%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET904+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 02:44:15 PM UTC 2026
% Result : Theorem 5.93s 6.18s
% Output : Proof 5.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 24 unt; 0 def)
% Number of atoms : 48 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 35 ( 23 ~; 6 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 34 ( 2 sgn 16 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f6_nnf,plain,
? [A] : empty(A),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
empty(sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f6_nnf]) ).
cnf(c6,plain,
empty(sk0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t1,plain,
empty(sk0) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t26,plain,
empty(sk0) = true,
inference(orient,[status(thm)],[t1]) ).
fof(f9,axiom,
! [A,B] :
( subset(set_union2(singleton(A),B),B)
=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).
fof(f9_nnf,plain,
! [A,B] :
( in(A,B)
| ~ subset(set_union2(singleton(A),B),B) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] :
( in(A,B)
| ~ subset(set_union2(singleton(A),B),B) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c10,plain,
( in(X0,X1)
| ~ subset(set_union2(singleton(X0),X1),X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi7,axiom,
ifeq(subset(set_union2(singleton(X0),X1),X1),true,in(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
fof(f8,conjecture,
! [A,B] :
( subset(set_union2(singleton(A),B),B)
=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_zfmisc_1) ).
fof(f8_neg,negated_conjecture,
~ ! [A,B] :
( subset(set_union2(singleton(A),B),B)
=> in(A,B) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [A,B] :
( ~ in(A,B)
& subset(set_union2(singleton(A),B),B) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( ~ in(sk2,sk3)
& subset(set_union2(singleton(sk2),sk3),sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f8_nnf]) ).
cnf(c8,plain,
subset(set_union2(singleton(sk2),sk3),sk3),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi6,negated_conjecture,
subset(set_union2(singleton(sk2),sk3),sk3) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t2,plain,
in(sk2,sk3) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi6]) ).
cnf(t29,plain,
in(sk2,sk3) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
fof(f5,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f5_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f7,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f7_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ empty(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f7_nnf]) ).
cnf(c7,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(c9,plain,
~ in(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5,c7,c9]) ).
cnf(g0_0,plain,
true != ifeq(in(sk2,sk3),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(in(sk2,sk3),true,false,empty(sk0)),
inference(rw,[status(thm)],[g0_0,t26]) ).
cnf(g0_2,plain,
true != ifeq(in(sk2,sk3),in(sk2,sk3),false,empty(sk0)),
inference(rw,[status(thm)],[g0_1,t29]) ).
cnf(g0_3,plain,
true != false,
inference(rw,[status(thm)],[g0_2,t14]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET904+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n015.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 12:24:45 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.93/6.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.93/6.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------