%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET913+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 02:44:16 PM UTC 2026
% Result : Theorem 6.69s 1.38s
% Output : Proof 6.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 38 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 35 ( 23 ~; 6 |; 5 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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; 5 con; 0-4 aty)
% Number of variables : 26 ( 0 sgn 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f5_nnf,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c6,plain,
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi6,axiom,
ifeq(disjoint(singleton(X0),X1),true,ifeq(in(X0,X1),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
fof(f4,conjecture,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_zfmisc_1) ).
fof(f4_neg,negated_conjecture,
~ ! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
? [A,B] :
( in(A,B)
& disjoint(singleton(A),B) ),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
( in(sk2,sk3)
& disjoint(singleton(sk2),sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f4_nnf]) ).
cnf(c4,plain,
disjoint(singleton(sk2),sk3),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi2,negated_conjecture,
disjoint(singleton(sk2),sk3) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(c5,plain,
in(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,negated_conjecture,
in(sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi6,hi2,hi3]) ).
cnf(t20,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f1_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f3,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f3_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ empty(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f3_nnf]) ).
cnf(c3,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c1,c3,c6]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t20]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET913+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n005.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:21:48 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.69/1.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.69/1.38 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------