%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET581+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 02:43:30 PM UTC 2026
% Result : Theorem 45.05s 11.13s
% Output : Proof 45.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of formulae : 95 ( 73 unt; 0 def)
% Number of atoms : 157 ( 78 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 106 ( 44 ~; 32 |; 23 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 105 ( 8 sgn 45 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t21,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t264,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t21]) ).
fof(f5,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
fof(f5_nnf,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [B,C] :
( ( member(sk1(B),B)
| empty(B) )
& ( ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f5_nnf]) ).
cnf(c13,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t74,plain,
or(not(empty(X1)),not(member(X2,X1))) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t272,plain,
or(not(empty(X1)),not(member(X2,X1))) = true,
inference(orient,[status(thm)],[t74]) ).
fof(f0,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f0_nnf,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [D,B,C] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c2,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,axiom,
ifeq(member(X0,X1),true,ifeq(member(X0,X2),true,member(X0,intersection(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
fof(f6,conjecture,
! [B,C,D] :
( ( member(B,D)
& member(B,C) )
=> not_equal(intersection(C,D),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th24) ).
fof(f6_neg,negated_conjecture,
~ ! [B,C,D] :
( ( member(B,D)
& member(B,C) )
=> not_equal(intersection(C,D),empty_set) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [B,C,D] :
( ~ not_equal(intersection(C,D),empty_set)
& member(B,D)
& member(B,C) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( ~ not_equal(intersection(sk3,sk4),empty_set)
& member(sk2,sk4)
& member(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f6_nnf]) ).
cnf(c15,plain,
member(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi10,negated_conjecture,
member(sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(c16,plain,
member(sk2,sk4),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi11,negated_conjecture,
member(sk2,sk4) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h2,plain,
member(sk2,intersection(sk3,sk4)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi10,hi11]) ).
fof(f2,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f2_nnf,plain,
! [B,C] :
( ( ? [D] :
( ( member(D,C)
& ~ member(D,B) )
| ( ~ member(D,C)
& member(D,B) ) )
| B = C )
& ( ! [D] :
( ( ~ member(D,C)
| member(D,B) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C,D] :
( ( ( member(sk0(B,C),C)
& ~ member(sk0(B,C),B) )
| ( ~ member(sk0(B,C),C)
& member(sk0(B,C),B) )
| B = C )
& ( ( ( ~ member(D,C)
| member(D,B) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| member(X2,X0)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi4,axiom,
ifeq(X0,X1,ifeq(member(X2,X1),true,member(X2,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(hi22,axiom,
or(false,X0) = X0,
introduced(definition) ).
cnf(h24,plain,
member(sk2,or(false,intersection(sk3,sk4))) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi22,h2]) ).
cnf(t194,plain,
member(sk2,or(false,or(false,intersection(sk3,sk4)))) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi22,h24]) ).
cnf(t8,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t257,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t529,plain,
member(sk2,or(false,intersection(sk3,sk4))) = true,
inference(step,[status(thm)],[t194,t257]) ).
cnf(t530,plain,
member(sk2,intersection(sk3,sk4)) = true,
inference(step,[status(thm)],[t529,t257]) ).
fof(f4,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f4_nnf,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c12,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t11,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t281,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t531,plain,
member(sk2,intersection(sk4,sk3)) = true,
inference(step,[status(thm)],[t530,t281]) ).
cnf(t289,plain,
member(sk2,intersection(sk4,sk3)) = true,
inference(orient,[status(thm)],[t531]) ).
cnf(t290,plain,
true = or(not(empty(intersection(sk4,sk3))),not(true)),
inference(cp,[status(thm)],[t272,t289]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t265,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t563,plain,
true = or(not(empty(intersection(sk4,sk3))),false),
inference(step,[status(thm)],[t290,t265]) ).
cnf(t6,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t256,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t564,plain,
true = not(empty(intersection(sk4,sk3))),
inference(step,[status(thm)],[t563,t256]) ).
cnf(t480,plain,
not(empty(intersection(sk4,sk3))) = true,
inference(orient,[status(thm)],[t564]) ).
cnf(t481,plain,
false = ifeq(true,true,empty(intersection(sk4,sk3)),false),
inference(cp,[status(thm)],[t264,t480]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t565,plain,
false = empty(intersection(sk4,sk3)),
inference(step,[status(thm)],[t481,t258]) ).
cnf(t482,plain,
empty(intersection(sk4,sk3)) = false,
inference(orient,[status(thm)],[t565]) ).
cnf(t22,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t260,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t22]) ).
fof(f3,axiom,
! [B,C] :
( not_equal(B,C)
<=> B != C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f3_nnf,plain,
! [B,C] :
( ( B = C
| not_equal(B,C) )
& ( B != C
| ~ not_equal(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C] :
( ( B = C
| not_equal(B,C) )
& ( B != C
| ~ not_equal(B,C) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c11,plain,
( X0 = X1
| not_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t73,plain,
or(not_equal(X1,X2),eq(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t274,plain,
or(not_equal(X1,X2),eq(X1,X2)) = true,
inference(orient,[status(thm)],[t73]) ).
cnf(c17,plain,
~ not_equal(intersection(sk3,sk4),empty_set),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t20,plain,
not_equal(intersection(sk3,sk4),empty_set) = false,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t267,plain,
not_equal(intersection(sk3,sk4),empty_set) = false,
inference(orient,[status(thm)],[t20]) ).
cnf(t282,plain,
not_equal(intersection(sk3,sk4),empty_set) = false,
inference(rw,[status(thm)],[t267]) ).
cnf(t559,plain,
not_equal(intersection(sk4,sk3),empty_set) = false,
inference(step,[status(thm)],[t282,t281]) ).
cnf(t470,plain,
not_equal(intersection(sk4,sk3),empty_set) = false,
inference(orient,[status(thm)],[t559]) ).
cnf(t472,plain,
true = or(false,eq(intersection(sk4,sk3),empty_set)),
inference(cp,[status(thm)],[t274,t470]) ).
cnf(t569,plain,
true = eq(intersection(sk4,sk3),empty_set),
inference(step,[status(thm)],[t472,t257]) ).
cnf(t490,plain,
eq(intersection(sk4,sk3),empty_set) = true,
inference(orient,[status(thm)],[t569]) ).
cnf(t491,plain,
empty_set = ifeq(true,true,intersection(sk4,sk3),empty_set),
inference(cp,[status(thm)],[t260,t490]) ).
cnf(t570,plain,
empty_set = intersection(sk4,sk3),
inference(step,[status(thm)],[t491,t258]) ).
cnf(t492,plain,
intersection(sk4,sk3) = empty_set,
inference(orient,[status(thm)],[t570]) ).
cnf(t571,plain,
empty(empty_set) = false,
inference(step,[status(thm)],[t482,t492]) ).
cnf(c14,plain,
( member(sk1(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t72,plain,
or(empty(X1),member(sk1(X1),X1)) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t279,plain,
or(empty(X1),member(sk1(X1),X1)) = true,
inference(orient,[status(thm)],[t72]) ).
fof(f1,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f1_nnf,plain,
! [B] : ~ member(B,empty_set),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B] : ~ member(B,empty_set),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t3,plain,
member(X1,empty_set) = false,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t261,plain,
member(X1,empty_set) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t280,plain,
true = or(empty(empty_set),false),
inference(cp,[status(thm)],[t279,t261]) ).
cnf(t547,plain,
true = empty(empty_set),
inference(step,[status(thm)],[t280,t256]) ).
cnf(t437,plain,
empty(empty_set) = true,
inference(orient,[status(thm)],[t547]) ).
cnf(t572,plain,
true = false,
inference(step,[status(thm)],[t571,t437]) ).
cnf(t496,plain,
true = false,
inference(rw,[status(thm)],[t572]) ).
cnf(t500,plain,
false = true,
inference(orient,[status(thm)],[t496]) ).
cnf(c10,plain,
( X0 != X1
| ~ not_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c10,c13,c17]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t500]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET581+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n008.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 11:21:32 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 45.05/11.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.05/11.13 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------