%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET983+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 : n001.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 02:44:24 PM UTC 2026
% Result : Theorem 3.46s 1.81s
% Output : Proof 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 22 unt; 0 def)
% Number of atoms : 78 ( 20 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 78 ( 34 ~; 20 |; 19 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 66 ( 0 sgn 40 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f2_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( in(D,B)
& in(D,A)
& ~ in(D,C) )
| ( ( ~ in(D,B)
| ~ in(D,A) )
& in(D,C) ) )
| C = set_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [C,A,B,D] :
( ( ( in(sk0(A,B,C),B)
& in(sk0(A,B,C),A)
& ~ in(sk0(A,B,C),C) )
| ( ( ~ in(sk0(A,B,C),B)
| ~ in(sk0(A,B,C),A) )
& in(sk0(A,B,C),C) )
| C = set_intersection2(A,B) )
& ( ( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c4,plain,
( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2)
| X2 != set_intersection2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi3,axiom,
ifeq(X0,set_intersection2(X1,X2),ifeq(in(X3,X1),true,ifeq(in(X3,X2),true,in(X3,X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
fof(f6,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(f6_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)],[f6]) ).
fof(f6_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)],[f6_nnf]) ).
cnf(c14,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)],[f6_sk]) ).
cnf(hi9,axiom,
cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(equality_encoding,[status(esa)],[c14]) ).
fof(f7,conjecture,
! [A,B,C,D,E] :
( ( in(A,cartesian_product2(D,E))
& in(A,cartesian_product2(B,C)) )
=> in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A,B,C,D,E] :
( ( in(A,cartesian_product2(D,E))
& in(A,cartesian_product2(B,C)) )
=> in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A,B,C,D,E] :
( ~ in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E)))
& in(A,cartesian_product2(D,E))
& in(A,cartesian_product2(B,C)) ),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
( ~ in(sk3,cartesian_product2(set_intersection2(sk4,sk6),set_intersection2(sk5,sk7)))
& in(sk3,cartesian_product2(sk6,sk7))
& in(sk3,cartesian_product2(sk4,sk5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5,sk6,sk7])],[f7_nnf]) ).
cnf(c15,plain,
in(sk3,cartesian_product2(sk4,sk5)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi10,negated_conjecture,
in(sk3,cartesian_product2(sk4,sk5)) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(c16,plain,
in(sk3,cartesian_product2(sk6,sk7)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi11,negated_conjecture,
in(sk3,cartesian_product2(sk6,sk7)) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h462,plain,
in(sk3,cartesian_product2(set_intersection2(sk4,sk6),set_intersection2(sk5,sk7))) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi9,hi10,hi11]) ).
cnf(c17,plain,
~ in(sk3,cartesian_product2(set_intersection2(sk4,sk6),set_intersection2(sk5,sk7))),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi14,negated_conjecture,
ifeq(in(sk3,cartesian_product2(set_intersection2(sk4,sk6),set_intersection2(sk5,sk7))),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi14,h462]) ).
cnf(t279,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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(f5,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f5_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ empty(sk2),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f5_nnf]) ).
cnf(c13,plain,
~ empty(sk2),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c13,c17]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t279]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET983+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.58 % Computer : n001.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Thu Sep 24 12:36:22 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.46/1.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.46/1.81 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------