%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU167+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 3.60s 1.20s
% Output : Proof 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 25 unt; 0 def)
% Number of atoms : 62 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 44 ( 20 ~; 10 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 58 ( 2 sgn 26 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,conjecture,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f4_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)],[f4]) ).
fof(f4_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)],[f4_neg]) ).
fof(f4_sk,plain,
( ~ subset(cartesian_product2(sk2,sk4),cartesian_product2(sk3,sk5))
& subset(sk4,sk5)
& subset(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4,sk5])],[f4_nnf]) ).
cnf(c7,plain,
~ subset(cartesian_product2(sk2,sk4),cartesian_product2(sk3,sk5)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t16,plain,
ifeq(subset(cartesian_product2(sk2,sk4),cartesian_product2(sk3,sk5)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f3,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/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f3_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)],[f3]) ).
fof(f3_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)],[f3_nnf]) ).
cnf(c4,plain,
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(subset(X0,X1),true,subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(c6,plain,
subset(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi5,negated_conjecture,
subset(sk4,sk5) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h3,plain,
subset(cartesian_product2(V0,sk4),cartesian_product2(V0,sk5)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi5]) ).
cnf(c3,plain,
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi2,axiom,
ifeq(subset(X0,X1),true,subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(c5,plain,
subset(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,negated_conjecture,
subset(sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h2,plain,
subset(cartesian_product2(sk2,V0),cartesian_product2(sk3,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi4]) ).
fof(f5,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f5_nnf,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c8,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi6,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X1,X2),true,subset(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t12,plain,
subset(cartesian_product2(sk2,sk4),cartesian_product2(sk3,sk5)) = true,
inference(hyper_resolution,[status(thm)],[hi6,h2,h3]) ).
cnf(t99,plain,
subset(cartesian_product2(sk2,sk4),cartesian_product2(sk3,sk5)) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t292,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t16,t99]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t65,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t293,plain,
false = true,
inference(step,[status(thm)],[t292,t65]) ).
cnf(t291,plain,
false = true,
inference(orient,[status(thm)],[t293]) ).
fof(f1,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f1_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ empty(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f1_nnf]) ).
cnf(c1,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c1,c7]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t291]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU167+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:59:38 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.60/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.60/1.20 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------