%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET971+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 : n005.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 3.54s 6.06s
% Output : Proof 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 49 unt; 0 def)
% Number of atoms : 69 ( 46 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 23 ~; 3 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-4 aty)
% Number of variables : 68 ( 2 sgn 32 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f2_nnf,plain,
? [A] : empty(A),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
empty(sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c2,plain,
empty(sk0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t0,plain,
empty(sk0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t24,plain,
empty(sk0) = true,
inference(orient,[status(thm)],[t0]) ).
fof(f7,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f7_nnf,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c9,plain,
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(subset(X0,X1),true,set_intersection2(X0,X1),X0) = X0,
inference(equality_encoding,[status(esa)],[c9]) ).
fof(f6,conjecture,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_zfmisc_1) ).
fof(f6_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [A,B,C,D] :
( set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) != cartesian_product2(A,C)
& subset(C,D)
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( set_intersection2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,sk4)) != cartesian_product2(sk2,sk4)
& subset(sk4,sk5)
& subset(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4,sk5])],[f6_nnf]) ).
cnf(c6,plain,
subset(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi5,negated_conjecture,
subset(sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t2,plain,
set_intersection2(sk2,sk3) = sk2,
inference(hyper_resolution,[status(thm)],[hi7,hi5]) ).
fof(f0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f0_nnf,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t8,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t25,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t41,plain,
set_intersection2(sk3,sk2) = sk2,
inference(step,[status(thm)],[t2,t25]) ).
cnf(t33,plain,
set_intersection2(sk3,sk2) = sk2,
inference(orient,[status(thm)],[t41]) ).
cnf(c7,plain,
subset(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,negated_conjecture,
subset(sk4,sk5) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t3,plain,
set_intersection2(sk4,sk5) = sk4,
inference(hyper_resolution,[status(thm)],[hi7,hi6]) ).
cnf(t42,plain,
set_intersection2(sk5,sk4) = sk4,
inference(step,[status(thm)],[t3,t25]) ).
cnf(t37,plain,
set_intersection2(sk5,sk4) = sk4,
inference(orient,[status(thm)],[t42]) ).
fof(f5,axiom,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(f5_nnf,plain,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t12,plain,
set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)) = cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4)),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t28,plain,
cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
inference(orient,[status(thm)],[t12]) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t7]) ).
fof(f3,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f3_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ empty(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f3_nnf]) ).
cnf(c3,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(c8,plain,
set_intersection2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,sk4)) != cartesian_product2(sk2,sk4),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c8]) ).
cnf(g0_0,plain,
true != ifeq(set_intersection2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,sk4)),cartesian_product2(sk2,sk4),false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(set_intersection2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,sk4)),cartesian_product2(sk2,sk4),false,empty(sk0)),
inference(rw,[status(thm)],[g0_0,t24]) ).
cnf(g0_2,plain,
true != ifeq(set_intersection2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,sk4)),cartesian_product2(set_intersection2(sk3,sk2),sk4),false,empty(sk0)),
inference(rw,[status(thm)],[g0_1,t33]) ).
cnf(g0_3,plain,
true != ifeq(set_intersection2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,sk4)),cartesian_product2(set_intersection2(sk2,sk3),sk4),false,empty(sk0)),
inference(rw,[status(thm)],[g0_2,t25]) ).
cnf(g0_4,plain,
true != ifeq(set_intersection2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,sk4)),cartesian_product2(set_intersection2(sk2,sk3),set_intersection2(sk5,sk4)),false,empty(sk0)),
inference(rw,[status(thm)],[g0_3,t37]) ).
cnf(g0_5,plain,
true != ifeq(set_intersection2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,sk4)),cartesian_product2(set_intersection2(sk2,sk3),set_intersection2(sk4,sk5)),false,empty(sk0)),
inference(rw,[status(thm)],[g0_4,t25]) ).
cnf(g0_6,plain,
true != ifeq(set_intersection2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,sk4)),cartesian_product2(set_intersection2(sk3,sk2),set_intersection2(sk4,sk5)),false,empty(sk0)),
inference(rw,[status(thm)],[g0_5,t25]) ).
cnf(g0_7,plain,
true != ifeq(set_intersection2(cartesian_product2(sk3,sk4),cartesian_product2(sk2,sk5)),cartesian_product2(set_intersection2(sk3,sk2),set_intersection2(sk4,sk5)),false,empty(sk0)),
inference(rw,[status(thm)],[g0_6,t25]) ).
cnf(g0_8,plain,
true != ifeq(set_intersection2(cartesian_product2(sk3,sk4),cartesian_product2(sk2,sk5)),cartesian_product2(set_intersection2(sk3,sk2),set_intersection2(sk4,sk5)),false,true),
inference(rw,[status(thm)],[g0_7,t24]) ).
cnf(g0_9,plain,
true != ifeq(set_intersection2(cartesian_product2(sk3,sk4),cartesian_product2(sk2,sk5)),set_intersection2(cartesian_product2(sk3,sk4),cartesian_product2(sk2,sk5)),false,true),
inference(rw,[status(thm)],[g0_8,t28]) ).
cnf(g0_10,plain,
true != false,
inference(rw,[status(thm)],[g0_9,t14]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET971+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.38 % Computer : n005.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 12:28:52 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.54/6.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.54/6.06 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------