%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET954+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 02:44:21 PM UTC 2026
% Result : Theorem 6.80s 1.33s
% Output : Proof 6.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 28 unt; 0 def)
% Number of atoms : 66 ( 17 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 55 ( 31 ~; 13 |; 7 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 76 ( 10 sgn 38 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f4_nnf,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi1,axiom,
ifeq(in(ordered_pair(X0,X1),cartesian_product2(X2,X3)),true,in(X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
fof(f7,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
=> in(ordered_pair(B,A),cartesian_product2(D,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
=> in(ordered_pair(B,A),cartesian_product2(D,C)) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A,B,C,D] :
( ~ in(ordered_pair(B,A),cartesian_product2(D,C))
& in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
( ~ in(ordered_pair(sk3,sk2),cartesian_product2(sk5,sk4))
& in(ordered_pair(sk2,sk3),cartesian_product2(sk4,sk5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4,sk5])],[f7_nnf]) ).
cnf(c9,plain,
in(ordered_pair(sk2,sk3),cartesian_product2(sk4,sk5)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi6,negated_conjecture,
in(ordered_pair(sk2,sk3),cartesian_product2(sk4,sk5)) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
fof(f2,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f2_nnf,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h1,plain,
in(sk2,sk4) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi6,hi2]) ).
cnf(c5,plain,
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(in(ordered_pair(X0,X1),cartesian_product2(X2,X3)),true,in(X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h0,plain,
in(sk3,sk5) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi6,hi2]) ).
cnf(c6,plain,
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
ifeq(in(X0,X1),true,ifeq(in(X2,X3),true,in(ordered_pair(X0,X2),cartesian_product2(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h4,plain,
in(unordered_pair(unordered_pair(sk3,sk2),singleton(sk3)),cartesian_product2(sk5,sk4)) = true,
inference(hyper_resolution,[status(thm)],[hi4,h0,h1,hi2]) ).
cnf(c10,plain,
~ in(ordered_pair(sk3,sk2),cartesian_product2(sk5,sk4)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi10,negated_conjecture,
ifeq(in(ordered_pair(sk3,sk2),cartesian_product2(sk5,sk4)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi10,h4,hi2]) ).
cnf(t77,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/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(f3,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f3_nnf,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f6,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f6_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ empty(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f6_nnf]) ).
cnf(c8,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c3,c8,c10]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t77]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET954+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:32:14 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.80/1.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.80/1.33 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------