%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET601+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 : n011.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 02:43:33 PM UTC 2026
% Result : Theorem 63.88s 8.47s
% Output : Proof 63.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of formulae : 89 ( 89 unt; 0 def)
% Number of atoms : 89 ( 88 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 194 ( 23 sgn 54 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f9_nnf,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c15,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t12,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t623,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(orient,[status(thm)],[t12]) ).
fof(f4,axiom,
! [B,C,D] : union(B,intersection(C,D)) = intersection(union(B,C),union(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_distributes_over_intersection) ).
fof(f4_nnf,plain,
! [B,C,D] : union(B,intersection(C,D)) = intersection(union(B,C),union(B,D)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [B,C,D] : union(B,intersection(C,D)) = intersection(union(B,C),union(B,D)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
union(X0,intersection(X1,X2)) = intersection(union(X0,X1),union(X0,X2)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t28,plain,
intersection(union(X1,X2),union(X1,X3)) = union(X1,intersection(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t614,plain,
intersection(union(X1,X2),union(X1,X3)) = union(X1,intersection(X2,X3)),
inference(orient,[status(thm)],[t28]) ).
fof(f8,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f8_nnf,plain,
! [B,C] : union(B,C) = union(C,B),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [B,C] : union(B,C) = union(C,B),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c14,plain,
union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t13,plain,
union(X1,X2) = union(X2,X1),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t602,plain,
union(X1,X2) = union(X2,X1),
inference(orient,[status(thm)],[t13]) ).
cnf(t616,plain,
union(X1,intersection(X2,X3)) = intersection(union(X2,X1),union(X1,X3)),
inference(cp,[status(thm)],[t614,t602]) ).
cnf(t1009,plain,
intersection(union(X1,X2),union(X2,X3)) = union(X2,intersection(X1,X3)),
inference(orient,[status(thm)],[t616]) ).
cnf(t1037,plain,
union(X1,intersection(X2,X3)) = intersection(union(X2,X1),union(X3,X1)),
inference(cp,[status(thm)],[t1009,t602]) ).
cnf(t1450,plain,
intersection(union(X1,X2),union(X3,X2)) = union(X2,intersection(X1,X3)),
inference(orient,[status(thm)],[t1037]) ).
fof(f3,axiom,
! [B,C] : union(B,intersection(B,C)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection) ).
fof(f3_nnf,plain,
! [B,C] : union(B,intersection(B,C)) = B,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C] : union(B,intersection(B,C)) = B,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
union(X0,intersection(X0,X1)) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t14,plain,
union(X1,intersection(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t256,plain,
union(X1,intersection(X1,X2)) = X1,
inference(orient,[status(thm)],[t14]) ).
cnf(t625,plain,
X1 = union(X1,intersection(X2,X1)),
inference(cp,[status(thm)],[t256,t623]) ).
cnf(t648,plain,
union(X1,intersection(X2,X1)) = X1,
inference(orient,[status(thm)],[t625]) ).
cnf(t1467,plain,
union(intersection(X1,X2),intersection(X2,X3)) = intersection(X2,union(X3,intersection(X1,X2))),
inference(cp,[status(thm)],[t1450,t648]) ).
fof(f1,axiom,
! [B] : intersection(B,B) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotency_of_intersection) ).
fof(f1_nnf,plain,
! [B] : intersection(B,B) = B,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B] : intersection(B,B) = B,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
intersection(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t1,plain,
intersection(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t257,plain,
intersection(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t258,plain,
X1 = union(X1,X1),
inference(cp,[status(thm)],[t256,t257]) ).
cnf(t640,plain,
union(X1,X1) = X1,
inference(orient,[status(thm)],[t258]) ).
cnf(t642,plain,
union(X1,intersection(X1,X2)) = intersection(X1,union(X1,X2)),
inference(cp,[status(thm)],[t614,t640]) ).
cnf(t46642,plain,
X1 = intersection(X1,union(X1,X2)),
inference(step,[status(thm)],[t642,t256]) ).
cnf(t657,plain,
intersection(X1,union(X1,X2)) = X1,
inference(orient,[status(thm)],[t46642]) ).
cnf(t659,plain,
X1 = intersection(X1,union(X2,X1)),
inference(cp,[status(thm)],[t657,t602]) ).
cnf(t664,plain,
intersection(X1,union(X2,X1)) = X1,
inference(orient,[status(thm)],[t659]) ).
fof(f0,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(f0_nnf,plain,
! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t22,plain,
union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t606,plain,
union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(orient,[status(thm)],[t22]) ).
cnf(t667,plain,
X1 = intersection(X1,union(X2,union(X3,X1))),
inference(cp,[status(thm)],[t664,t606]) ).
cnf(t750,plain,
intersection(X1,union(X2,union(X3,X1))) = X1,
inference(orient,[status(thm)],[t667]) ).
cnf(t755,plain,
intersection(X1,X2) = intersection(intersection(X1,X2),union(X3,X1)),
inference(cp,[status(thm)],[t750,t256]) ).
fof(f2,axiom,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_intersection) ).
fof(f2_nnf,plain,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t19,plain,
intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t627,plain,
intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
inference(orient,[status(thm)],[t19]) ).
cnf(t46648,plain,
intersection(X1,X2) = intersection(X1,intersection(X2,union(X3,X1))),
inference(step,[status(thm)],[t755,t627]) ).
cnf(t942,plain,
intersection(X1,intersection(X2,union(X3,X1))) = intersection(X1,X2),
inference(orient,[status(thm)],[t46648]) ).
cnf(t945,plain,
intersection(X1,union(X2,X3)) = intersection(X1,union(X2,intersection(X3,X1))),
inference(cp,[status(thm)],[t942,t614]) ).
cnf(t1414,plain,
intersection(X1,union(X2,intersection(X3,X1))) = intersection(X1,union(X2,X3)),
inference(orient,[status(thm)],[t945]) ).
cnf(t46663,plain,
union(intersection(X1,X2),intersection(X2,X3)) = intersection(X2,union(X3,X1)),
inference(step,[status(thm)],[t1467,t1414]) ).
cnf(t1699,plain,
union(intersection(X1,X2),intersection(X2,X3)) = intersection(X2,union(X3,X1)),
inference(orient,[status(thm)],[t46663]) ).
cnf(t1023,plain,
union(X1,intersection(union(X2,X3),Y3)) = intersection(union(X2,union(X3,X1)),union(X1,Y3)),
inference(cp,[status(thm)],[t1009,t606]) ).
cnf(t18131,plain,
intersection(union(X1,union(X2,X3)),union(X3,Y3)) = union(X3,intersection(union(X1,X2),Y3)),
inference(orient,[status(thm)],[t1023]) ).
cnf(t650,plain,
X1 = union(X1,intersection(X2,intersection(X3,X1))),
inference(cp,[status(thm)],[t648,t627]) ).
cnf(t733,plain,
union(X1,intersection(X2,intersection(X3,X1))) = X1,
inference(orient,[status(thm)],[t650]) ).
cnf(t738,plain,
union(X1,X2) = union(union(X1,X2),intersection(X3,X1)),
inference(cp,[status(thm)],[t733,t657]) ).
cnf(t46647,plain,
union(X1,X2) = union(X1,union(X2,intersection(X3,X1))),
inference(step,[status(thm)],[t738,t606]) ).
cnf(t915,plain,
union(X1,union(X2,intersection(X3,X1))) = union(X1,X2),
inference(orient,[status(thm)],[t46647]) ).
cnf(t18152,plain,
union(intersection(X1,X2),intersection(union(X2,X3),Y3)) = intersection(union(X2,X3),union(intersection(X1,X2),Y3)),
inference(cp,[status(thm)],[t18131,t915]) ).
cnf(t46144,plain,
intersection(union(X1,X2),union(intersection(X3,X1),Y3)) = union(intersection(X3,X1),intersection(union(X1,X2),Y3)),
inference(orient,[status(thm)],[t18152]) ).
fof(f13,conjecture,
! [B,C,D] : union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) = intersection(intersection(union(B,C),union(C,D)),union(D,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th72) ).
fof(f13_neg,negated_conjecture,
~ ! [B,C,D] : union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) = intersection(intersection(union(B,C),union(C,D)),union(D,B)),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [B,C,D] : union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) != intersection(intersection(union(B,C),union(C,D)),union(D,B)),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
union(union(intersection(sk2,sk3),intersection(sk3,sk4)),intersection(sk4,sk2)) != intersection(intersection(union(sk2,sk3),union(sk3,sk4)),union(sk4,sk2)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f13_nnf]) ).
cnf(c26,plain,
union(union(intersection(sk2,sk3),intersection(sk3,sk4)),intersection(sk4,sk2)) != intersection(intersection(union(sk2,sk3),union(sk3,sk4)),union(sk4,sk2)),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
union(union(intersection(sk2,sk3),intersection(sk3,sk4)),intersection(sk4,sk2)) != intersection(intersection(union(sk2,sk3),union(sk3,sk4)),union(sk4,sk2)),
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(g0_0,plain,
union(union(intersection(sk2,sk3),intersection(sk3,sk4)),intersection(sk4,sk2)) != union(union(intersection(sk2,sk3),intersection(sk3,sk4)),intersection(sk2,sk4)),
inference(rw,[status(thm)],[goal_0,t623]) ).
cnf(g0_1,plain,
union(union(intersection(sk2,sk3),intersection(sk3,sk4)),intersection(sk4,sk2)) != union(intersection(sk3,union(sk4,sk2)),intersection(sk2,sk4)),
inference(rw,[status(thm)],[g0_0,t1699]) ).
cnf(g0_2,plain,
union(union(intersection(sk2,sk3),intersection(sk3,sk4)),intersection(sk4,sk2)) != union(intersection(union(sk4,sk2),sk3),intersection(sk2,sk4)),
inference(rw,[status(thm)],[g0_1,t623]) ).
cnf(g0_3,plain,
union(union(intersection(sk2,sk3),intersection(sk3,sk4)),intersection(sk4,sk2)) != union(intersection(sk2,sk4),intersection(union(sk4,sk2),sk3)),
inference(rw,[status(thm)],[g0_2,t602]) ).
cnf(g0_4,plain,
intersection(union(sk3,intersection(sk2,sk4)),union(sk4,sk2)) != union(intersection(sk2,sk4),intersection(union(sk4,sk2),sk3)),
inference(rw,[status(thm)],[g0_3,t1009]) ).
cnf(g0_5,plain,
intersection(union(intersection(sk2,sk4),sk3),union(sk4,sk2)) != union(intersection(sk2,sk4),intersection(union(sk4,sk2),sk3)),
inference(rw,[status(thm)],[g0_4,t602]) ).
cnf(g0_6,plain,
intersection(union(sk4,sk2),union(intersection(sk2,sk4),sk3)) != union(intersection(sk2,sk4),intersection(union(sk4,sk2),sk3)),
inference(rw,[status(thm)],[g0_5,t623]) ).
cnf(g0_7,plain,
union(intersection(sk2,sk4),intersection(union(sk4,sk2),sk3)) != union(intersection(sk2,sk4),intersection(union(sk4,sk2),sk3)),
inference(rw,[status(thm)],[g0_6,t46144]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET601+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n011.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Thu Sep 24 11:24:42 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 63.88/8.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 63.88/8.47 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------