%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL042+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 : n026.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 02:36:06 PM UTC 2026
% Result : Theorem 53.08s 7.27s
% Output : Proof 53.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 114
% Number of leaves : 13
% Syntax : Number of formulae : 334 ( 330 unt; 0 def)
% Number of atoms : 338 ( 337 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 508 ( 30 sgn 72 !; 1 ?)
% 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(t4,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)],[t4]) ).
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(t187219,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)],[t187219]) ).
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(t5,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)],[t5]) ).
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(t6,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)],[t6]) ).
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(t1,plain,
converse(converse(X1)) = X1,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t18,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t53,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t51,t18]) ).
cnf(t136,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(t137,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t136,t17]) ).
cnf(t187224,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t137,t18]) ).
cnf(t151,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t187224]) ).
cnf(t152,plain,
one = converse(one),
inference(cp,[status(thm)],[t151,t17]) ).
cnf(t158,plain,
converse(one) = one,
inference(orient,[status(thm)],[t152]) ).
cnf(t187225,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t151,t158]) ).
cnf(t168,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t187225]) ).
cnf(t169,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t168]) ).
cnf(t172,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t30,t169]) ).
cnf(t187227,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t172,t158]) ).
cnf(t187228,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t187227,t169]) ).
cnf(t196,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t187228]) ).
cnf(t206,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t39,t196]) ).
cnf(t213,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t206]) ).
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(t187240,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t20,t19]) ).
cnf(t187241,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t187240,t39]) ).
cnf(t187242,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t187241,t19]) ).
cnf(t295,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t187242]) ).
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(t3,plain,
meet(X1,complement(X1)) = zero,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t58,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t296,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t295,t58]) ).
cnf(t187249,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t296,t39]) ).
cnf(t333,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t187249]) ).
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(t2,plain,
join(X1,complement(X1)) = top,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t24,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t40,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t39,t24]) ).
cnf(t187220,plain,
zero = complement(top),
inference(step,[status(thm)],[t40,t58]) ).
cnf(t63,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t187220]) ).
cnf(t200,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t196,t63]) ).
cnf(t187229,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t200,t63]) ).
cnf(t187230,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t187229,t63]) ).
cnf(t207,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t187230]) ).
cnf(t208,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t21,t207]) ).
cnf(t224,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t208]) ).
cnf(t335,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t224,t333]) ).
cnf(t187250,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t335,t333]) ).
cnf(t337,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t187250]) ).
cnf(t187251,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t333,t337]) ).
cnf(t344,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t187251]) ).
cnf(t360,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t344]) ).
cnf(t187257,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t213,t360]) ).
cnf(t362,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t187257]) ).
cnf(t369,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t362]) ).
cnf(t379,plain,
complement(complement(X1)) = join(X1,composition(converse(X2),complement(composition(X2,complement(X1))))),
inference(cp,[status(thm)],[t30,t369]) ).
cnf(t188537,plain,
X1 = join(X1,composition(converse(X2),complement(composition(X2,complement(X1))))),
inference(step,[status(thm)],[t379,t369]) ).
cnf(t134347,plain,
join(X1,composition(converse(X2),complement(composition(X2,complement(X1))))) = X1,
inference(orient,[status(thm)],[t188537]) ).
cnf(t371,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t196,t369]) ).
cnf(t187264,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t371,t369]) ).
cnf(t187265,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t187264,t369]) ).
cnf(t381,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t187265]) ).
cnf(t383,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t21,t381]) ).
cnf(t456,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t383]) ).
cnf(t458,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1),
inference(cp,[status(thm)],[t456,t295]) ).
cnf(t187269,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t458,t295]) ).
cnf(t187270,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t187269,t19]) ).
cnf(t462,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t187270]) ).
cnf(t41,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t39,t19]) ).
cnf(t187222,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t41,t39]) ).
cnf(t73,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t187222]) ).
cnf(t464,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t462,t73]) ).
cnf(t469,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t464]) ).
cnf(t472,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t21,t469]) ).
cnf(t1133,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t472]) ).
cnf(t370,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(cp,[status(thm)],[t369,t39]) ).
cnf(t619,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t370]) ).
cnf(t622,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(cp,[status(thm)],[t619,t369]) ).
cnf(t650,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(orient,[status(thm)],[t622]) ).
cnf(t660,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t369,t650]) ).
cnf(t699,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t660]) ).
cnf(t187292,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(step,[status(thm)],[t295,t699]) ).
cnf(t726,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[t187292]) ).
cnf(t1925,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(orient,[status(thm)],[t726]) ).
cnf(t1968,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(cp,[status(thm)],[t1133,t1925]) ).
cnf(t1978,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t1968]) ).
cnf(t1982,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(cp,[status(thm)],[t1978,t73]) ).
cnf(t2012,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t1982]) ).
cnf(t2021,plain,
join(complement(X1),X2) = join(complement(X1),meet(X1,X2)),
inference(cp,[status(thm)],[t2012,t369]) ).
cnf(t2817,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t2021]) ).
cnf(t460,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(cp,[status(thm)],[t456,t19]) ).
cnf(t475,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t460]) ).
cnf(t26,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(cp,[status(thm)],[t21,t24]) ).
cnf(t257,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(orient,[status(thm)],[t26]) ).
cnf(t218,plain,
top = join(complement(X1),meet(X1,X1)),
inference(cp,[status(thm)],[t24,t213]) ).
cnf(t235,plain,
join(complement(X1),meet(X1,X1)) = top,
inference(orient,[status(thm)],[t218]) ).
cnf(t261,plain,
join(top,meet(X1,X1)) = join(X1,top),
inference(cp,[status(thm)],[t257,t235]) ).
cnf(t263,plain,
join(top,complement(X1)) = join(X1,complement(X1)),
inference(cp,[status(thm)],[t257,t196]) ).
cnf(t187235,plain,
join(top,complement(X1)) = top,
inference(step,[status(thm)],[t263,t24]) ).
cnf(t274,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t187235]) ).
cnf(t275,plain,
top = join(top,meet(X1,X2)),
inference(cp,[status(thm)],[t274,t39]) ).
cnf(t282,plain,
join(top,meet(X1,X2)) = top,
inference(orient,[status(thm)],[t275]) ).
cnf(t187237,plain,
top = join(X1,top),
inference(step,[status(thm)],[t261,t282]) ).
cnf(t289,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t187237]) ).
cnf(t290,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t289,t19]) ).
cnf(t317,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t290]) ).
cnf(t187243,plain,
join(X1,join(complement(X1),X2)) = top,
inference(step,[status(thm)],[t257,t317]) ).
cnf(t318,plain,
join(X1,join(complement(X1),X2)) = top,
inference(orient,[status(thm)],[t187243]) ).
cnf(t477,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),top),
inference(cp,[status(thm)],[t475,t318]) ).
cnf(t187278,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),top),
inference(step,[status(thm)],[t477,t21]) ).
cnf(t187279,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,top)),
inference(step,[status(thm)],[t187278,t21]) ).
cnf(t187280,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),top),
inference(step,[status(thm)],[t187279,t289]) ).
cnf(t187281,plain,
join(complement(X1),join(X2,X1)) = top,
inference(step,[status(thm)],[t187280,t289]) ).
cnf(t533,plain,
join(complement(X1),join(X2,X1)) = top,
inference(orient,[status(thm)],[t187281]) ).
cnf(t540,plain,
top = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t533,t469]) ).
cnf(t187287,plain,
top = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t540,t19]) ).
cnf(t568,plain,
join(X1,complement(meet(X2,X1))) = top,
inference(orient,[status(thm)],[t187287]) ).
cnf(t573,plain,
meet(X1,meet(X2,complement(X1))) = complement(top),
inference(cp,[status(thm)],[t39,t568]) ).
cnf(t187289,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t573,t63]) ).
cnf(t582,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t187289]) ).
cnf(t583,plain,
zero = meet(complement(X1),meet(X2,X1)),
inference(cp,[status(thm)],[t582,t369]) ).
cnf(t593,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t583]) ).
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(t7,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)],[t7]) ).
cnf(t36,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t34,t18]) ).
cnf(t105,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t36]) ).
cnf(t106,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(cp,[status(thm)],[t105,t24]) ).
cnf(t240,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(orient,[status(thm)],[t106]) ).
cnf(t320,plain,
top = converse(top),
inference(cp,[status(thm)],[t317,t240]) ).
cnf(t323,plain,
converse(top) = top,
inference(orient,[status(thm)],[t320]) ).
cnf(t187247,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(step,[status(thm)],[t240,t323]) ).
cnf(t326,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(orient,[status(thm)],[t187247]) ).
cnf(t702,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = complement(top),
inference(cp,[status(thm)],[t699,t326]) ).
cnf(t187318,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(step,[status(thm)],[t702,t63]) ).
cnf(t1920,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(orient,[status(thm)],[t187318]) ).
cnf(t2015,plain,
join(X1,complement(converse(complement(converse(complement(complement(X1))))))) = join(X1,zero),
inference(cp,[status(thm)],[t2012,t1920]) ).
cnf(t187323,plain,
join(X1,complement(converse(complement(converse(X1))))) = join(X1,zero),
inference(step,[status(thm)],[t2015,t369]) ).
cnf(t341,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t337,t19]) ).
cnf(t356,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t341]) ).
cnf(t187324,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t187323,t356]) ).
cnf(t2187,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t187324]) ).
cnf(t2219,plain,
join(X1,converse(complement(converse(complement(converse(converse(X1))))))) = converse(converse(X1)),
inference(cp,[status(thm)],[t105,t2187]) ).
cnf(t187330,plain,
join(X1,converse(complement(converse(complement(X1))))) = converse(converse(X1)),
inference(step,[status(thm)],[t2219,t18]) ).
cnf(t187331,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(step,[status(thm)],[t187330,t18]) ).
cnf(t2445,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(orient,[status(thm)],[t187331]) ).
cnf(t2467,plain,
meet(X1,complement(converse(complement(converse(complement(complement(X1))))))) = complement(complement(X1)),
inference(cp,[status(thm)],[t699,t2445]) ).
cnf(t187332,plain,
meet(X1,complement(converse(complement(converse(X1))))) = complement(complement(X1)),
inference(step,[status(thm)],[t2467,t369]) ).
cnf(t187333,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t187332,t369]) ).
cnf(t2474,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t187333]) ).
cnf(t2496,plain,
zero = meet(complement(complement(converse(complement(converse(X1))))),X1),
inference(cp,[status(thm)],[t593,t2474]) ).
cnf(t187334,plain,
zero = meet(X1,complement(complement(converse(complement(converse(X1)))))),
inference(step,[status(thm)],[t2496,t73]) ).
cnf(t187335,plain,
zero = meet(X1,converse(complement(converse(X1)))),
inference(step,[status(thm)],[t187334,t369]) ).
cnf(t2511,plain,
meet(X1,converse(complement(converse(X1)))) = zero,
inference(orient,[status(thm)],[t187335]) ).
cnf(t2524,plain,
zero = meet(converse(X1),converse(complement(X1))),
inference(cp,[status(thm)],[t2511,t18]) ).
cnf(t2529,plain,
meet(converse(X1),converse(complement(X1))) = zero,
inference(orient,[status(thm)],[t2524]) ).
cnf(t2836,plain,
join(complement(converse(X1)),converse(complement(X1))) = join(complement(converse(X1)),zero),
inference(cp,[status(thm)],[t2817,t2529]) ).
cnf(t187348,plain,
join(converse(complement(X1)),complement(converse(X1))) = join(complement(converse(X1)),zero),
inference(step,[status(thm)],[t2836,t19]) ).
cnf(t187349,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(step,[status(thm)],[t187348,t356]) ).
cnf(t3250,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(orient,[status(thm)],[t187349]) ).
cnf(t3255,plain,
complement(converse(complement(X1))) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t3250,t369]) ).
cnf(t2197,plain,
converse(X1) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t2187,t18]) ).
cnf(t3055,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(orient,[status(thm)],[t2197]) ).
cnf(t187350,plain,
complement(converse(complement(X1))) = converse(X1),
inference(step,[status(thm)],[t3255,t3055]) ).
cnf(t3290,plain,
complement(converse(complement(X1))) = converse(X1),
inference(orient,[status(thm)],[t187350]) ).
cnf(t3295,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(cp,[status(thm)],[t3290,t369]) ).
cnf(t3331,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(orient,[status(thm)],[t3295]) ).
cnf(t3343,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(cp,[status(thm)],[t3331,t105]) ).
cnf(t4165,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(orient,[status(thm)],[t3343]) ).
cnf(t3352,plain,
complement(meet(converse(X1),X2)) = join(converse(complement(X1)),complement(X2)),
inference(cp,[status(thm)],[t619,t3331]) ).
cnf(t4368,plain,
join(converse(complement(X1)),complement(X2)) = complement(meet(converse(X1),X2)),
inference(orient,[status(thm)],[t3352]) ).
cnf(t4409,plain,
complement(join(complement(X1),converse(complement(X2)))) = converse(complement(complement(meet(converse(X1),X2)))),
inference(cp,[status(thm)],[t4165,t4368]) ).
cnf(t187406,plain,
meet(X1,complement(converse(complement(X2)))) = converse(complement(complement(meet(converse(X1),X2)))),
inference(step,[status(thm)],[t4409,t699]) ).
cnf(t187407,plain,
meet(X1,converse(X2)) = converse(complement(complement(meet(converse(X1),X2)))),
inference(step,[status(thm)],[t187406,t3290]) ).
cnf(t187408,plain,
meet(X1,converse(X2)) = converse(meet(converse(X1),X2)),
inference(step,[status(thm)],[t187407,t369]) ).
cnf(t4415,plain,
converse(meet(converse(X1),X2)) = meet(X1,converse(X2)),
inference(orient,[status(thm)],[t187408]) ).
cnf(t4461,plain,
composition(converse(X1),meet(converse(X2),X3)) = converse(composition(meet(X2,converse(X3)),X1)),
inference(cp,[status(thm)],[t136,t4415]) ).
cnf(t67551,plain,
converse(composition(meet(X1,converse(X2)),X3)) = composition(converse(X3),meet(converse(X1),X2)),
inference(orient,[status(thm)],[t4461]) ).
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(t329,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(cp,[status(thm)],[t51,t323]) ).
cnf(t424,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(orient,[status(thm)],[t329]) ).
cnf(t3338,plain,
converse(complement(composition(top,X1))) = complement(composition(converse(X1),top)),
inference(cp,[status(thm)],[t3331,t424]) ).
cnf(t3614,plain,
complement(composition(converse(X1),top)) = converse(complement(composition(top,X1))),
inference(orient,[status(thm)],[t3338]) ).
cnf(t3665,plain,
complement(top) = join(complement(top),composition(converse(converse(X1)),converse(complement(composition(top,X1))))),
inference(cp,[status(thm)],[t30,t3614]) ).
cnf(t187363,plain,
zero = join(complement(top),composition(converse(converse(X1)),converse(complement(composition(top,X1))))),
inference(step,[status(thm)],[t3665,t63]) ).
cnf(t187364,plain,
zero = join(zero,composition(converse(converse(X1)),converse(complement(composition(top,X1))))),
inference(step,[status(thm)],[t187363,t63]) ).
cnf(t187365,plain,
zero = composition(converse(converse(X1)),converse(complement(composition(top,X1)))),
inference(step,[status(thm)],[t187364,t337]) ).
cnf(t187366,plain,
zero = converse(composition(complement(composition(top,X1)),converse(X1))),
inference(step,[status(thm)],[t187365,t51]) ).
cnf(t52,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(cp,[status(thm)],[t51,t18]) ).
cnf(t124,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(orient,[status(thm)],[t52]) ).
cnf(t187367,plain,
zero = composition(X1,converse(complement(composition(top,X1)))),
inference(step,[status(thm)],[t187366,t124]) ).
cnf(t3934,plain,
composition(X1,converse(complement(composition(top,X1)))) = zero,
inference(orient,[status(thm)],[t187367]) ).
cnf(t3950,plain,
composition(converse(converse(complement(composition(top,converse(X1))))),X1) = converse(zero),
inference(cp,[status(thm)],[t136,t3934]) ).
cnf(t187402,plain,
composition(complement(composition(top,converse(X1))),X1) = converse(zero),
inference(step,[status(thm)],[t3950,t18]) ).
cnf(t328,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(cp,[status(thm)],[t51,t323]) ).
cnf(t412,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(orient,[status(thm)],[t328]) ).
cnf(t3341,plain,
converse(complement(composition(X1,top))) = complement(composition(top,converse(X1))),
inference(cp,[status(thm)],[t3331,t412]) ).
cnf(t3737,plain,
complement(composition(top,converse(X1))) = converse(complement(composition(X1,top))),
inference(orient,[status(thm)],[t3341]) ).
cnf(t187403,plain,
composition(converse(complement(composition(X1,top))),X1) = converse(zero),
inference(step,[status(thm)],[t187402,t3737]) ).
cnf(t340,plain,
converse(complement(converse(zero))) = top,
inference(cp,[status(thm)],[t337,t326]) ).
cnf(t387,plain,
converse(complement(converse(zero))) = top,
inference(orient,[status(thm)],[t340]) ).
cnf(t388,plain,
complement(converse(zero)) = converse(top),
inference(cp,[status(thm)],[t18,t387]) ).
cnf(t187267,plain,
complement(converse(zero)) = top,
inference(step,[status(thm)],[t388,t323]) ).
cnf(t399,plain,
complement(converse(zero)) = top,
inference(orient,[status(thm)],[t187267]) ).
cnf(t400,plain,
converse(zero) = complement(top),
inference(cp,[status(thm)],[t369,t399]) ).
cnf(t187268,plain,
converse(zero) = zero,
inference(step,[status(thm)],[t400,t63]) ).
cnf(t406,plain,
converse(zero) = zero,
inference(orient,[status(thm)],[t187268]) ).
cnf(t187404,plain,
composition(converse(complement(composition(X1,top))),X1) = zero,
inference(step,[status(thm)],[t187403,t406]) ).
cnf(t4053,plain,
composition(converse(complement(composition(X1,top))),X1) = zero,
inference(orient,[status(thm)],[t187404]) ).
cnf(t4057,plain,
composition(join(converse(complement(composition(X1,top))),X2),X1) = join(zero,composition(X2,X1)),
inference(cp,[status(thm)],[t27,t4053]) ).
cnf(t188970,plain,
composition(join(converse(complement(composition(X1,top))),X2),X1) = composition(X2,X1),
inference(step,[status(thm)],[t4057,t337]) ).
cnf(t176750,plain,
composition(join(converse(complement(composition(X1,top))),X2),X1) = composition(X2,X1),
inference(orient,[status(thm)],[t188970]) ).
cnf(t3348,plain,
join(complement(converse(X1)),X2) = join(converse(complement(X1)),meet(converse(X1),X2)),
inference(cp,[status(thm)],[t2817,t3331]) ).
cnf(t188303,plain,
join(converse(complement(X1)),X2) = join(converse(complement(X1)),meet(converse(X1),X2)),
inference(step,[status(thm)],[t3348,t3331]) ).
cnf(t108575,plain,
join(converse(complement(X1)),meet(converse(X1),X2)) = join(converse(complement(X1)),X2),
inference(orient,[status(thm)],[t188303]) ).
cnf(t176754,plain,
composition(meet(converse(composition(X1,top)),X2),X1) = composition(join(converse(complement(composition(X1,top))),X2),X1),
inference(cp,[status(thm)],[t176750,t108575]) ).
cnf(t188971,plain,
composition(meet(composition(top,converse(X1)),X2),X1) = composition(join(converse(complement(composition(X1,top))),X2),X1),
inference(step,[status(thm)],[t176754,t412]) ).
cnf(t188972,plain,
composition(meet(composition(top,converse(X1)),X2),X1) = composition(X2,X1),
inference(step,[status(thm)],[t188971,t176750]) ).
cnf(t177038,plain,
composition(meet(composition(top,converse(X1)),X2),X1) = composition(X2,X1),
inference(orient,[status(thm)],[t188972]) ).
cnf(t177329,plain,
composition(converse(X1),meet(converse(composition(top,converse(X1))),X2)) = converse(composition(converse(X2),X1)),
inference(cp,[status(thm)],[t67551,t177038]) ).
cnf(t189085,plain,
composition(converse(X1),meet(composition(converse(converse(X1)),top),X2)) = converse(composition(converse(X2),X1)),
inference(step,[status(thm)],[t177329,t424]) ).
cnf(t189086,plain,
composition(converse(X1),meet(composition(X1,top),X2)) = converse(composition(converse(X2),X1)),
inference(step,[status(thm)],[t189085,t18]) ).
cnf(t189087,plain,
composition(converse(X1),meet(composition(X1,top),X2)) = composition(converse(X1),X2),
inference(step,[status(thm)],[t189086,t136]) ).
cnf(t185355,plain,
composition(converse(X1),meet(composition(X1,top),X2)) = composition(converse(X1),X2),
inference(orient,[status(thm)],[t189087]) ).
cnf(t621,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(cp,[status(thm)],[t619,t369]) ).
cnf(t628,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t621]) ).
cnf(t639,plain,
meet(complement(X1),X2) = complement(join(X1,complement(X2))),
inference(cp,[status(thm)],[t369,t628]) ).
cnf(t672,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(orient,[status(thm)],[t639]) ).
cnf(t688,plain,
meet(complement(X1),join(X2,complement(X3))) = complement(join(X1,meet(complement(X2),X3))),
inference(cp,[status(thm)],[t672,t672]) ).
cnf(t58158,plain,
complement(join(X1,meet(complement(X2),X3))) = meet(complement(X1),join(X2,complement(X3))),
inference(orient,[status(thm)],[t688]) ).
cnf(t1939,plain,
X1 = join(meet(X2,X1),meet(X1,complement(X2))),
inference(cp,[status(thm)],[t1925,t73]) ).
cnf(t6439,plain,
join(meet(X1,X2),meet(X2,complement(X1))) = X2,
inference(orient,[status(thm)],[t1939]) ).
cnf(t6482,plain,
X1 = join(meet(X2,X1),meet(complement(X2),X1)),
inference(cp,[status(thm)],[t6439,t73]) ).
cnf(t8032,plain,
join(meet(X1,X2),meet(complement(X1),X2)) = X2,
inference(orient,[status(thm)],[t6482]) ).
cnf(t58172,plain,
meet(complement(meet(X1,X2)),join(X1,complement(X2))) = complement(X2),
inference(cp,[status(thm)],[t58158,t8032]) ).
cnf(t188072,plain,
meet(join(X1,complement(X2)),complement(meet(X1,X2))) = complement(X2),
inference(step,[status(thm)],[t58172,t73]) ).
cnf(t85196,plain,
meet(join(X1,complement(X2)),complement(meet(X1,X2))) = complement(X2),
inference(orient,[status(thm)],[t188072]) ).
fof(f13,conjecture,
! [X0] :
( ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero
=> join(composition(converse(X0),X0),one) = one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0] :
( ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero
=> join(composition(converse(X0),X0),one) = one ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0] :
( join(composition(converse(X0),X0),one) != one
& ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
! [X1] :
( join(composition(converse(sk0),sk0),one) != one
& meet(composition(sk0,X1),composition(sk0,complement(X1))) = zero ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f13_nnf]) ).
cnf(c13,plain,
meet(composition(sk0,X1),composition(sk0,complement(X1))) = zero,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t8,plain,
meet(composition(sk0,X1),composition(sk0,complement(X1))) = zero,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t60,plain,
meet(composition(sk0,X1),composition(sk0,complement(X1))) = zero,
inference(orient,[status(thm)],[t8]) ).
cnf(t1937,plain,
composition(sk0,X1) = join(zero,meet(composition(sk0,X1),complement(composition(sk0,complement(X1))))),
inference(cp,[status(thm)],[t1925,t60]) ).
cnf(t188932,plain,
composition(sk0,X1) = meet(composition(sk0,X1),complement(composition(sk0,complement(X1)))),
inference(step,[status(thm)],[t1937,t337]) ).
cnf(t170579,plain,
meet(composition(sk0,X1),complement(composition(sk0,complement(X1)))) = composition(sk0,X1),
inference(orient,[status(thm)],[t188932]) ).
cnf(t170647,plain,
complement(complement(composition(sk0,complement(X1)))) = meet(join(composition(sk0,X1),complement(complement(composition(sk0,complement(X1))))),complement(composition(sk0,X1))),
inference(cp,[status(thm)],[t85196,t170579]) ).
cnf(t188933,plain,
composition(sk0,complement(X1)) = meet(join(composition(sk0,X1),complement(complement(composition(sk0,complement(X1))))),complement(composition(sk0,X1))),
inference(step,[status(thm)],[t170647,t369]) ).
cnf(t188934,plain,
composition(sk0,complement(X1)) = meet(join(composition(sk0,X1),composition(sk0,complement(X1))),complement(composition(sk0,X1))),
inference(step,[status(thm)],[t188933,t369]) ).
cnf(t144,plain,
converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)),
inference(cp,[status(thm)],[t34,t136]) ).
cnf(t55457,plain,
converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)),
inference(orient,[status(thm)],[t144]) ).
cnf(t56,plain,
composition(join(X1,converse(X2)),converse(X3)) = join(composition(X1,converse(X3)),converse(composition(X3,X2))),
inference(cp,[status(thm)],[t27,t51]) ).
cnf(t31167,plain,
join(composition(X1,converse(X2)),converse(composition(X2,X3))) = composition(join(X1,converse(X3)),converse(X2)),
inference(orient,[status(thm)],[t56]) ).
cnf(t55465,plain,
join(composition(converse(converse(X1)),X2),converse(converse(composition(X1,X3)))) = converse(composition(join(converse(X2),converse(X3)),converse(X1))),
inference(cp,[status(thm)],[t55457,t31167]) ).
cnf(t187927,plain,
join(composition(X1,X2),converse(converse(composition(X1,X3)))) = converse(composition(join(converse(X2),converse(X3)),converse(X1))),
inference(step,[status(thm)],[t55465,t18]) ).
cnf(t187928,plain,
join(composition(X1,X2),composition(X1,X3)) = converse(composition(join(converse(X2),converse(X3)),converse(X1))),
inference(step,[status(thm)],[t187927,t18]) ).
cnf(t110,plain,
converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))),
inference(cp,[status(thm)],[t51,t105]) ).
cnf(t49052,plain,
converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))),
inference(orient,[status(thm)],[t110]) ).
cnf(t187929,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(converse(converse(X1)),join(X2,converse(converse(X3)))),
inference(step,[status(thm)],[t187928,t49052]) ).
cnf(t187930,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,converse(converse(X3)))),
inference(step,[status(thm)],[t187929,t18]) ).
cnf(t187931,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(step,[status(thm)],[t187930,t18]) ).
cnf(t55757,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(orient,[status(thm)],[t187931]) ).
cnf(t188935,plain,
composition(sk0,complement(X1)) = meet(composition(sk0,join(X1,complement(X1))),complement(composition(sk0,X1))),
inference(step,[status(thm)],[t188934,t55757]) ).
cnf(t188936,plain,
composition(sk0,complement(X1)) = meet(composition(sk0,top),complement(composition(sk0,X1))),
inference(step,[status(thm)],[t188935,t24]) ).
cnf(t170726,plain,
meet(composition(sk0,top),complement(composition(sk0,X1))) = composition(sk0,complement(X1)),
inference(orient,[status(thm)],[t188936]) ).
cnf(t185431,plain,
composition(converse(sk0),complement(composition(sk0,X1))) = composition(converse(sk0),composition(sk0,complement(X1))),
inference(cp,[status(thm)],[t185355,t170726]) ).
cnf(t186873,plain,
composition(converse(sk0),complement(composition(sk0,X1))) = composition(converse(sk0),composition(sk0,complement(X1))),
inference(orient,[status(thm)],[t185431]) ).
cnf(t186936,plain,
X1 = join(X1,composition(converse(sk0),composition(sk0,complement(complement(X1))))),
inference(cp,[status(thm)],[t134347,t186873]) ).
cnf(t189100,plain,
X1 = join(X1,composition(converse(sk0),composition(sk0,X1))),
inference(step,[status(thm)],[t186936,t369]) ).
cnf(t186954,plain,
join(X1,composition(converse(sk0),composition(sk0,X1))) = X1,
inference(orient,[status(thm)],[t189100]) ).
cnf(t186980,plain,
one = join(one,composition(converse(sk0),sk0)),
inference(cp,[status(thm)],[t186954,t17]) ).
cnf(t187145,plain,
join(one,composition(converse(sk0),sk0)) = one,
inference(orient,[status(thm)],[t186980]) ).
cnf(c14,plain,
join(composition(converse(sk0),sk0),one) != one,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
join(composition(converse(sk0),sk0),one) != one,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
join(one,composition(converse(sk0),sk0)) != one,
inference(rw,[status(thm)],[goal_0,t19]) ).
cnf(g0_1,plain,
one != one,
inference(rw,[status(thm)],[g0_0,t187145]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL042+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n026.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 07:37:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 53.08/7.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 53.08/7.27 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------