%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU167+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 02:51:12 PM UTC 2026
% Result : Theorem 8.21s 1.53s
% Output : Proof 8.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 52 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 16 ~; 10 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 50 ( 0 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f2_nnf,plain,
! [A,B,C] :
( ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) )
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] :
( ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) )
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(subset(X0,X1),true,subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
fof(f3,conjecture,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f3_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f3_nnf,plain,
? [A,B,C,D] :
( ~ subset(cartesian_product2(A,C),cartesian_product2(B,D))
& subset(C,D)
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f3_neg]) ).
fof(f3_sk,plain,
( ~ subset(cartesian_product2(sk0,sk2),cartesian_product2(sk1,sk3))
& subset(sk2,sk3)
& subset(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f3_nnf]) ).
cnf(c5,plain,
subset(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi4,negated_conjecture,
subset(sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h3,plain,
subset(cartesian_product2(V0,sk2),cartesian_product2(V0,sk3)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi4]) ).
cnf(c2,plain,
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi1,axiom,
ifeq(subset(X0,X1),true,subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(c4,plain,
subset(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,negated_conjecture,
subset(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h2,plain,
subset(cartesian_product2(sk0,V0),cartesian_product2(sk1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi3]) ).
fof(f4,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f4_nnf,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c7,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi5,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X1,X2),true,subset(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t9,plain,
subset(cartesian_product2(sk0,sk2),cartesian_product2(sk1,sk3)) = true,
inference(hyper_resolution,[status(thm)],[hi5,h2,h3]) ).
cnf(t30,plain,
subset(cartesian_product2(sk0,sk2),cartesian_product2(sk1,sk3)) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(c6,plain,
~ subset(cartesian_product2(sk0,sk2),cartesian_product2(sk1,sk3)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
subset(cartesian_product2(sk0,sk2),cartesian_product2(sk1,sk3)) != true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t30]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU167+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.43 % Computer : n015.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Thu Sep 24 13:04:40 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.21/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.21/1.53 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------