%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET586+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 : n016.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 7.96s 1.55s
% Output : Proof 7.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 6
% Syntax : Number of formulae : 78 ( 62 unt; 0 def)
% Number of atoms : 114 ( 59 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 63 ( 27 ~; 20 |; 11 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 102 ( 8 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f2_nnf,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c6,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t8,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t52,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(orient,[status(thm)],[t8]) ).
fof(f5,conjecture,
! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_of_subset) ).
fof(f5_neg,negated_conjecture,
~ ! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [B,C,D] :
( ~ subset(intersection(B,D),intersection(C,D))
& subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
( ~ subset(intersection(sk2,sk4),intersection(sk3,sk4))
& subset(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f5_nnf]) ).
cnf(c15,plain,
~ subset(intersection(sk2,sk4),intersection(sk3,sk4)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t10,plain,
subset(intersection(sk2,sk4),intersection(sk3,sk4)) = false,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t418,plain,
subset(intersection(sk4,sk2),intersection(sk3,sk4)) = false,
inference(step,[status(thm)],[t10,t52]) ).
cnf(t419,plain,
subset(intersection(sk4,sk2),intersection(sk4,sk3)) = false,
inference(step,[status(thm)],[t418,t52]) ).
cnf(t54,plain,
subset(intersection(sk4,sk2),intersection(sk4,sk3)) = false,
inference(orient,[status(thm)],[t419]) ).
fof(f1,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f1_nnf,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( ( ( ~ member(sk0(B,C),C)
& member(sk0(B,C),B) )
| subset(B,C) )
& ( member(D,C)
| ~ member(D,B)
| ~ subset(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c5,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t14,plain,
ifeq(member(sk0(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t37,plain,
ifeq(member(sk0(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(orient,[status(thm)],[t14]) ).
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(t19,plain,
ifeq(member(X1,X2),true,ifeq(member(X1,X3),true,member(X1,intersection(X2,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t30,plain,
ifeq(member(X1,X2),true,ifeq(member(X1,X3),true,member(X1,intersection(X2,X3)),true),true) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(c0,plain,
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t12,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t34,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X2),true) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(c4,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t11,plain,
or(subset(X1,X2),member(sk0(X1,X2),X1)) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t43,plain,
or(subset(X1,X2),member(sk0(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t55,plain,
true = or(false,member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),intersection(sk4,sk2))),
inference(cp,[status(thm)],[t43,t54]) ).
cnf(t3,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t25,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t421,plain,
true = member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),intersection(sk4,sk2)),
inference(step,[status(thm)],[t55,t25]) ).
cnf(t75,plain,
member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),intersection(sk4,sk2)) = true,
inference(orient,[status(thm)],[t421]) ).
cnf(t80,plain,
true = ifeq(true,true,member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),sk4),true),
inference(cp,[status(thm)],[t34,t75]) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t21,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t7]) ).
cnf(t422,plain,
true = member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),sk4),
inference(step,[status(thm)],[t80,t21]) ).
cnf(t89,plain,
member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),sk4) = true,
inference(orient,[status(thm)],[t422]) ).
cnf(t98,plain,
true = ifeq(true,true,ifeq(member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),X1),true,member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),intersection(sk4,X1)),true),true),
inference(cp,[status(thm)],[t30,t89]) ).
cnf(t438,plain,
true = ifeq(member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),X1),true,member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),intersection(sk4,X1)),true),
inference(step,[status(thm)],[t98,t21]) ).
cnf(t382,plain,
ifeq(member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),X1),true,member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),intersection(sk4,X1)),true) = true,
inference(orient,[status(thm)],[t438]) ).
cnf(c3,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t17,plain,
ifeq(subset(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t38,plain,
ifeq(subset(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(c14,plain,
subset(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t6,plain,
subset(sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t48,plain,
subset(sk2,sk3) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t49,plain,
true = ifeq(true,true,ifeq(member(X1,sk2),true,member(X1,sk3),true),true),
inference(cp,[status(thm)],[t38,t48]) ).
cnf(t420,plain,
true = ifeq(member(X1,sk2),true,member(X1,sk3),true),
inference(step,[status(thm)],[t49,t21]) ).
cnf(t69,plain,
ifeq(member(X1,sk2),true,member(X1,sk3),true) = true,
inference(orient,[status(thm)],[t420]) ).
cnf(c1,plain,
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t13,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t31,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X3),true) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t82,plain,
true = ifeq(true,true,member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),sk2),true),
inference(cp,[status(thm)],[t31,t75]) ).
cnf(t423,plain,
true = member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),sk2),
inference(step,[status(thm)],[t82,t21]) ).
cnf(t100,plain,
member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),sk2) = true,
inference(orient,[status(thm)],[t423]) ).
cnf(t101,plain,
true = ifeq(true,true,member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),sk3),true),
inference(cp,[status(thm)],[t69,t100]) ).
cnf(t424,plain,
true = member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),sk3),
inference(step,[status(thm)],[t101,t21]) ).
cnf(t112,plain,
member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),sk3) = true,
inference(orient,[status(thm)],[t424]) ).
cnf(t383,plain,
true = ifeq(true,true,member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),intersection(sk4,sk3)),true),
inference(cp,[status(thm)],[t382,t112]) ).
cnf(t439,plain,
true = member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),intersection(sk4,sk3)),
inference(step,[status(thm)],[t383,t21]) ).
cnf(t391,plain,
member(sk0(intersection(sk4,sk2),intersection(sk4,sk3)),intersection(sk4,sk3)) = true,
inference(orient,[status(thm)],[t439]) ).
cnf(t396,plain,
true = ifeq(true,true,subset(intersection(sk4,sk2),intersection(sk4,sk3)),true),
inference(cp,[status(thm)],[t37,t391]) ).
cnf(t443,plain,
true = subset(intersection(sk4,sk2),intersection(sk4,sk3)),
inference(step,[status(thm)],[t396,t21]) ).
cnf(t444,plain,
true = false,
inference(step,[status(thm)],[t443,t54]) ).
cnf(t412,plain,
false = true,
inference(orient,[status(thm)],[t444]) ).
cnf(t445,plain,
subset(intersection(sk4,sk2),intersection(sk4,sk3)) = true,
inference(step,[status(thm)],[t54,t412]) ).
cnf(t413,plain,
subset(intersection(sk4,sk2),intersection(sk4,sk3)) = true,
inference(orient,[status(thm)],[t445]) ).
cnf(goal_0,negated_conjecture,
subset(intersection(sk2,sk4),intersection(sk3,sk4)) != true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(g0_0,plain,
subset(intersection(sk4,sk2),intersection(sk3,sk4)) != true,
inference(rw,[status(thm)],[goal_0,t52]) ).
cnf(g0_1,plain,
subset(intersection(sk4,sk2),intersection(sk4,sk3)) != true,
inference(rw,[status(thm)],[g0_0,t52]) ).
cnf(g0_2,plain,
true != true,
inference(rw,[status(thm)],[g0_1,t413]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET586+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 11:26:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.96/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.96/1.55 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------