%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET968+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 : n009.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 02:44:23 PM UTC 2026
% Result : Theorem 3.08s 0.85s
% Output : Proof 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 54 unt; 0 def)
% Number of atoms : 60 ( 55 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 24 ~; 0 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 77 ( 2 sgn 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,conjecture,
! [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) != set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
cartesian_product2(set_union2(sk2,sk3),set_union2(sk4,sk5)) != set_union2(set_union2(set_union2(cartesian_product2(sk2,sk4),cartesian_product2(sk2,sk5)),cartesian_product2(sk3,sk4)),cartesian_product2(sk3,sk5)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4,sk5])],[f7_nnf]) ).
cnf(c8,plain,
cartesian_product2(set_union2(sk2,sk3),set_union2(sk4,sk5)) != set_union2(set_union2(set_union2(cartesian_product2(sk2,sk4),cartesian_product2(sk2,sk5)),cartesian_product2(sk3,sk4)),cartesian_product2(sk3,sk5)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t10,plain,
ifeq(cartesian_product2(set_union2(sk2,sk3),set_union2(sk4,sk5)),set_union2(set_union2(set_union2(cartesian_product2(sk2,sk4),cartesian_product2(sk2,sk5)),cartesian_product2(sk3,sk4)),cartesian_product2(sk3,sk5)),false,true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
fof(f0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f0_nnf,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t3,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t13,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(orient,[status(thm)],[t3]) ).
cnf(t27,plain,
ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk4,sk5)),set_union2(set_union2(set_union2(cartesian_product2(sk2,sk4),cartesian_product2(sk2,sk5)),cartesian_product2(sk3,sk4)),cartesian_product2(sk3,sk5)),false,true) = true,
inference(step,[status(thm)],[t10,t13]) ).
cnf(t28,plain,
ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(set_union2(set_union2(cartesian_product2(sk2,sk4),cartesian_product2(sk2,sk5)),cartesian_product2(sk3,sk4)),cartesian_product2(sk3,sk5)),false,true) = true,
inference(step,[status(thm)],[t27,t13]) ).
fof(f8,axiom,
! [A,B,C] : set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).
fof(f8_nnf,plain,
! [A,B,C] : set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C] : set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c9,plain,
set_union2(set_union2(X0,X1),X2) = set_union2(X0,set_union2(X1,X2)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t7,plain,
set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t14,plain,
set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
inference(orient,[status(thm)],[t7]) ).
cnf(t29,plain,
ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(set_union2(cartesian_product2(sk2,sk4),cartesian_product2(sk2,sk5)),set_union2(cartesian_product2(sk3,sk4),cartesian_product2(sk3,sk5))),false,true) = true,
inference(step,[status(thm)],[t28,t14]) ).
cnf(t30,plain,
ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(cartesian_product2(sk2,sk4),set_union2(cartesian_product2(sk2,sk5),set_union2(cartesian_product2(sk3,sk4),cartesian_product2(sk3,sk5)))),false,true) = true,
inference(step,[status(thm)],[t29,t14]) ).
fof(f6,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(f6_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)],[f6]) ).
fof(f6_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)],[f6_nnf]) ).
cnf(c7,plain,
cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t8,plain,
set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X3)) = cartesian_product2(X1,set_union2(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t22,plain,
set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X3)) = cartesian_product2(X1,set_union2(X2,X3)),
inference(orient,[status(thm)],[t8]) ).
cnf(t31,plain,
ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(cartesian_product2(sk2,sk4),set_union2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,set_union2(sk4,sk5)))),false,true) = true,
inference(step,[status(thm)],[t30,t22]) ).
cnf(t32,plain,
ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(cartesian_product2(sk2,sk4),set_union2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,set_union2(sk5,sk4)))),false,true) = true,
inference(step,[status(thm)],[t31,t13]) ).
cnf(t26,plain,
ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(cartesian_product2(sk2,sk4),set_union2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,set_union2(sk5,sk4)))),false,true) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(c6,plain,
cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t9,plain,
set_union2(cartesian_product2(X1,X2),cartesian_product2(X3,X2)) = cartesian_product2(set_union2(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t19,plain,
set_union2(cartesian_product2(X1,X2),cartesian_product2(X3,X2)) = cartesian_product2(set_union2(X1,X3),X2),
inference(orient,[status(thm)],[t9]) ).
cnf(t2,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t2]) ).
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(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f5_nnf]) ).
cnf(c5,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5,c8]) ).
cnf(g0_0,plain,
true != ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(cartesian_product2(sk2,sk4),set_union2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,set_union2(sk5,sk4)))),false,true),
inference(rw,[status(thm)],[goal_0,t26]) ).
cnf(g0_1,plain,
true != ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(cartesian_product2(sk2,sk4),set_union2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,set_union2(sk4,sk5)))),false,true),
inference(rw,[status(thm)],[g0_0,t13]) ).
cnf(g0_2,plain,
true != ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(cartesian_product2(sk2,sk4),set_union2(cartesian_product2(sk3,set_union2(sk4,sk5)),cartesian_product2(sk2,sk5))),false,true),
inference(rw,[status(thm)],[g0_1,t13]) ).
cnf(g0_3,plain,
true != ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(set_union2(cartesian_product2(sk3,set_union2(sk4,sk5)),cartesian_product2(sk2,sk5)),cartesian_product2(sk2,sk4)),false,true),
inference(rw,[status(thm)],[g0_2,t13]) ).
cnf(g0_4,plain,
true != ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(set_union2(cartesian_product2(sk3,set_union2(sk5,sk4)),cartesian_product2(sk2,sk5)),cartesian_product2(sk2,sk4)),false,true),
inference(rw,[status(thm)],[g0_3,t13]) ).
cnf(g0_5,plain,
true != ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk4,sk5)),set_union2(set_union2(cartesian_product2(sk3,set_union2(sk5,sk4)),cartesian_product2(sk2,sk5)),cartesian_product2(sk2,sk4)),false,true),
inference(rw,[status(thm)],[g0_4,t13]) ).
cnf(g0_6,plain,
true != ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk4,sk5)),set_union2(set_union2(cartesian_product2(sk2,sk5),cartesian_product2(sk3,set_union2(sk5,sk4))),cartesian_product2(sk2,sk4)),false,true),
inference(rw,[status(thm)],[g0_5,t13]) ).
cnf(g0_7,plain,
true != ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk4,sk5)),set_union2(cartesian_product2(sk2,sk5),set_union2(cartesian_product2(sk3,set_union2(sk5,sk4)),cartesian_product2(sk2,sk4))),false,true),
inference(rw,[status(thm)],[g0_6,t14]) ).
cnf(g0_8,plain,
true != ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk4,sk5)),set_union2(set_union2(cartesian_product2(sk3,set_union2(sk5,sk4)),cartesian_product2(sk2,sk4)),cartesian_product2(sk2,sk5)),false,true),
inference(rw,[status(thm)],[g0_7,t13]) ).
cnf(g0_9,plain,
true != ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(set_union2(cartesian_product2(sk3,set_union2(sk5,sk4)),cartesian_product2(sk2,sk4)),cartesian_product2(sk2,sk5)),false,true),
inference(rw,[status(thm)],[g0_8,t13]) ).
cnf(g0_10,plain,
true != ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(cartesian_product2(sk3,set_union2(sk5,sk4)),set_union2(cartesian_product2(sk2,sk4),cartesian_product2(sk2,sk5))),false,true),
inference(rw,[status(thm)],[g0_9,t14]) ).
cnf(g0_11,plain,
true != ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(cartesian_product2(sk3,set_union2(sk5,sk4)),cartesian_product2(sk2,set_union2(sk4,sk5))),false,true),
inference(rw,[status(thm)],[g0_10,t22]) ).
cnf(g0_12,plain,
true != ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),set_union2(cartesian_product2(sk3,set_union2(sk5,sk4)),cartesian_product2(sk2,set_union2(sk5,sk4))),false,true),
inference(rw,[status(thm)],[g0_11,t13]) ).
cnf(g0_13,plain,
true != ifeq(cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),cartesian_product2(set_union2(sk3,sk2),set_union2(sk5,sk4)),false,true),
inference(rw,[status(thm)],[g0_12,t19]) ).
cnf(g0_14,plain,
true != false,
inference(rw,[status(thm)],[g0_13,t12]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 12:28:59 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.08/0.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.08/0.85 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------