32]) ).
fof(f25,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f25_nnf,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c42,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
fof(f3,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f3_nnf,plain,
! [A] :
? [B] : element(B,A),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] : element(sk0(A),A),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f3_nnf]) ).
cnf(c3,plain,
element(sk0(X0),X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p1461,plain,
( in(sk0(X0),X0)
| empty(X0) ),
inference(resolution,[status(thm)],[c42,c3]) ).
cnf(p1471,plain,
( empty(X0)
| apply(sk9(X0),sk0(X0)) = empty_set ),
inference(resolution,[status(thm)],[p1357,p1461]) ).
fof(f20,axiom,
! [A] :
? [B] :
( ! [C] :
( in(C,A)
=> apply(B,C) = n1 )
& relation_dom(B) = A
& function(B)
& relation(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e7_14__funct_1) ).
fof(f20_nnf,plain,
! [A] :
? [B] :
( ! [C] :
( apply(B,C) = n1
| ~ in(C,A) )
& relation_dom(B) = A
& function(B)
& relation(B) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,C] :
( ( apply(sk10(A),C) = n1
| ~ in(C,A) )
& relation_dom(sk10(A)) = A
& function(sk10(A))
& relation(sk10(A)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f20_nnf]) ).
cnf(c35,plain,
relation_dom(sk10(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(c34,plain,
function(sk10(X0)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(c33,plain,
relation(sk10(X0)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f23,conjecture,
! [A] :
( ! [B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_dom(C) = A
& relation_dom(B) = A )
=> B = C ) ) )
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_1) ).
fof(f23_neg,negated_conjecture,
~ ! [A] :
( ! [B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_dom(C) = A
& relation_dom(B) = A )
=> B = C ) ) )
=> A = empty_set ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f23_nnf,plain,
? [A] :
( A != empty_set
& ! [B] :
( ! [C] :
( B = C
| relation_dom(C) != A
| relation_dom(B) != A
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ) ),
inference(nnf_transformation,[status(thm)],[f23_neg]) ).
fof(f23_sk,plain,
! [B,C] :
( sk11 != empty_set
& ( B = C
| relation_dom(C) != sk11
| relation_dom(B) != sk11
| ~ function(C)
| ~ relation(C)
| ~ function(B)
| ~ relation(B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f23_nnf]) ).
cnf(c39,plain,
( X1 = X2
| relation_dom(X2) != sk11
| relation_dom(X1) != sk11
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p72,plain,
( sk10(X0) = X1
| relation_dom(X1) != sk11
| relation_dom(sk10(X0)) != sk11
| ~ function(X1)
| ~ relation(X1)
| ~ function(sk10(X0)) ),
inference(resolution,[status(thm)],[c33,c39]) ).
cnf(p77,plain,
( sk10(X1) = X0
| relation_dom(X0) != sk11
| relation_dom(sk10(X1)) != sk11
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[c34,p72]) ).
cnf(c29,plain,
relation(sk9(X0)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p83,plain,
( sk10(X1) = sk9(X0)
| relation_dom(sk9(X0)) != sk11
| relation_dom(sk10(X1)) != sk11
| ~ function(sk9(X0)) ),
inference(resolution,[status(thm)],[p77,c29]) ).
cnf(c30,plain,
function(sk9(X0)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p86,plain,
( sk10(X0) = sk9(X1)
| relation_dom(sk9(X1)) != sk11
| relation_dom(sk10(X0)) != sk11 ),
inference(resolution,[status(thm)],[p83,c30]) ).
cnf(p236,plain,
( sk10(sk11) = sk9(X0)
| X0 != sk11 ),
inference(resolution,[status(thm)],[c35,p86]) ).
cnf(p253,plain,
sk10(sk11) = sk9(sk11),
inference(equality_resolution,[status(thm)],[p236]) ).
cnf(c36,plain,
( apply(sk10(X0),X2) = n1
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p1466,plain,
( apply(sk10(X0),sk0(X0)) = n1
| empty(X0) ),
inference(resolution,[status(thm)],[p1461,c36]) ).
cnf(p1474,plain,
( apply(sk9(sk11),sk0(sk11)) = n1
| empty(sk11) ),
inference(superposition,[status(thm)],[p253,p1466]) ).
cnf(p1475,plain,
( empty_set = n1
| empty(sk11)
| empty(sk11) ),
inference(superposition,[status(thm)],[p1471,p1474]) ).
cnf(p1477,plain,
( empty_set = n1
| empty(sk11) ),
inference(factoring,[status(thm)],[p1475]) ).
fof(f22,axiom,
~ empty(n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',spc1_boole) ).
fof(f22_nnf,plain,
~ empty(n1),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
~ empty(n1),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c38,plain,
~ empty(n1),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p1478,plain,
( ~ empty(empty_set)
| empty(sk11) ),
inference(superposition,[status(thm)],[p1477,c38]) ).
fof(f4,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f4_nnf,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p1480,plain,
empty(sk11),
inference(resolution,[status(thm)],[p1478,c4]) ).
cnf(p1485,plain,
sk11 = empty_set,
inference(resolution,[status(thm)],[p1480,c47]) ).
cnf(c40,plain,
sk11 != empty_set,
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p1487,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p1485,c40]) ).
cnf(p1574,plain,
$false,
inference(equality_resolution,[status(thm)],[p1487]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET994+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 12:35:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 21.08/3.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.08/3.16 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------