%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL021+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 02:34:48 PM UTC 2026
% Result : Theorem 194.30s 28.54s
% Output : Proof 194.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 126
% Number of leaves : 14
% Syntax : Number of formulae : 388 ( 384 unt; 0 def)
% Number of atoms : 392 ( 391 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 12 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 593 ( 86 sgn 79 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f0_nnf,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t5,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t19,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t5]) ).
fof(f3,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f3_nnf,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t6,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t39,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t6]) ).
cnf(t41,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t39,t19]) ).
cnf(t383310,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t41,t39]) ).
cnf(t74,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t383310]) ).
fof(f10,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f10_nnf,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t12,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t383307,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t12,t19]) ).
cnf(t30,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t383307]) ).
fof(f9,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f9_nnf,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t7,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t51,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(orient,[status(thm)],[t7]) ).
fof(f7,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f7_nnf,plain,
! [X0] : converse(converse(X0)) = X0,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X0] : converse(converse(X0)) = X0,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
converse(converse(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t2,plain,
converse(converse(X1)) = X1,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t18,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t53,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t51,t18]) ).
cnf(t137,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t53]) ).
fof(f5,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
fof(f5_nnf,plain,
! [X0] : composition(X0,one) = X0,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X0] : composition(X0,one) = X0,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
composition(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t0,plain,
composition(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t17,plain,
composition(X1,one) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t138,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t137,t17]) ).
cnf(t383312,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t138,t18]) ).
cnf(t152,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t383312]) ).
cnf(t153,plain,
one = converse(one),
inference(cp,[status(thm)],[t152,t17]) ).
cnf(t159,plain,
converse(one) = one,
inference(orient,[status(thm)],[t153]) ).
cnf(t383313,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t152,t159]) ).
cnf(t169,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t383313]) ).
cnf(t170,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t169]) ).
cnf(t173,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t30,t170]) ).
cnf(t383315,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t173,t159]) ).
cnf(t383316,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t383315,t170]) ).
cnf(t197,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t383316]) ).
cnf(t207,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t39,t197]) ).
cnf(t214,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t207]) ).
fof(f2,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(f2_nnf,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t13,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t14,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t20,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t14]) ).
cnf(t383326,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t20,t19]) ).
cnf(t383327,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t383326,t39]) ).
cnf(t383328,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t383327,t19]) ).
cnf(t296,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t383328]) ).
fof(f12,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
fof(f12_nnf,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t4,plain,
meet(X1,complement(X1)) = zero,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t63,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t297,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t296,t63]) ).
cnf(t383329,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t297,t39]) ).
cnf(t321,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t383329]) ).
fof(f1,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
fof(f1_nnf,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t10,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t21,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
fof(f11,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
fof(f11_nnf,plain,
! [X0] : top = join(X0,complement(X0)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X0] : top = join(X0,complement(X0)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
top = join(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t3,plain,
join(X1,complement(X1)) = top,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t24,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t3]) ).
cnf(t40,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t39,t24]) ).
cnf(t383308,plain,
zero = complement(top),
inference(step,[status(thm)],[t40,t63]) ).
cnf(t65,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t383308]) ).
cnf(t201,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t197,t65]) ).
cnf(t383317,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t201,t65]) ).
cnf(t383318,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t383317,t65]) ).
cnf(t208,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t383318]) ).
cnf(t209,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t21,t208]) ).
cnf(t224,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t209]) ).
cnf(t323,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t224,t321]) ).
cnf(t383330,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t323,t321]) ).
cnf(t325,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t383330]) ).
cnf(t383331,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t321,t325]) ).
cnf(t333,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t383331]) ).
cnf(t351,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t333]) ).
cnf(t383338,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t214,t351]) ).
cnf(t354,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t383338]) ).
cnf(t380,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t354]) ).
cnf(t381,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(cp,[status(thm)],[t380,t39]) ).
cnf(t760,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t381]) ).
cnf(t763,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(cp,[status(thm)],[t760,t380]) ).
cnf(t791,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(orient,[status(thm)],[t763]) ).
cnf(t801,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t380,t791]) ).
cnf(t837,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t801]) ).
cnf(t382,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t197,t380]) ).
cnf(t383349,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t382,t380]) ).
cnf(t383350,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t383349,t380]) ).
cnf(t395,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t383350]) ).
cnf(t397,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t21,t395]) ).
cnf(t473,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t397]) ).
cnf(t475,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1),
inference(cp,[status(thm)],[t473,t296]) ).
cnf(t383357,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t475,t296]) ).
cnf(t383358,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t383357,t19]) ).
cnf(t479,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t383358]) ).
cnf(t481,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t479,t74]) ).
cnf(t487,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t481]) ).
cnf(t491,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t21,t487]) ).
cnf(t1543,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t491]) ).
cnf(t383383,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(step,[status(thm)],[t296,t837]) ).
cnf(t863,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[t383383]) ).
cnf(t3545,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(orient,[status(thm)],[t863]) ).
cnf(t3597,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(cp,[status(thm)],[t1543,t3545]) ).
cnf(t3610,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t3597]) ).
cnf(t762,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(cp,[status(thm)],[t760,t380]) ).
cnf(t771,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t762]) ).
cnf(t780,plain,
meet(complement(X1),X2) = complement(join(X1,complement(X2))),
inference(cp,[status(thm)],[t380,t771]) ).
cnf(t813,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(orient,[status(thm)],[t780]) ).
cnf(t820,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(cp,[status(thm)],[t813,t380]) ).
cnf(t864,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(orient,[status(thm)],[t820]) ).
cnf(t3615,plain,
join(X1,complement(X2)) = join(X1,complement(join(X2,X1))),
inference(cp,[status(thm)],[t3610,t864]) ).
cnf(t4184,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t3615]) ).
cnf(t4251,plain,
meet(X1,complement(complement(join(X2,complement(X1))))) = complement(join(complement(X1),complement(X2))),
inference(cp,[status(thm)],[t837,t4184]) ).
cnf(t383455,plain,
meet(X1,join(X2,complement(X1))) = complement(join(complement(X1),complement(X2))),
inference(step,[status(thm)],[t4251,t380]) ).
cnf(t383456,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(step,[status(thm)],[t383455,t39]) ).
cnf(t4260,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t383456]) ).
cnf(t4275,plain,
meet(X1,X2) = meet(X1,join(complement(X1),X2)),
inference(cp,[status(thm)],[t4260,t19]) ).
cnf(t4292,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t4275]) ).
cnf(t484,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t21,t479]) ).
cnf(t1383,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t484]) ).
cnf(t4308,plain,
meet(X1,join(meet(complement(X1),X2),X3)) = meet(X1,join(complement(X1),X3)),
inference(cp,[status(thm)],[t4292,t1383]) ).
cnf(t383797,plain,
meet(X1,join(meet(complement(X1),X2),X3)) = meet(X1,X3),
inference(step,[status(thm)],[t4308,t4292]) ).
cnf(t16898,plain,
meet(X1,join(meet(complement(X1),X2),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t383797]) ).
fof(f4,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
fof(f4_nnf,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t9,plain,
composition(composition(X1,X2),X3) = composition(X1,composition(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t46,plain,
composition(composition(X1,X2),X3) = composition(X1,composition(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t31,plain,
complement(X1) = join(complement(X1),composition(X2,complement(composition(converse(X2),X1)))),
inference(cp,[status(thm)],[t30,t18]) ).
cnf(t5078,plain,
join(complement(X1),composition(X2,complement(composition(converse(X2),X1)))) = complement(X1),
inference(orient,[status(thm)],[t31]) ).
cnf(t5085,plain,
complement(top) = join(zero,composition(X1,complement(composition(converse(X1),top)))),
inference(cp,[status(thm)],[t5078,t65]) ).
cnf(t383480,plain,
zero = join(zero,composition(X1,complement(composition(converse(X1),top)))),
inference(step,[status(thm)],[t5085,t65]) ).
cnf(t383481,plain,
zero = composition(X1,complement(composition(converse(X1),top))),
inference(step,[status(thm)],[t383480,t325]) ).
cnf(t3617,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(cp,[status(thm)],[t3610,t74]) ).
cnf(t3654,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t3617]) ).
cnf(t3665,plain,
join(complement(X1),X2) = join(complement(X1),meet(X1,X2)),
inference(cp,[status(thm)],[t3654,t380]) ).
cnf(t4467,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t3665]) ).
cnf(t477,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(cp,[status(thm)],[t473,t19]) ).
cnf(t494,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t477]) ).
cnf(t26,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(cp,[status(thm)],[t21,t24]) ).
cnf(t270,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(orient,[status(thm)],[t26]) ).
cnf(t276,plain,
join(top,complement(X1)) = join(X1,complement(X1)),
inference(cp,[status(thm)],[t270,t197]) ).
cnf(t383324,plain,
join(top,complement(X1)) = top,
inference(step,[status(thm)],[t276,t24]) ).
cnf(t288,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t383324]) ).
cnf(t289,plain,
top = join(top,meet(X1,X2)),
inference(cp,[status(thm)],[t288,t39]) ).
cnf(t316,plain,
join(top,meet(X1,X2)) = top,
inference(orient,[status(thm)],[t289]) ).
cnf(t352,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t316,t351]) ).
cnf(t360,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t352]) ).
cnf(t383343,plain,
join(X1,join(complement(X1),X2)) = top,
inference(step,[status(thm)],[t270,t360]) ).
cnf(t361,plain,
join(X1,join(complement(X1),X2)) = top,
inference(orient,[status(thm)],[t383343]) ).
cnf(t496,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),top),
inference(cp,[status(thm)],[t494,t361]) ).
cnf(t383367,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),top),
inference(step,[status(thm)],[t496,t21]) ).
cnf(t383368,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,top)),
inference(step,[status(thm)],[t383367,t21]) ).
cnf(t364,plain,
top = join(X1,top),
inference(cp,[status(thm)],[t360,t19]) ).
cnf(t392,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t364]) ).
cnf(t383369,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),top),
inference(step,[status(thm)],[t383368,t392]) ).
cnf(t383370,plain,
join(complement(X1),join(X2,X1)) = top,
inference(step,[status(thm)],[t383369,t392]) ).
cnf(t563,plain,
join(complement(X1),join(X2,X1)) = top,
inference(orient,[status(thm)],[t383370]) ).
cnf(t570,plain,
top = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t563,t487]) ).
cnf(t383376,plain,
top = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t570,t19]) ).
cnf(t606,plain,
join(X1,complement(meet(X2,X1))) = top,
inference(orient,[status(thm)],[t383376]) ).
cnf(t613,plain,
meet(X1,meet(X2,complement(X1))) = complement(top),
inference(cp,[status(thm)],[t39,t606]) ).
cnf(t383379,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t613,t65]) ).
cnf(t626,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t383379]) ).
cnf(t627,plain,
zero = meet(complement(X1),meet(X2,X1)),
inference(cp,[status(thm)],[t626,t380]) ).
cnf(t639,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t627]) ).
fof(f8,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
fof(f8_nnf,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t8,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t34,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t8]) ).
cnf(t36,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t34,t18]) ).
cnf(t106,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t36]) ).
cnf(t107,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(cp,[status(thm)],[t106,t24]) ).
cnf(t240,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(orient,[status(thm)],[t107]) ).
cnf(t363,plain,
top = converse(top),
inference(cp,[status(thm)],[t360,t240]) ).
cnf(t368,plain,
converse(top) = top,
inference(orient,[status(thm)],[t363]) ).
cnf(t383347,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(step,[status(thm)],[t240,t368]) ).
cnf(t371,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(orient,[status(thm)],[t383347]) ).
cnf(t840,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = complement(top),
inference(cp,[status(thm)],[t837,t371]) ).
cnf(t383438,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(step,[status(thm)],[t840,t65]) ).
cnf(t3538,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(orient,[status(thm)],[t383438]) ).
cnf(t3658,plain,
join(X1,complement(converse(complement(converse(complement(complement(X1))))))) = join(X1,zero),
inference(cp,[status(thm)],[t3654,t3538]) ).
cnf(t383441,plain,
join(X1,complement(converse(complement(converse(X1))))) = join(X1,zero),
inference(step,[status(thm)],[t3658,t380]) ).
cnf(t329,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t325,t19]) ).
cnf(t346,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t329]) ).
cnf(t383442,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t383441,t346]) ).
cnf(t3725,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t383442]) ).
cnf(t3764,plain,
join(X1,converse(complement(converse(complement(converse(converse(X1))))))) = converse(converse(X1)),
inference(cp,[status(thm)],[t106,t3725]) ).
cnf(t383448,plain,
join(X1,converse(complement(converse(complement(X1))))) = converse(converse(X1)),
inference(step,[status(thm)],[t3764,t18]) ).
cnf(t383449,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(step,[status(thm)],[t383448,t18]) ).
cnf(t4003,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(orient,[status(thm)],[t383449]) ).
cnf(t4031,plain,
meet(X1,complement(converse(complement(converse(complement(complement(X1))))))) = complement(complement(X1)),
inference(cp,[status(thm)],[t837,t4003]) ).
cnf(t383450,plain,
meet(X1,complement(converse(complement(converse(X1))))) = complement(complement(X1)),
inference(step,[status(thm)],[t4031,t380]) ).
cnf(t383451,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t383450,t380]) ).
cnf(t4039,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t383451]) ).
cnf(t4063,plain,
zero = meet(complement(complement(converse(complement(converse(X1))))),X1),
inference(cp,[status(thm)],[t639,t4039]) ).
cnf(t383452,plain,
zero = meet(X1,complement(complement(converse(complement(converse(X1)))))),
inference(step,[status(thm)],[t4063,t74]) ).
cnf(t383453,plain,
zero = meet(X1,converse(complement(converse(X1)))),
inference(step,[status(thm)],[t383452,t380]) ).
cnf(t4079,plain,
meet(X1,converse(complement(converse(X1)))) = zero,
inference(orient,[status(thm)],[t383453]) ).
cnf(t4092,plain,
zero = meet(converse(X1),converse(complement(X1))),
inference(cp,[status(thm)],[t4079,t18]) ).
cnf(t4099,plain,
meet(converse(X1),converse(complement(X1))) = zero,
inference(orient,[status(thm)],[t4092]) ).
cnf(t4494,plain,
join(complement(converse(X1)),converse(complement(X1))) = join(complement(converse(X1)),zero),
inference(cp,[status(thm)],[t4467,t4099]) ).
cnf(t383467,plain,
join(converse(complement(X1)),complement(converse(X1))) = join(complement(converse(X1)),zero),
inference(step,[status(thm)],[t4494,t19]) ).
cnf(t383468,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(step,[status(thm)],[t383467,t346]) ).
cnf(t4948,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(orient,[status(thm)],[t383468]) ).
cnf(t4953,plain,
complement(converse(complement(X1))) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t4948,t380]) ).
cnf(t3735,plain,
converse(X1) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t3725,t18]) ).
cnf(t4747,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(orient,[status(thm)],[t3735]) ).
cnf(t383469,plain,
complement(converse(complement(X1))) = converse(X1),
inference(step,[status(thm)],[t4953,t4747]) ).
cnf(t4989,plain,
complement(converse(complement(X1))) = converse(X1),
inference(orient,[status(thm)],[t383469]) ).
cnf(t4994,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(cp,[status(thm)],[t4989,t380]) ).
cnf(t5031,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(orient,[status(thm)],[t4994]) ).
cnf(t374,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(cp,[status(thm)],[t51,t368]) ).
cnf(t438,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(orient,[status(thm)],[t374]) ).
cnf(t5038,plain,
converse(complement(composition(top,X1))) = complement(composition(converse(X1),top)),
inference(cp,[status(thm)],[t5031,t438]) ).
cnf(t5379,plain,
complement(composition(converse(X1),top)) = converse(complement(composition(top,X1))),
inference(orient,[status(thm)],[t5038]) ).
cnf(t383482,plain,
zero = composition(X1,converse(complement(composition(top,X1)))),
inference(step,[status(thm)],[t383481,t5379]) ).
cnf(t5625,plain,
composition(X1,converse(complement(composition(top,X1)))) = zero,
inference(orient,[status(thm)],[t383482]) ).
cnf(t373,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(cp,[status(thm)],[t51,t368]) ).
cnf(t418,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(orient,[status(thm)],[t373]) ).
fof(f13,conjecture,
! [X0,X1] :
( composition(X0,top) = X0
=> join(composition(meet(X0,one),X1),meet(X0,X1)) = meet(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0,X1] :
( composition(X0,top) = X0
=> join(composition(meet(X0,one),X1),meet(X0,X1)) = meet(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0,X1] :
( join(composition(meet(X0,one),X1),meet(X0,X1)) != meet(X0,X1)
& composition(X0,top) = X0 ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( join(composition(meet(sk0,one),sk1),meet(sk0,sk1)) != meet(sk0,sk1)
& composition(sk0,top) = sk0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f13_nnf]) ).
cnf(c13,plain,
composition(sk0,top) = sk0,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t1,plain,
composition(sk0,top) = sk0,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t58,plain,
composition(sk0,top) = sk0,
inference(orient,[status(thm)],[t1]) ).
cnf(t421,plain,
composition(top,converse(sk0)) = converse(sk0),
inference(cp,[status(thm)],[t418,t58]) ).
cnf(t433,plain,
composition(top,converse(sk0)) = converse(sk0),
inference(orient,[status(thm)],[t421]) ).
cnf(t5631,plain,
zero = composition(converse(sk0),converse(complement(converse(sk0)))),
inference(cp,[status(thm)],[t5625,t433]) ).
cnf(t383483,plain,
zero = converse(composition(complement(converse(sk0)),sk0)),
inference(step,[status(thm)],[t5631,t51]) ).
cnf(t383484,plain,
zero = converse(composition(converse(complement(sk0)),sk0)),
inference(step,[status(thm)],[t383483,t5031]) ).
cnf(t383485,plain,
zero = composition(converse(sk0),complement(sk0)),
inference(step,[status(thm)],[t383484,t137]) ).
cnf(t5650,plain,
composition(converse(sk0),complement(sk0)) = zero,
inference(orient,[status(thm)],[t383485]) ).
cnf(t5651,plain,
composition(converse(sk0),composition(complement(sk0),X1)) = composition(zero,X1),
inference(cp,[status(thm)],[t46,t5650]) ).
fof(f6,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
fof(f6_nnf,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t11,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t27,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(orient,[status(thm)],[t11]) ).
cnf(t434,plain,
composition(top,composition(converse(sk0),X1)) = composition(converse(sk0),X1),
inference(cp,[status(thm)],[t46,t433]) ).
cnf(t1078,plain,
composition(top,composition(converse(sk0),X1)) = composition(converse(sk0),X1),
inference(orient,[status(thm)],[t434]) ).
cnf(t5656,plain,
composition(converse(sk0),complement(sk0)) = composition(top,zero),
inference(cp,[status(thm)],[t1078,t5650]) ).
cnf(t383486,plain,
zero = composition(top,zero),
inference(step,[status(thm)],[t5656,t5650]) ).
cnf(t5658,plain,
composition(top,zero) = zero,
inference(orient,[status(thm)],[t383486]) ).
cnf(t5664,plain,
composition(join(top,X1),zero) = join(zero,composition(X1,zero)),
inference(cp,[status(thm)],[t27,t5658]) ).
cnf(t383498,plain,
composition(top,zero) = join(zero,composition(X1,zero)),
inference(step,[status(thm)],[t5664,t360]) ).
cnf(t383499,plain,
zero = join(zero,composition(X1,zero)),
inference(step,[status(thm)],[t383498,t5658]) ).
cnf(t383500,plain,
zero = composition(X1,zero),
inference(step,[status(thm)],[t383499,t325]) ).
cnf(t5673,plain,
composition(X1,zero) = zero,
inference(orient,[status(thm)],[t383500]) ).
cnf(t5681,plain,
composition(converse(zero),X1) = converse(zero),
inference(cp,[status(thm)],[t137,t5673]) ).
cnf(t37,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(cp,[status(thm)],[t34,t18]) ).
cnf(t115,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(orient,[status(thm)],[t37]) ).
cnf(t332,plain,
join(converse(zero),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t115,t325]) ).
cnf(t383355,plain,
join(converse(zero),X1) = X1,
inference(step,[status(thm)],[t332,t18]) ).
cnf(t403,plain,
join(converse(zero),X1) = X1,
inference(orient,[status(thm)],[t383355]) ).
cnf(t404,plain,
zero = converse(zero),
inference(cp,[status(thm)],[t403,t346]) ).
cnf(t409,plain,
converse(zero) = zero,
inference(orient,[status(thm)],[t404]) ).
cnf(t383513,plain,
composition(zero,X1) = converse(zero),
inference(step,[status(thm)],[t5681,t409]) ).
cnf(t383514,plain,
composition(zero,X1) = zero,
inference(step,[status(thm)],[t383513,t409]) ).
cnf(t5684,plain,
composition(zero,X1) = zero,
inference(orient,[status(thm)],[t383514]) ).
cnf(t383552,plain,
composition(converse(sk0),composition(complement(sk0),X1)) = zero,
inference(step,[status(thm)],[t5651,t5684]) ).
cnf(t7170,plain,
composition(converse(sk0),composition(complement(sk0),X1)) = zero,
inference(orient,[status(thm)],[t383552]) ).
cnf(t7176,plain,
complement(composition(complement(sk0),X1)) = join(complement(composition(complement(sk0),X1)),composition(converse(converse(sk0)),complement(zero))),
inference(cp,[status(thm)],[t30,t7170]) ).
cnf(t383750,plain,
complement(composition(complement(sk0),X1)) = join(complement(composition(complement(sk0),X1)),composition(sk0,complement(zero))),
inference(step,[status(thm)],[t7176,t18]) ).
cnf(t383751,plain,
complement(composition(complement(sk0),X1)) = join(composition(sk0,complement(zero)),complement(composition(complement(sk0),X1))),
inference(step,[status(thm)],[t383750,t19]) ).
cnf(t327,plain,
complement(zero) = top,
inference(cp,[status(thm)],[t325,t24]) ).
cnf(t337,plain,
complement(zero) = top,
inference(orient,[status(thm)],[t327]) ).
cnf(t383752,plain,
complement(composition(complement(sk0),X1)) = join(composition(sk0,top),complement(composition(complement(sk0),X1))),
inference(step,[status(thm)],[t383751,t337]) ).
cnf(t383753,plain,
complement(composition(complement(sk0),X1)) = join(sk0,complement(composition(complement(sk0),X1))),
inference(step,[status(thm)],[t383752,t58]) ).
cnf(t14756,plain,
join(sk0,complement(composition(complement(sk0),X1))) = complement(composition(complement(sk0),X1)),
inference(orient,[status(thm)],[t383753]) ).
cnf(t14787,plain,
meet(complement(sk0),composition(complement(sk0),X1)) = complement(complement(composition(complement(sk0),X1))),
inference(cp,[status(thm)],[t813,t14756]) ).
cnf(t383768,plain,
meet(complement(sk0),composition(complement(sk0),X1)) = composition(complement(sk0),X1),
inference(step,[status(thm)],[t14787,t380]) ).
cnf(t15055,plain,
meet(complement(sk0),composition(complement(sk0),X1)) = composition(complement(sk0),X1),
inference(orient,[status(thm)],[t383768]) ).
cnf(t16938,plain,
meet(sk0,X1) = meet(sk0,join(composition(complement(sk0),X2),X1)),
inference(cp,[status(thm)],[t16898,t15055]) ).
cnf(t20808,plain,
meet(sk0,join(composition(complement(sk0),X1),X2)) = meet(sk0,X2),
inference(orient,[status(thm)],[t16938]) ).
cnf(t20809,plain,
meet(sk0,composition(X1,X2)) = meet(sk0,composition(join(complement(sk0),X1),X2)),
inference(cp,[status(thm)],[t20808,t27]) ).
cnf(t381927,plain,
meet(sk0,composition(join(complement(sk0),X1),X2)) = meet(sk0,composition(X1,X2)),
inference(orient,[status(thm)],[t20809]) ).
cnf(t3640,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,join(meet(X3,X1),X2)),
inference(cp,[status(thm)],[t1543,t3610]) ).
cnf(t383790,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,X2),
inference(step,[status(thm)],[t3640,t1543]) ).
cnf(t16280,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,X2),
inference(orient,[status(thm)],[t383790]) ).
cnf(t16290,plain,
join(X1,X2) = join(X1,meet(X2,join(X3,complement(X1)))),
inference(cp,[status(thm)],[t16280,t771]) ).
cnf(t17504,plain,
join(X1,meet(X2,join(X3,complement(X1)))) = join(X1,X2),
inference(orient,[status(thm)],[t16290]) ).
cnf(t17554,plain,
meet(X1,meet(X2,join(X3,complement(complement(X1))))) = meet(X1,join(complement(X1),X2)),
inference(cp,[status(thm)],[t4292,t17504]) ).
cnf(t383816,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,join(complement(X1),X2)),
inference(step,[status(thm)],[t17554,t380]) ).
cnf(t383817,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(step,[status(thm)],[t383816,t4292]) ).
cnf(t17583,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t383817]) ).
cnf(t17603,plain,
meet(X1,X2) = meet(X1,meet(join(X3,X1),X2)),
inference(cp,[status(thm)],[t17583,t74]) ).
cnf(t17743,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t17603]) ).
cnf(t17845,plain,
meet(X1,X2) = meet(X1,meet(join(X1,X3),X2)),
inference(cp,[status(thm)],[t17743,t19]) ).
cnf(t18048,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t17845]) ).
cnf(t429,plain,
join(converse(X1),composition(X2,top)) = converse(join(X1,composition(top,converse(X2)))),
inference(cp,[status(thm)],[t115,t418]) ).
cnf(t52518,plain,
converse(join(X1,composition(top,converse(X2)))) = join(converse(X1),composition(X2,top)),
inference(orient,[status(thm)],[t429]) ).
cnf(t55,plain,
composition(join(converse(X1),X2),converse(X3)) = join(converse(composition(X3,X1)),composition(X2,converse(X3))),
inference(cp,[status(thm)],[t27,t51]) ).
cnf(t22929,plain,
join(converse(composition(X1,X2)),composition(X3,converse(X1))) = composition(join(converse(X2),X3),converse(X1)),
inference(orient,[status(thm)],[t55]) ).
cnf(t52520,plain,
join(converse(converse(composition(X1,X2))),composition(X1,top)) = converse(composition(join(converse(X2),top),converse(X1))),
inference(cp,[status(thm)],[t52518,t22929]) ).
cnf(t384808,plain,
join(composition(X1,X2),composition(X1,top)) = converse(composition(join(converse(X2),top),converse(X1))),
inference(step,[status(thm)],[t52520,t18]) ).
cnf(t111,plain,
converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))),
inference(cp,[status(thm)],[t51,t106]) ).
cnf(t33719,plain,
converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))),
inference(orient,[status(thm)],[t111]) ).
cnf(t384809,plain,
join(composition(X1,X2),composition(X1,top)) = composition(converse(converse(X1)),join(X2,converse(top))),
inference(step,[status(thm)],[t384808,t33719]) ).
cnf(t384810,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,join(X2,converse(top))),
inference(step,[status(thm)],[t384809,t18]) ).
cnf(t384811,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,join(X2,top)),
inference(step,[status(thm)],[t384810,t368]) ).
cnf(t384812,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,top),
inference(step,[status(thm)],[t384811,t392]) ).
cnf(t52654,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,top),
inference(orient,[status(thm)],[t384812]) ).
cnf(t52657,plain,
composition(X1,top) = join(X1,composition(X1,top)),
inference(cp,[status(thm)],[t52654,t17]) ).
cnf(t52801,plain,
join(X1,composition(X1,top)) = composition(X1,top),
inference(orient,[status(thm)],[t52657]) ).
cnf(t52828,plain,
meet(X1,X2) = meet(X1,meet(composition(X1,top),X2)),
inference(cp,[status(thm)],[t18048,t52801]) ).
cnf(t55477,plain,
meet(X1,meet(composition(X1,top),X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t52828]) ).
cnf(t55566,plain,
join(complement(X1),meet(composition(X1,top),X2)) = join(complement(X1),meet(X1,X2)),
inference(cp,[status(thm)],[t4467,t55477]) ).
cnf(t386473,plain,
join(complement(X1),meet(composition(X1,top),X2)) = join(complement(X1),X2),
inference(step,[status(thm)],[t55566,t4467]) ).
cnf(t201145,plain,
join(complement(X1),meet(composition(X1,top),X2)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t386473]) ).
cnf(t381988,plain,
meet(sk0,composition(meet(composition(sk0,top),X1),X2)) = meet(sk0,composition(join(complement(sk0),X1),X2)),
inference(cp,[status(thm)],[t381927,t201145]) ).
cnf(t387410,plain,
meet(sk0,composition(meet(sk0,X1),X2)) = meet(sk0,composition(join(complement(sk0),X1),X2)),
inference(step,[status(thm)],[t381988,t58]) ).
cnf(t388,plain,
top = join(complement(X1),join(X1,X2)),
inference(cp,[status(thm)],[t361,t380]) ).
cnf(t505,plain,
join(complement(X1),join(X1,X2)) = top,
inference(orient,[status(thm)],[t388]) ).
cnf(t520,plain,
X1 = join(meet(X1,join(X1,X2)),complement(top)),
inference(cp,[status(thm)],[t296,t505]) ).
cnf(t383359,plain,
X1 = join(complement(top),meet(X1,join(X1,X2))),
inference(step,[status(thm)],[t520,t19]) ).
cnf(t383360,plain,
X1 = join(zero,meet(X1,join(X1,X2))),
inference(step,[status(thm)],[t383359,t65]) ).
cnf(t383361,plain,
X1 = meet(X1,join(X1,X2)),
inference(step,[status(thm)],[t383360,t325]) ).
cnf(t521,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t383361]) ).
cnf(t527,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t521,t19]) ).
cnf(t531,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t527]) ).
cnf(t435,plain,
composition(join(top,X1),converse(sk0)) = join(converse(sk0),composition(X1,converse(sk0))),
inference(cp,[status(thm)],[t27,t433]) ).
cnf(t383402,plain,
composition(top,converse(sk0)) = join(converse(sk0),composition(X1,converse(sk0))),
inference(step,[status(thm)],[t435,t360]) ).
cnf(t383403,plain,
converse(sk0) = join(converse(sk0),composition(X1,converse(sk0))),
inference(step,[status(thm)],[t383402,t433]) ).
cnf(t1098,plain,
join(converse(sk0),composition(X1,converse(sk0))) = converse(sk0),
inference(orient,[status(thm)],[t383403]) ).
cnf(t1105,plain,
join(sk0,converse(composition(X1,converse(sk0)))) = converse(converse(sk0)),
inference(cp,[status(thm)],[t106,t1098]) ).
cnf(t52,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(cp,[status(thm)],[t51,t18]) ).
cnf(t125,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(orient,[status(thm)],[t52]) ).
cnf(t383404,plain,
join(sk0,composition(sk0,converse(X1))) = converse(converse(sk0)),
inference(step,[status(thm)],[t1105,t125]) ).
cnf(t383405,plain,
join(sk0,composition(sk0,converse(X1))) = sk0,
inference(step,[status(thm)],[t383404,t18]) ).
cnf(t1108,plain,
join(sk0,composition(sk0,converse(X1))) = sk0,
inference(orient,[status(thm)],[t383405]) ).
cnf(t1116,plain,
sk0 = join(sk0,composition(sk0,X1)),
inference(cp,[status(thm)],[t1108,t18]) ).
cnf(t1135,plain,
join(sk0,composition(sk0,X1)) = sk0,
inference(orient,[status(thm)],[t1116]) ).
cnf(t1137,plain,
join(sk0,join(composition(sk0,X1),X2)) = join(sk0,X2),
inference(cp,[status(thm)],[t21,t1135]) ).
cnf(t1787,plain,
join(sk0,join(composition(sk0,X1),X2)) = join(sk0,X2),
inference(orient,[status(thm)],[t1137]) ).
cnf(t1789,plain,
join(sk0,composition(X1,X2)) = join(sk0,composition(join(sk0,X1),X2)),
inference(cp,[status(thm)],[t1787,t27]) ).
cnf(t14041,plain,
join(sk0,composition(join(sk0,X1),X2)) = join(sk0,composition(X1,X2)),
inference(orient,[status(thm)],[t1789]) ).
cnf(t14084,plain,
join(sk0,composition(meet(sk0,X1),X2)) = join(sk0,composition(sk0,X2)),
inference(cp,[status(thm)],[t14041,t479]) ).
cnf(t383737,plain,
join(sk0,composition(meet(sk0,X1),X2)) = sk0,
inference(step,[status(thm)],[t14084,t1135]) ).
cnf(t14130,plain,
join(sk0,composition(meet(sk0,X1),X2)) = sk0,
inference(orient,[status(thm)],[t383737]) ).
cnf(t14149,plain,
composition(meet(sk0,X1),X2) = meet(composition(meet(sk0,X1),X2),sk0),
inference(cp,[status(thm)],[t531,t14130]) ).
cnf(t383784,plain,
composition(meet(sk0,X1),X2) = meet(sk0,composition(meet(sk0,X1),X2)),
inference(step,[status(thm)],[t14149,t74]) ).
cnf(t16014,plain,
meet(sk0,composition(meet(sk0,X1),X2)) = composition(meet(sk0,X1),X2),
inference(orient,[status(thm)],[t383784]) ).
cnf(t387411,plain,
composition(meet(sk0,X1),X2) = meet(sk0,composition(join(complement(sk0),X1),X2)),
inference(step,[status(thm)],[t387410,t16014]) ).
cnf(t387412,plain,
composition(meet(sk0,X1),X2) = meet(sk0,composition(X1,X2)),
inference(step,[status(thm)],[t387411,t381927]) ).
cnf(t382679,plain,
composition(meet(sk0,X1),X2) = meet(sk0,composition(X1,X2)),
inference(orient,[status(thm)],[t387412]) ).
cnf(c14,plain,
join(composition(meet(sk0,one),sk1),meet(sk0,sk1)) != meet(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
join(composition(meet(sk0,one),sk1),meet(sk0,sk1)) != meet(sk0,sk1),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
join(meet(sk0,sk1),composition(meet(sk0,one),sk1)) != meet(sk0,sk1),
inference(rw,[status(thm)],[goal_0,t19]) ).
cnf(g0_1,plain,
join(meet(sk1,sk0),composition(meet(sk0,one),sk1)) != meet(sk0,sk1),
inference(rw,[status(thm)],[g0_0,t74]) ).
cnf(g0_2,plain,
join(meet(sk1,sk0),meet(sk0,composition(one,sk1))) != meet(sk0,sk1),
inference(rw,[status(thm)],[g0_1,t382679]) ).
cnf(g0_3,plain,
join(meet(sk1,sk0),meet(sk0,sk1)) != meet(sk0,sk1),
inference(rw,[status(thm)],[g0_2,t170]) ).
cnf(g0_4,plain,
join(meet(sk1,sk0),meet(sk1,sk0)) != meet(sk0,sk1),
inference(rw,[status(thm)],[g0_3,t74]) ).
cnf(g0_5,plain,
meet(sk1,sk0) != meet(sk0,sk1),
inference(rw,[status(thm)],[g0_4,t395]) ).
cnf(g0_6,plain,
meet(sk1,sk0) != meet(sk1,sk0),
inference(rw,[status(thm)],[g0_5,t74]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL021+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.42 % Computer : n009.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Thu Sep 24 07:17:13 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 194.30/28.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 194.30/28.54 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------