%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET619+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 02:43:37 PM UTC 2026
% Result : Theorem 39.67s 5.42s
% Output : Proof 39.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 56 unt; 0 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 112 ( 5 sgn 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_union) ).
fof(f1_nnf,plain,
! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t21,plain,
union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t604,plain,
union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(orient,[status(thm)],[t21]) ).
fof(f3,axiom,
! [B,C] : union(intersection(B,C),difference(B,C)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection_difference) ).
fof(f3_nnf,plain,
! [B,C] : union(intersection(B,C),difference(B,C)) = B,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C] : union(intersection(B,C),difference(B,C)) = B,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
union(intersection(X0,X1),difference(X0,X1)) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t18,plain,
union(intersection(X1,X2),difference(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t257,plain,
union(intersection(X1,X2),difference(X1,X2)) = X1,
inference(orient,[status(thm)],[t18]) ).
cnf(t608,plain,
union(intersection(X1,X2),union(difference(X1,X2),X3)) = union(X1,X3),
inference(cp,[status(thm)],[t604,t257]) ).
cnf(t2255,plain,
union(intersection(X1,X2),union(difference(X1,X2),X3)) = union(X1,X3),
inference(orient,[status(thm)],[t608]) ).
fof(f0,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f0_nnf,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t19,plain,
union(difference(X1,X2),difference(X2,X1)) = symmetric_difference(X1,X2),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t613,plain,
union(difference(X1,X2),difference(X2,X1)) = symmetric_difference(X1,X2),
inference(orient,[status(thm)],[t19]) ).
cnf(t2261,plain,
union(X1,difference(X2,X1)) = union(intersection(X1,X2),symmetric_difference(X1,X2)),
inference(cp,[status(thm)],[t2255,t613]) ).
fof(f2,axiom,
! [B,C] : union(B,intersection(B,C)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection) ).
fof(f2_nnf,plain,
! [B,C] : union(B,intersection(B,C)) = B,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C] : union(B,intersection(B,C)) = B,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
union(X0,intersection(X0,X1)) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t14,plain,
union(X1,intersection(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t256,plain,
union(X1,intersection(X1,X2)) = X1,
inference(orient,[status(thm)],[t14]) ).
cnf(t607,plain,
union(X1,union(intersection(X1,X2),X3)) = union(X1,X3),
inference(cp,[status(thm)],[t604,t256]) ).
cnf(t673,plain,
union(X1,union(intersection(X1,X2),X3)) = union(X1,X3),
inference(orient,[status(thm)],[t607]) ).
fof(f8,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f8_nnf,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c14,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t11,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t625,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t627,plain,
X1 = union(intersection(X2,X1),difference(X1,X2)),
inference(cp,[status(thm)],[t257,t625]) ).
cnf(t665,plain,
union(intersection(X1,X2),difference(X2,X1)) = X2,
inference(orient,[status(thm)],[t627]) ).
cnf(t676,plain,
union(X1,difference(X2,X1)) = union(X1,X2),
inference(cp,[status(thm)],[t673,t665]) ).
cnf(t694,plain,
union(X1,difference(X2,X1)) = union(X1,X2),
inference(orient,[status(thm)],[t676]) ).
cnf(t2462,plain,
union(X1,X2) = union(intersection(X1,X2),symmetric_difference(X1,X2)),
inference(step,[status(thm)],[t2261,t694]) ).
fof(f7,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f7_nnf,plain,
! [B,C] : union(B,C) = union(C,B),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [B,C] : union(B,C) = union(C,B),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c13,plain,
union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t13,plain,
union(X1,X2) = union(X2,X1),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t600,plain,
union(X1,X2) = union(X2,X1),
inference(orient,[status(thm)],[t13]) ).
cnf(t2463,plain,
union(X1,X2) = union(symmetric_difference(X1,X2),intersection(X1,X2)),
inference(step,[status(thm)],[t2462,t600]) ).
cnf(t2386,plain,
union(symmetric_difference(X1,X2),intersection(X1,X2)) = union(X1,X2),
inference(orient,[status(thm)],[t2463]) ).
fof(f13,conjecture,
! [B,C] : union(B,C) = union(symmetric_difference(B,C),intersection(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th95) ).
fof(f13_neg,negated_conjecture,
~ ! [B,C] : union(B,C) = union(symmetric_difference(B,C),intersection(B,C)),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [B,C] : union(B,C) != union(symmetric_difference(B,C),intersection(B,C)),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
union(sk2,sk3) != union(symmetric_difference(sk2,sk3),intersection(sk2,sk3)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f13_nnf]) ).
cnf(c26,plain,
union(sk2,sk3) != union(symmetric_difference(sk2,sk3),intersection(sk2,sk3)),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
union(symmetric_difference(sk2,sk3),intersection(sk2,sk3)) != union(sk2,sk3),
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(g0_0,plain,
union(sk2,sk3) != union(sk2,sk3),
inference(rw,[status(thm)],[goal_0,t2386]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET619+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n008.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 11:29:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 39.67/5.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.67/5.42 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------