%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET979+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 : n014.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 5.82s 11.24s
% Output : Proof 5.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 19 unt; 0 def)
% Number of atoms : 35 ( 30 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 13 ~; 3 |; 5 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 42 ( 0 sgn 21 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,conjecture,
! [A,B,C] :
( cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B)))
& cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_zfmisc_1) ).
fof(f8_neg,negated_conjecture,
~ ! [A,B,C] :
( cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B)))
& cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [A,B,C] :
( cartesian_product2(C,unordered_pair(A,B)) != set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B)))
| cartesian_product2(unordered_pair(A,B),C) != set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( cartesian_product2(sk4,unordered_pair(sk2,sk3)) != set_union2(cartesian_product2(sk4,singleton(sk2)),cartesian_product2(sk4,singleton(sk3)))
| cartesian_product2(unordered_pair(sk2,sk3),sk4) != set_union2(cartesian_product2(singleton(sk2),sk4),cartesian_product2(singleton(sk3),sk4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f8_nnf]) ).
cnf(c9,plain,
( cartesian_product2(sk4,unordered_pair(sk2,sk3)) != set_union2(cartesian_product2(sk4,singleton(sk2)),cartesian_product2(sk4,singleton(sk3)))
| cartesian_product2(unordered_pair(sk2,sk3),sk4) != set_union2(cartesian_product2(singleton(sk2),sk4),cartesian_product2(singleton(sk3),sk4)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi10,negated_conjecture,
ifeq(cartesian_product2(unordered_pair(sk2,sk3),sk4),set_union2(cartesian_product2(singleton(sk2),sk4),cartesian_product2(singleton(sk3),sk4)),ifeq(cartesian_product2(sk4,unordered_pair(sk2,sk3)),set_union2(cartesian_product2(sk4,singleton(sk2)),cartesian_product2(sk4,singleton(sk3))),false,true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
fof(f7,axiom,
! [A,B,C] :
( cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B))
& cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
fof(f7_nnf,plain,
! [A,B,C] :
( cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B))
& cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] :
( cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B))
& cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(c8,plain,
cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi8,axiom,
cartesian_product2(X0,set_union2(X1,X2)) = set_union2(cartesian_product2(X0,X1),cartesian_product2(X0,X2)),
inference(equality_encoding,[status(esa)],[c8]) ).
fof(f9,axiom,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_enumset1) ).
fof(f9_nnf,plain,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c10,plain,
unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi1,axiom,
unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi10,hi7,hi8,hi1]) ).
cnf(t24,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f6,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/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(c6,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c6,c9]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t24]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET979+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/10.39 % Computer : n014.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Thu Sep 24 12:29:57 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.82/11.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.82/11.24 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------