%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU186+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 : n005.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 02:51:16 PM UTC 2026
% Result : Theorem 2.15s 0.79s
% Output : Proof 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 71 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 67 ( 28 ~; 23 |; 9 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 2 sgn 34 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f21_nnf,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c26,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f10,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f10_nnf,plain,
! [A] :
? [B] : element(B,A),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] : element(sk3(A),A),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f10_nnf]) ).
cnf(c12,plain,
element(sk3(X0),X0),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p49,plain,
( in(sk3(X0),X0)
| empty(X0) ),
inference(resolution,[status(thm)],[c26,c12]) ).
fof(f3,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f3_nnf,plain,
! [A] :
( ( ? [B] :
( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) )
| relation(A) )
& ( ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( ( ( sk2(A) != ordered_pair(C,D)
& in(sk2(A),A) )
| relation(A) )
& ( B = ordered_pair(sk0(A,B),sk1(A,B))
| ~ in(B,A)
| ~ relation(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f3_nnf]) ).
cnf(c3,plain,
( X1 = ordered_pair(sk0(X0,X1),sk1(X0,X1))
| ~ in(X1,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f22,conjecture,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
fof(f22_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f22_nnf,plain,
? [A] :
( A != empty_set
& ! [B,C] : ~ in(ordered_pair(B,C),A)
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f22_neg]) ).
fof(f22_sk,plain,
! [B,C] :
( sk8 != empty_set
& ~ in(ordered_pair(B,C),sk8)
& relation(sk8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8])],[f22_nnf]) ).
cnf(c27,plain,
relation(sk8),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p35,plain,
( X0 = ordered_pair(sk0(sk8,X0),sk1(sk8,X0))
| ~ in(X0,sk8) ),
inference(resolution,[status(thm)],[c3,c27]) ).
cnf(p51,plain,
( sk3(sk8) = ordered_pair(sk0(sk8,sk3(sk8)),sk1(sk8,sk3(sk8)))
| empty(sk8) ),
inference(resolution,[status(thm)],[p49,p35]) ).
cnf(c28,plain,
~ in(ordered_pair(X1,X2),sk8),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p52,plain,
( ~ in(sk3(sk8),sk8)
| empty(sk8) ),
inference(superposition,[status(thm)],[p51,c28]) ).
cnf(p56,plain,
( empty(sk8)
| empty(sk8) ),
inference(resolution,[status(thm)],[p52,p49]) ).
cnf(p57,plain,
empty(sk8),
inference(factoring,[status(thm)],[p56]) ).
fof(f23,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f23_nnf,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c30,plain,
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p58,plain,
sk8 = empty_set,
inference(resolution,[status(thm)],[p57,c30]) ).
cnf(c29,plain,
sk8 != empty_set,
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p60,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p58,c29]) ).
cnf(p62,plain,
$false,
inference(equality_resolution,[status(thm)],[p60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU186+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 13:05:47 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.15/0.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.15/0.79 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------