%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET183+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 03:31:45 PM UTC 2025
% Result : Theorem 14.41s 2.15s
% Output : CNFRefutation 14.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 75 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 65 ( 28 ~; 29 |; 1 &)
% ( 4 <=>; 3 =>; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 2 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subset_intersection,plain,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_intersection) ).
fof(prove_subset_intersection_negated,plain,
~ ! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
inference(negate_conjecture,[status(cth)],[prove_subset_intersection]) ).
cnf(18,plain,
subset(sK3,sK4),
inference(cnf,[status(esa)],[prove_subset_intersection_negated]) ).
cnf(l0,plain,
subset(sK3,sK4),
inference(instantiation,[status(thm)],[18]) ).
fof(subset_defn,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
cnf(4,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l1,plain,
( ~ member(sK2(intersection(sK3,sK4),sK3),sK3)
| ~ subset(sK3,sK4)
| member(sK2(intersection(sK3,sK4),sK3),sK4) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l119,plain,
( ~ member(sK2(intersection(sK3,sK4),sK3),intersection(sK4,sK3))
| ~ subset(intersection(sK4,sK3),sK3)
| member(sK2(intersection(sK3,sK4),sK3),sK3) ),
inference(instantiation,[status(thm)],[4]) ).
fof(intersection_defn,plain,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
cnf(2,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l3,plain,
( ~ member(sK2(intersection(sK3,sK4),sK3),sK3)
| ~ member(sK2(intersection(sK3,sK4),sK3),sK4)
| member(sK2(intersection(sK3,sK4),sK3),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[2]) ).
fof(commutativity_of_intersection,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
cnf(10,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_intersection]) ).
cnf(l137,plain,
intersection(sK4,sK3) = intersection(sK3,sK4),
inference(instantiation,[status(thm)],[10]) ).
fof(equal_member_defn,plain,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
cnf(17,plain,
( member(sK2(X0,X1),X1)
| ~ sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l55,plain,
( member(sK2(intersection(sK3,sK4),sK3),sK3)
| ~ sP0(sK3,intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(l32,plain,
( ~ member(sK2(intersection(sK3,sK4),sK3),intersection(sK3,sK4))
| ~ subset(intersection(sK3,sK4),sK3)
| member(sK2(intersection(sK3,sK4),sK3),sK3) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(15,plain,
( ~ member(sK2(X0,X1),X1)
| X0 = X1
| sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l79,plain,
( ~ member(sK2(intersection(sK3,sK4),sK3),sK3)
| intersection(sK3,sK4) = sK3
| sP0(sK3,intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(16,plain,
( ~ member(sK2(X0,X1),X0)
| ~ sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l86,plain,
( ~ member(sK2(intersection(sK3,sK4),sK3),intersection(sK3,sK4))
| ~ sP0(sK3,intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(19,plain,
intersection(sK3,sK4) != sK3,
inference(cnf,[status(esa)],[prove_subset_intersection_negated]) ).
cnf(l105,plain,
intersection(sK3,sK4) != sK3,
inference(instantiation,[status(thm)],[19]) ).
cnf(l121,plain,
intersection(sK3,sK4) = intersection(sK4,sK3),
inference(instantiation,[status(thm)],[10]) ).
cnf(14,plain,
( member(sK2(X0,X1),X0)
| X0 = X1
| sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l62,plain,
( member(sK2(intersection(sK3,sK4),sK3),intersection(sK3,sK4))
| intersection(sK3,sK4) = sK3
| sP0(sK3,intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(l126,plain,
( member(sK2(intersection(sK3,sK4),sK3),intersection(sK3,sK4))
| intersection(sK3,sK4) = sK3
| sP0(sK3,intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(l131,plain,
intersection(sK3,sK4) != sK3,
inference(instantiation,[status(thm)],[19]) ).
fof(intersection_is_subset,plain,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_is_subset) ).
cnf(3,plain,
subset(intersection(X0,X1),X0),
inference(cnf,[status(esa)],[intersection_is_subset]) ).
cnf(l149,plain,
subset(intersection(sK3,sK4),sK3),
inference(instantiation,[status(thm)],[3]) ).
cnf(l132,plain,
( member(sK2(intersection(sK3,sK4),sK3),sK3)
| ~ sP0(sK3,intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(0,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l64,plain,
( ~ member(sK2(intersection(sK3,sK4),sK3),intersection(sK3,sK4))
| member(sK2(intersection(sK3,sK4),sK3),sK3) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l73,plain,
intersection(sK3,sK4) != sK3,
inference(instantiation,[status(thm)],[19]) ).
cnf(l68,plain,
subset(intersection(sK3,sK4),sK3),
inference(instantiation,[status(thm)],[3]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l119,l3,l137,l55,l32,l79,l86,l105,l121,l62,l126,l131,l149,l132,l64,l73,l68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET183+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.32 % Computer : n024.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 21 20:20:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % launching worker at depth: 1
% 0.12/0.33 % launching worker at depth: 6
% 0.12/0.33 % launching worker at depth: 8
% 0.12/0.33 % launching worker at depth: 2
% 0.12/0.33 % launching worker at depth: 5
% 0.12/0.33 % launching worker at depth: 4
% 0.12/0.33 % launching worker at depth: 7
% 0.12/0.33 % launching worker at depth: 3
% 0.12/0.33 % launching worker at depth: 9
% 0.12/0.33 % launching worker at depth: 10
% 0.12/0.35 % launching worker at depth: 11
% 1.68/0.54 % launching worker at depth: 12
% 14.41/2.15 % SZS status Theorem for theBenchmark
% 14.41/2.15 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------