%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL018+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 : n019.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 02:34:46 PM UTC 2026
% Result : Theorem 17.00s 2.69s
% Output : Proof 17.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 113
% Number of leaves : 13
% Syntax : Number of formulae : 339 ( 335 unt; 0 def)
% Number of atoms : 343 ( 342 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 440 ( 42 sgn 68 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
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]) ).
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]) ).
cnf(t26951,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)],[t26951]) ).
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(t26956,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t138,t18]) ).
cnf(t152,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t26956]) ).
cnf(t153,plain,
one = converse(one),
inference(cp,[status(thm)],[t152,t17]) ).
cnf(t159,plain,
converse(one) = one,
inference(orient,[status(thm)],[t153]) ).
cnf(t26957,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t152,t159]) ).
cnf(t169,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t26957]) ).
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(t26959,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t173,t159]) ).
cnf(t26960,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t26959,t170]) ).
cnf(t197,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t26960]) ).
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(t26970,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t20,t19]) ).
cnf(t26971,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t26970,t39]) ).
cnf(t26972,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t26971,t19]) ).
cnf(t296,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t26972]) ).
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(t26973,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)],[t26973]) ).
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(t26952,plain,
zero = complement(top),
inference(step,[status(thm)],[t40,t63]) ).
cnf(t65,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t26952]) ).
cnf(t201,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t197,t65]) ).
cnf(t26961,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t201,t65]) ).
cnf(t26962,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t26961,t65]) ).
cnf(t208,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t26962]) ).
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(t26974,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t323,t321]) ).
cnf(t325,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t26974]) ).
cnf(t26975,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t321,t325]) ).
cnf(t333,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t26975]) ).
cnf(t351,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t333]) ).
cnf(t26982,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t214,t351]) ).
cnf(t354,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t26982]) ).
cnf(t380,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t354]) ).
cnf(t382,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t197,t380]) ).
cnf(t26993,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t382,t380]) ).
cnf(t26994,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t26993,t380]) ).
cnf(t395,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t26994]) ).
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(t27001,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t475,t296]) ).
cnf(t27002,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t27001,t19]) ).
cnf(t479,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t27002]) ).
cnf(t41,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t39,t19]) ).
cnf(t26954,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)],[t26954]) ).
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(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(t27027,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)],[t27027]) ).
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(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(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(t3657,plain,
join(X1,complement(X2)) = join(X1,complement(join(X1,X2))),
inference(cp,[status(thm)],[t3654,t864]) ).
cnf(t4387,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t3657]) ).
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(t502,plain,
join(X1,join(X2,X3)) = join(X1,join(X2,join(X3,X1))),
inference(cp,[status(thm)],[t494,t21]) ).
cnf(t12948,plain,
join(X1,join(X2,join(X3,X1))) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t502]) ).
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]) ).
fof(f13,conjecture,
! [X0] :
( composition(X0,top) = X0
=> composition(complement(X0),top) = complement(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0] :
( composition(X0,top) = X0
=> composition(complement(X0),top) = complement(X0) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0] :
( composition(complement(X0),top) != complement(X0)
& composition(X0,top) = X0 ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( composition(complement(sk0),top) != complement(sk0)
& composition(sk0,top) = sk0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[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(t60,plain,
composition(join(sk0,X1),top) = join(sk0,composition(X1,top)),
inference(cp,[status(thm)],[t27,t58]) ).
cnf(t257,plain,
composition(join(sk0,X1),top) = join(sk0,composition(X1,top)),
inference(orient,[status(thm)],[t60]) ).
cnf(t258,plain,
join(sk0,composition(complement(sk0),top)) = composition(top,top),
inference(cp,[status(thm)],[t257,t24]) ).
cnf(t878,plain,
join(sk0,composition(complement(sk0),top)) = composition(top,top),
inference(orient,[status(thm)],[t258]) ).
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(t27124,plain,
zero = join(zero,composition(X1,complement(composition(converse(X1),top)))),
inference(step,[status(thm)],[t5085,t65]) ).
cnf(t27125,plain,
zero = composition(X1,complement(composition(converse(X1),top))),
inference(step,[status(thm)],[t27124,t325]) ).
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(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(t26968,plain,
join(top,complement(X1)) = top,
inference(step,[status(thm)],[t276,t24]) ).
cnf(t288,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t26968]) ).
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(t26987,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)],[t26987]) ).
cnf(t496,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),top),
inference(cp,[status(thm)],[t494,t361]) ).
cnf(t27011,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),top),
inference(step,[status(thm)],[t496,t21]) ).
cnf(t27012,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,top)),
inference(step,[status(thm)],[t27011,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(t27013,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),top),
inference(step,[status(thm)],[t27012,t392]) ).
cnf(t27014,plain,
join(complement(X1),join(X2,X1)) = top,
inference(step,[status(thm)],[t27013,t392]) ).
cnf(t563,plain,
join(complement(X1),join(X2,X1)) = top,
inference(orient,[status(thm)],[t27014]) ).
cnf(t570,plain,
top = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t563,t487]) ).
cnf(t27020,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)],[t27020]) ).
cnf(t613,plain,
meet(X1,meet(X2,complement(X1))) = complement(top),
inference(cp,[status(thm)],[t39,t606]) ).
cnf(t27023,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)],[t27023]) ).
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(t26991,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)],[t26991]) ).
cnf(t840,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = complement(top),
inference(cp,[status(thm)],[t837,t371]) ).
cnf(t27082,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)],[t27082]) ).
cnf(t3658,plain,
join(X1,complement(converse(complement(converse(complement(complement(X1))))))) = join(X1,zero),
inference(cp,[status(thm)],[t3654,t3538]) ).
cnf(t27085,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(t27086,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t27085,t346]) ).
cnf(t3725,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t27086]) ).
cnf(t3764,plain,
join(X1,converse(complement(converse(complement(converse(converse(X1))))))) = converse(converse(X1)),
inference(cp,[status(thm)],[t106,t3725]) ).
cnf(t27092,plain,
join(X1,converse(complement(converse(complement(X1))))) = converse(converse(X1)),
inference(step,[status(thm)],[t3764,t18]) ).
cnf(t27093,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(step,[status(thm)],[t27092,t18]) ).
cnf(t4003,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(orient,[status(thm)],[t27093]) ).
cnf(t4031,plain,
meet(X1,complement(converse(complement(converse(complement(complement(X1))))))) = complement(complement(X1)),
inference(cp,[status(thm)],[t837,t4003]) ).
cnf(t27094,plain,
meet(X1,complement(converse(complement(converse(X1))))) = complement(complement(X1)),
inference(step,[status(thm)],[t4031,t380]) ).
cnf(t27095,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t27094,t380]) ).
cnf(t4039,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t27095]) ).
cnf(t4063,plain,
zero = meet(complement(complement(converse(complement(converse(X1))))),X1),
inference(cp,[status(thm)],[t639,t4039]) ).
cnf(t27096,plain,
zero = meet(X1,complement(complement(converse(complement(converse(X1)))))),
inference(step,[status(thm)],[t4063,t74]) ).
cnf(t27097,plain,
zero = meet(X1,converse(complement(converse(X1)))),
inference(step,[status(thm)],[t27096,t380]) ).
cnf(t4079,plain,
meet(X1,converse(complement(converse(X1)))) = zero,
inference(orient,[status(thm)],[t27097]) ).
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(t27111,plain,
join(converse(complement(X1)),complement(converse(X1))) = join(complement(converse(X1)),zero),
inference(step,[status(thm)],[t4494,t19]) ).
cnf(t27112,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(step,[status(thm)],[t27111,t346]) ).
cnf(t4948,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(orient,[status(thm)],[t27112]) ).
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(t27113,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)],[t27113]) ).
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(t27126,plain,
zero = composition(X1,converse(complement(composition(top,X1)))),
inference(step,[status(thm)],[t27125,t5379]) ).
cnf(t5625,plain,
composition(X1,converse(complement(composition(top,X1)))) = zero,
inference(orient,[status(thm)],[t27126]) ).
cnf(t5393,plain,
converse(complement(composition(top,top))) = complement(composition(top,top)),
inference(cp,[status(thm)],[t5379,t368]) ).
cnf(t5435,plain,
converse(complement(composition(top,top))) = complement(composition(top,top)),
inference(orient,[status(thm)],[t5393]) ).
cnf(t5629,plain,
zero = composition(top,complement(composition(top,top))),
inference(cp,[status(thm)],[t5625,t5435]) ).
cnf(t5693,plain,
composition(top,complement(composition(top,top))) = zero,
inference(orient,[status(thm)],[t5629]) ).
cnf(t5697,plain,
composition(join(top,X1),complement(composition(top,top))) = join(zero,composition(X1,complement(composition(top,top)))),
inference(cp,[status(thm)],[t27,t5693]) ).
cnf(t27163,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(X1,complement(composition(top,top)))),
inference(step,[status(thm)],[t5697,t360]) ).
cnf(t27164,plain,
zero = join(zero,composition(X1,complement(composition(top,top)))),
inference(step,[status(thm)],[t27163,t5693]) ).
cnf(t27165,plain,
zero = composition(X1,complement(composition(top,top))),
inference(step,[status(thm)],[t27164,t325]) ).
cnf(t5715,plain,
composition(X1,complement(composition(top,top))) = zero,
inference(orient,[status(thm)],[t27165]) ).
cnf(t5716,plain,
zero = complement(composition(top,top)),
inference(cp,[status(thm)],[t5715,t170]) ).
cnf(t5721,plain,
complement(composition(top,top)) = zero,
inference(orient,[status(thm)],[t5716]) ).
cnf(t5728,plain,
composition(top,top) = complement(zero),
inference(cp,[status(thm)],[t380,t5721]) ).
cnf(t327,plain,
complement(zero) = top,
inference(cp,[status(thm)],[t325,t24]) ).
cnf(t337,plain,
complement(zero) = top,
inference(orient,[status(thm)],[t327]) ).
cnf(t27166,plain,
composition(top,top) = top,
inference(step,[status(thm)],[t5728,t337]) ).
cnf(t5745,plain,
composition(top,top) = top,
inference(orient,[status(thm)],[t27166]) ).
cnf(t27167,plain,
join(sk0,composition(complement(sk0),top)) = top,
inference(step,[status(thm)],[t878,t5745]) ).
cnf(t5746,plain,
join(sk0,composition(complement(sk0),top)) = top,
inference(orient,[status(thm)],[t27167]) ).
cnf(t12998,plain,
join(composition(complement(sk0),top),join(X1,sk0)) = join(composition(complement(sk0),top),join(X1,top)),
inference(cp,[status(thm)],[t12948,t5746]) ).
cnf(t22,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(cp,[status(thm)],[t21,t19]) ).
cnf(t658,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(orient,[status(thm)],[t22]) ).
cnf(t27368,plain,
join(sk0,join(composition(complement(sk0),top),X1)) = join(composition(complement(sk0),top),join(X1,top)),
inference(step,[status(thm)],[t12998,t658]) ).
cnf(t27369,plain,
join(sk0,join(composition(complement(sk0),top),X1)) = join(top,join(composition(complement(sk0),top),X1)),
inference(step,[status(thm)],[t27368,t658]) ).
cnf(t27370,plain,
join(sk0,join(composition(complement(sk0),top),X1)) = top,
inference(step,[status(thm)],[t27369,t360]) ).
cnf(t13070,plain,
join(sk0,join(composition(complement(sk0),top),X1)) = top,
inference(orient,[status(thm)],[t27370]) ).
cnf(t13088,plain,
join(sk0,complement(join(composition(complement(sk0),top),X1))) = join(sk0,complement(top)),
inference(cp,[status(thm)],[t4387,t13070]) ).
cnf(t27628,plain,
join(sk0,complement(join(composition(complement(sk0),top),X1))) = join(sk0,zero),
inference(step,[status(thm)],[t13088,t65]) ).
cnf(t27629,plain,
join(sk0,complement(join(composition(complement(sk0),top),X1))) = sk0,
inference(step,[status(thm)],[t27628,t346]) ).
cnf(t26613,plain,
join(sk0,complement(join(composition(complement(sk0),top),X1))) = sk0,
inference(orient,[status(thm)],[t27629]) ).
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(t26614,plain,
sk0 = join(sk0,complement(composition(complement(sk0),top))),
inference(cp,[status(thm)],[t26613,t4184]) ).
cnf(t23,plain,
join(X1,join(X2,X3)) = join(join(X2,X1),X3),
inference(cp,[status(thm)],[t21,t19]) ).
cnf(t27063,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(step,[status(thm)],[t23,t21]) ).
cnf(t1263,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(orient,[status(thm)],[t27063]) ).
cnf(t1273,plain,
join(X1,join(X2,meet(X3,X1))) = join(X2,X1),
inference(cp,[status(thm)],[t1263,t487]) ).
cnf(t1914,plain,
join(X1,join(X2,meet(X3,X1))) = join(X2,X1),
inference(orient,[status(thm)],[t1273]) ).
cnf(t3595,plain,
join(meet(X1,X2),complement(X2)) = join(complement(X2),X1),
inference(cp,[status(thm)],[t1914,t3545]) ).
cnf(t27098,plain,
join(complement(X2),meet(X1,X2)) = join(complement(X2),X1),
inference(step,[status(thm)],[t3595,t19]) ).
cnf(t4123,plain,
join(complement(X1),meet(X2,X1)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t27098]) ).
cnf(t4251,plain,
meet(X1,complement(complement(join(X2,complement(X1))))) = complement(join(complement(X1),complement(X2))),
inference(cp,[status(thm)],[t837,t4184]) ).
cnf(t27099,plain,
meet(X1,join(X2,complement(X1))) = complement(join(complement(X1),complement(X2))),
inference(step,[status(thm)],[t4251,t380]) ).
cnf(t27100,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(step,[status(thm)],[t27099,t39]) ).
cnf(t4260,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t27100]) ).
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(t4323,plain,
meet(complement(X1),X2) = meet(complement(X1),join(X1,X2)),
inference(cp,[status(thm)],[t4292,t380]) ).
cnf(t4634,plain,
meet(complement(X1),join(X1,X2)) = meet(complement(X1),X2),
inference(orient,[status(thm)],[t4323]) ).
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]) ).
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(t27127,plain,
zero = converse(composition(complement(converse(sk0)),sk0)),
inference(step,[status(thm)],[t5631,t51]) ).
cnf(t27128,plain,
zero = converse(composition(converse(complement(sk0)),sk0)),
inference(step,[status(thm)],[t27127,t5031]) ).
cnf(t27129,plain,
zero = composition(converse(sk0),complement(sk0)),
inference(step,[status(thm)],[t27128,t137]) ).
cnf(t5650,plain,
composition(converse(sk0),complement(sk0)) = zero,
inference(orient,[status(thm)],[t27129]) ).
cnf(t5657,plain,
composition(converse(complement(sk0)),sk0) = converse(zero),
inference(cp,[status(thm)],[t137,t5650]) ).
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(t26999,plain,
join(converse(zero),X1) = X1,
inference(step,[status(thm)],[t332,t18]) ).
cnf(t403,plain,
join(converse(zero),X1) = X1,
inference(orient,[status(thm)],[t26999]) ).
cnf(t404,plain,
zero = converse(zero),
inference(cp,[status(thm)],[t403,t346]) ).
cnf(t409,plain,
converse(zero) = zero,
inference(orient,[status(thm)],[t404]) ).
cnf(t27159,plain,
composition(converse(complement(sk0)),sk0) = zero,
inference(step,[status(thm)],[t5657,t409]) ).
cnf(t5685,plain,
composition(converse(complement(sk0)),sk0) = zero,
inference(orient,[status(thm)],[t27159]) ).
cnf(t5691,plain,
complement(sk0) = join(complement(sk0),composition(converse(converse(complement(sk0))),complement(zero))),
inference(cp,[status(thm)],[t30,t5685]) ).
cnf(t27181,plain,
complement(sk0) = join(complement(sk0),composition(complement(sk0),complement(zero))),
inference(step,[status(thm)],[t5691,t18]) ).
cnf(t27182,plain,
complement(sk0) = join(complement(sk0),composition(complement(sk0),top)),
inference(step,[status(thm)],[t27181,t337]) ).
cnf(t5862,plain,
join(complement(sk0),composition(complement(sk0),top)) = complement(sk0),
inference(orient,[status(thm)],[t27182]) ).
cnf(t5863,plain,
meet(complement(complement(sk0)),composition(complement(sk0),top)) = meet(complement(complement(sk0)),complement(sk0)),
inference(cp,[status(thm)],[t4634,t5862]) ).
cnf(t27183,plain,
meet(sk0,composition(complement(sk0),top)) = meet(complement(complement(sk0)),complement(sk0)),
inference(step,[status(thm)],[t5863,t380]) ).
cnf(t27184,plain,
meet(sk0,composition(complement(sk0),top)) = complement(join(complement(sk0),sk0)),
inference(step,[status(thm)],[t27183,t864]) ).
cnf(t27185,plain,
meet(sk0,composition(complement(sk0),top)) = meet(sk0,complement(sk0)),
inference(step,[status(thm)],[t27184,t837]) ).
cnf(t27186,plain,
meet(sk0,composition(complement(sk0),top)) = zero,
inference(step,[status(thm)],[t27185,t63]) ).
cnf(t5886,plain,
meet(sk0,composition(complement(sk0),top)) = zero,
inference(orient,[status(thm)],[t27186]) ).
cnf(t5887,plain,
join(complement(composition(complement(sk0),top)),sk0) = join(complement(composition(complement(sk0),top)),zero),
inference(cp,[status(thm)],[t4123,t5886]) ).
cnf(t27392,plain,
join(sk0,complement(composition(complement(sk0),top))) = join(complement(composition(complement(sk0),top)),zero),
inference(step,[status(thm)],[t5887,t19]) ).
cnf(t27393,plain,
join(sk0,complement(composition(complement(sk0),top))) = complement(composition(complement(sk0),top)),
inference(step,[status(thm)],[t27392,t346]) ).
cnf(t14728,plain,
join(sk0,complement(composition(complement(sk0),top))) = complement(composition(complement(sk0),top)),
inference(orient,[status(thm)],[t27393]) ).
cnf(t27630,plain,
sk0 = complement(composition(complement(sk0),top)),
inference(step,[status(thm)],[t26614,t14728]) ).
cnf(t26676,plain,
complement(composition(complement(sk0),top)) = sk0,
inference(orient,[status(thm)],[t27630]) ).
cnf(t26683,plain,
composition(complement(sk0),top) = complement(sk0),
inference(cp,[status(thm)],[t380,t26676]) ).
cnf(t26933,plain,
composition(complement(sk0),top) = complement(sk0),
inference(orient,[status(thm)],[t26683]) ).
cnf(c14,plain,
composition(complement(sk0),top) != complement(sk0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
composition(complement(sk0),top) != complement(sk0),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
complement(sk0) != complement(sk0),
inference(rw,[status(thm)],[goal_0,t26933]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL018+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 07:16:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.00/2.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.00/2.69 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------