%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET974+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 : n011.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 02:44:23 PM UTC 2026
% Result : Theorem 7.65s 1.52s
% Output : Proof 7.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 12
% Syntax : Number of formulae : 91 ( 72 unt; 0 def)
% Number of atoms : 126 ( 65 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 72 ( 37 ~; 18 |; 14 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-5 aty)
% Number of variables : 148 ( 22 sgn 52 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A,B,C,D,E] :
~ ( ! [F,G] :
~ ( in(G,set_intersection2(C,E))
& in(F,set_intersection2(B,D))
& A = ordered_pair(F,G) )
& in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).
fof(f9_nnf,plain,
! [A,B,C,D,E] :
( ? [F,G] :
( in(G,set_intersection2(C,E))
& in(F,set_intersection2(B,D))
& A = ordered_pair(F,G) )
| ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B,C,D,E] :
( ( in(sk3(A,B,C,D,E),set_intersection2(C,E))
& in(sk2(A,B,C,D,E),set_intersection2(B,D))
& A = ordered_pair(sk2(A,B,C,D,E),sk3(A,B,C,D,E)) )
| ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f9_nnf]) ).
cnf(c11,plain,
( in(sk3(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t27,plain,
ifeq(in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))),true,in(sk3(X1,X2,X3,X4,X5),set_intersection2(X3,X5)),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t39,plain,
ifeq(in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))),true,in(sk3(X1,X2,X3,X4,X5),set_intersection2(X3,X5)),true) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(t14,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t57,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t14]) ).
fof(f11,axiom,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f11_nnf,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,set_intersection2(A,B)) )
& ( in(sk8(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8])],[f11_nnf]) ).
cnf(c15,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t23,plain,
or(not(in(X1,set_intersection2(X2,X3))),not(disjoint(X2,X3))) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t53,plain,
or(not(in(X1,set_intersection2(X2,X3))),not(disjoint(X2,X3))) = true,
inference(orient,[status(thm)],[t23]) ).
fof(f2,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f2_nnf,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t11,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t72,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t78,plain,
true = or(not(in(X1,set_intersection2(X2,X3))),not(disjoint(X3,X2))),
inference(cp,[status(thm)],[t53,t72]) ).
cnf(t126,plain,
or(not(in(X1,set_intersection2(X2,X3))),not(disjoint(X3,X2))) = true,
inference(orient,[status(thm)],[t78]) ).
fof(f10,conjecture,
! [A,B,C,D] :
( ( disjoint(C,D)
| disjoint(A,B) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
fof(f10_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ( disjoint(C,D)
| disjoint(A,B) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [A,B,C,D] :
( ~ disjoint(cartesian_product2(A,C),cartesian_product2(B,D))
& ( disjoint(C,D)
| disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( ~ disjoint(cartesian_product2(sk4,sk6),cartesian_product2(sk5,sk7))
& ( disjoint(sk6,sk7)
| disjoint(sk4,sk5) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6,sk7])],[f10_nnf]) ).
cnf(c12,plain,
( disjoint(sk6,sk7)
| disjoint(sk4,sk5) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t16,plain,
or(disjoint(sk4,sk5),disjoint(sk6,sk7)) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t51,plain,
or(disjoint(sk4,sk5),disjoint(sk6,sk7)) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(c10,plain,
( in(sk2(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t26,plain,
ifeq(in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))),true,in(sk2(X1,X2,X3,X4,X5),set_intersection2(X2,X4)),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t36,plain,
ifeq(in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))),true,in(sk2(X1,X2,X3,X4,X5),set_intersection2(X2,X4)),true) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(c14,plain,
( in(sk8(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t22,plain,
or(disjoint(X1,X2),in(sk8(X1,X2),set_intersection2(X1,X2))) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t49,plain,
or(disjoint(X1,X2),in(sk8(X1,X2),set_intersection2(X1,X2))) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(c13,plain,
~ disjoint(cartesian_product2(sk4,sk6),cartesian_product2(sk5,sk7)),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t15,plain,
disjoint(cartesian_product2(sk4,sk6),cartesian_product2(sk5,sk7)) = false,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t58,plain,
disjoint(cartesian_product2(sk4,sk6),cartesian_product2(sk5,sk7)) = false,
inference(orient,[status(thm)],[t15]) ).
cnf(t61,plain,
true = or(false,in(sk8(cartesian_product2(sk4,sk6),cartesian_product2(sk5,sk7)),set_intersection2(cartesian_product2(sk4,sk6),cartesian_product2(sk5,sk7)))),
inference(cp,[status(thm)],[t49,t58]) ).
cnf(t6,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t32,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t390,plain,
true = in(sk8(cartesian_product2(sk4,sk6),cartesian_product2(sk5,sk7)),set_intersection2(cartesian_product2(sk4,sk6),cartesian_product2(sk5,sk7))),
inference(step,[status(thm)],[t61,t32]) ).
cnf(t391,plain,
true = in(sk8(cartesian_product2(sk4,sk6),cartesian_product2(sk5,sk7)),set_intersection2(cartesian_product2(sk5,sk7),cartesian_product2(sk4,sk6))),
inference(step,[status(thm)],[t390,t72]) ).
cnf(t189,plain,
in(sk8(cartesian_product2(sk4,sk6),cartesian_product2(sk5,sk7)),set_intersection2(cartesian_product2(sk5,sk7),cartesian_product2(sk4,sk6))) = true,
inference(orient,[status(thm)],[t391]) ).
cnf(t196,plain,
true = ifeq(true,true,in(sk2(sk8(cartesian_product2(sk4,sk6),cartesian_product2(sk5,sk7)),sk5,sk7,sk4,sk6),set_intersection2(sk5,sk4)),true),
inference(cp,[status(thm)],[t36,t189]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t29,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t405,plain,
true = in(sk2(sk8(cartesian_product2(sk4,sk6),cartesian_product2(sk5,sk7)),sk5,sk7,sk4,sk6),set_intersection2(sk5,sk4)),
inference(step,[status(thm)],[t196,t29]) ).
cnf(t229,plain,
in(sk2(sk8(cartesian_product2(sk4,sk6),cartesian_product2(sk5,sk7)),sk5,sk7,sk4,sk6),set_intersection2(sk5,sk4)) = true,
inference(orient,[status(thm)],[t405]) ).
cnf(t238,plain,
true = or(not(true),not(disjoint(sk4,sk5))),
inference(cp,[status(thm)],[t126,t229]) ).
cnf(t3,plain,
not(true) = false,
introduced(definition) ).
cnf(t64,plain,
not(true) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t406,plain,
true = or(false,not(disjoint(sk4,sk5))),
inference(step,[status(thm)],[t238,t64]) ).
cnf(t407,plain,
true = not(disjoint(sk4,sk5)),
inference(step,[status(thm)],[t406,t32]) ).
cnf(t240,plain,
not(disjoint(sk4,sk5)) = true,
inference(orient,[status(thm)],[t407]) ).
cnf(t241,plain,
false = ifeq(true,true,disjoint(sk4,sk5),false),
inference(cp,[status(thm)],[t57,t240]) ).
cnf(t408,plain,
false = disjoint(sk4,sk5),
inference(step,[status(thm)],[t241,t29]) ).
cnf(t242,plain,
disjoint(sk4,sk5) = false,
inference(orient,[status(thm)],[t408]) ).
cnf(t409,plain,
or(false,disjoint(sk6,sk7)) = true,
inference(step,[status(thm)],[t51,t242]) ).
cnf(t410,plain,
disjoint(sk6,sk7) = true,
inference(step,[status(thm)],[t409,t32]) ).
cnf(t249,plain,
disjoint(sk6,sk7) = true,
inference(rw,[status(thm)],[t410]) ).
cnf(t250,plain,
disjoint(sk6,sk7) = true,
inference(orient,[status(thm)],[t249]) ).
cnf(t255,plain,
true = or(not(in(X1,set_intersection2(sk7,sk6))),not(true)),
inference(cp,[status(thm)],[t126,t250]) ).
cnf(t415,plain,
true = or(not(in(X1,set_intersection2(sk7,sk6))),false),
inference(step,[status(thm)],[t255,t64]) ).
cnf(t4,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t31,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t416,plain,
true = not(in(X1,set_intersection2(sk7,sk6))),
inference(step,[status(thm)],[t415,t31]) ).
cnf(t269,plain,
not(in(X1,set_intersection2(sk7,sk6))) = true,
inference(orient,[status(thm)],[t416]) ).
cnf(t270,plain,
false = ifeq(true,true,in(X1,set_intersection2(sk7,sk6)),false),
inference(cp,[status(thm)],[t57,t269]) ).
cnf(t417,plain,
false = in(X1,set_intersection2(sk7,sk6)),
inference(step,[status(thm)],[t270,t29]) ).
cnf(t271,plain,
in(X1,set_intersection2(sk7,sk6)) = false,
inference(orient,[status(thm)],[t417]) ).
cnf(t279,plain,
true = ifeq(in(X1,set_intersection2(cartesian_product2(X2,sk7),cartesian_product2(X3,sk6))),true,false,true),
inference(cp,[status(thm)],[t39,t271]) ).
cnf(t335,plain,
ifeq(in(X1,set_intersection2(cartesian_product2(X2,sk7),cartesian_product2(X3,sk6))),true,false,true) = true,
inference(orient,[status(thm)],[t279]) ).
cnf(t336,plain,
true = ifeq(true,true,false,true),
inference(cp,[status(thm)],[t335,t189]) ).
cnf(t438,plain,
true = false,
inference(step,[status(thm)],[t336,t29]) ).
cnf(t340,plain,
false = true,
inference(orient,[status(thm)],[t438]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f0_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f4,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f4_nnf,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f7,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c4,c7,c13,c15]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t340]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET974+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % 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 12:29:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.65/1.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.65/1.52 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------