%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL025+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 : n005.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 02:34:51 PM UTC 2026
% Result : Theorem 38.42s 5.46s
% Output : Proof 38.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 143
% Number of leaves : 14
% Syntax : Number of formulae : 600 ( 596 unt; 0 def)
% Number of atoms : 604 ( 603 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 : 9 ( 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 : 813 ( 95 sgn 77 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(t107479,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)],[t107479]) ).
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(t53,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(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(t55,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t53,t18]) ).
cnf(t148,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t55]) ).
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(t149,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t148,t17]) ).
cnf(t107486,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t149,t18]) ).
cnf(t163,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t107486]) ).
cnf(t164,plain,
one = converse(one),
inference(cp,[status(thm)],[t163,t17]) ).
cnf(t170,plain,
converse(one) = one,
inference(orient,[status(thm)],[t164]) ).
cnf(t107487,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t163,t170]) ).
cnf(t180,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t107487]) ).
cnf(t181,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t180]) ).
cnf(t184,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t30,t181]) ).
cnf(t107490,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t184,t170]) ).
cnf(t107491,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t107490,t181]) ).
cnf(t213,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t107491]) ).
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(t41,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t6]) ).
cnf(t223,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t41,t213]) ).
cnf(t237,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t223]) ).
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(t107498,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t20,t19]) ).
cnf(t107499,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t107498,t41]) ).
cnf(t107500,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t107499,t19]) ).
cnf(t263,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t107500]) ).
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(t60,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t264,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t263,t60]) ).
cnf(t107501,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t264,t41]) ).
cnf(t281,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t107501]) ).
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(t42,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t41,t24]) ).
cnf(t107480,plain,
zero = complement(top),
inference(step,[status(thm)],[t42,t60]) ).
cnf(t62,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t107480]) ).
cnf(t217,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t213,t62]) ).
cnf(t107492,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t217,t62]) ).
cnf(t107493,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t107492,t62]) ).
cnf(t224,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t107493]) ).
cnf(t225,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t21,t224]) ).
cnf(t247,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t225]) ).
cnf(t283,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t247,t281]) ).
cnf(t107502,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t283,t281]) ).
cnf(t285,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t107502]) ).
cnf(t107503,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t281,t285]) ).
cnf(t292,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t107503]) ).
cnf(t312,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t292]) ).
cnf(t107510,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t237,t312]) ).
cnf(t314,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t107510]) ).
cnf(t321,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t314]) ).
cnf(t323,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t213,t321]) ).
cnf(t107517,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t323,t321]) ).
cnf(t107518,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t107517,t321]) ).
cnf(t331,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t107518]) ).
cnf(t333,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t21,t331]) ).
cnf(t425,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t333]) ).
cnf(t429,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1),
inference(cp,[status(thm)],[t425,t263]) ).
cnf(t107537,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t429,t263]) ).
cnf(t107538,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t107537,t19]) ).
cnf(t467,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t107538]) ).
cnf(t43,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t41,t19]) ).
cnf(t107482,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t43,t41]) ).
cnf(t71,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t107482]) ).
cnf(t469,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t467,t71]) ).
cnf(t474,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t469]) ).
cnf(t477,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t21,t474]) ).
cnf(t1950,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t477]) ).
cnf(t322,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(cp,[status(thm)],[t321,t41]) ).
cnf(t757,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t322]) ).
cnf(t760,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(cp,[status(thm)],[t757,t321]) ).
cnf(t836,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(orient,[status(thm)],[t760]) ).
cnf(t842,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t321,t836]) ).
cnf(t988,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t842]) ).
cnf(t107576,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(step,[status(thm)],[t263,t988]) ).
cnf(t1013,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[t107576]) ).
cnf(t4444,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(orient,[status(thm)],[t1013]) ).
cnf(t4506,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(cp,[status(thm)],[t1950,t4444]) ).
cnf(t4551,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t4506]) ).
cnf(t4560,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(cp,[status(thm)],[t4551,t71]) ).
cnf(t4636,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t4560]) ).
cnf(t4647,plain,
join(complement(X1),X2) = join(complement(X1),meet(X1,X2)),
inference(cp,[status(thm)],[t4636,t321]) ).
cnf(t5739,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t4647]) ).
cnf(t759,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(cp,[status(thm)],[t757,t321]) ).
cnf(t820,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t759]) ).
cnf(t827,plain,
meet(complement(X1),X2) = complement(join(X1,complement(X2))),
inference(cp,[status(thm)],[t321,t820]) ).
cnf(t852,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(orient,[status(thm)],[t827]) ).
cnf(t865,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(cp,[status(thm)],[t852,t321]) ).
cnf(t1014,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(orient,[status(thm)],[t865]) ).
cnf(t4554,plain,
join(X1,complement(X2)) = join(X1,complement(join(X2,X1))),
inference(cp,[status(thm)],[t4551,t1014]) ).
cnf(t4787,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t4554]) ).
cnf(t4884,plain,
meet(X1,complement(complement(join(X2,complement(X1))))) = complement(join(complement(X1),complement(X2))),
inference(cp,[status(thm)],[t988,t4787]) ).
cnf(t107664,plain,
meet(X1,join(X2,complement(X1))) = complement(join(complement(X1),complement(X2))),
inference(step,[status(thm)],[t4884,t321]) ).
cnf(t107665,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(step,[status(thm)],[t107664,t41]) ).
cnf(t5152,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t107665]) ).
cnf(t5174,plain,
meet(X1,X2) = meet(X1,join(complement(X1),X2)),
inference(cp,[status(thm)],[t5152,t19]) ).
cnf(t5192,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t5174]) ).
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(t117,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t36]) ).
cnf(t118,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(cp,[status(thm)],[t117,t24]) ).
cnf(t428,plain,
join(X1,complement(X1)) = join(X1,top),
inference(cp,[status(thm)],[t425,t24]) ).
cnf(t107529,plain,
top = join(X1,top),
inference(step,[status(thm)],[t428,t24]) ).
cnf(t435,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t107529]) ).
cnf(t439,plain,
join(X1,converse(top)) = converse(top),
inference(cp,[status(thm)],[t117,t435]) ).
cnf(t454,plain,
join(X1,converse(top)) = converse(top),
inference(orient,[status(thm)],[t439]) ).
cnf(t436,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t435,t19]) ).
cnf(t441,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t436]) ).
cnf(t455,plain,
converse(top) = top,
inference(cp,[status(thm)],[t454,t441]) ).
cnf(t459,plain,
converse(top) = top,
inference(orient,[status(thm)],[t455]) ).
cnf(t107577,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(step,[status(thm)],[t118,t459]) ).
cnf(t1028,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(orient,[status(thm)],[t107577]) ).
cnf(t5211,plain,
meet(X1,converse(complement(converse(complement(X1))))) = meet(X1,top),
inference(cp,[status(thm)],[t5192,t1028]) ).
cnf(t65,plain,
meet(top,X1) = complement(join(zero,complement(X1))),
inference(cp,[status(thm)],[t41,t62]) ).
cnf(t81,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(orient,[status(thm)],[t65]) ).
cnf(t107507,plain,
complement(complement(X1)) = meet(top,X1),
inference(step,[status(thm)],[t81,t285]) ).
cnf(t295,plain,
complement(complement(X1)) = meet(top,X1),
inference(rw,[status(thm)],[t107507]) ).
cnf(t107519,plain,
X1 = meet(top,X1),
inference(step,[status(thm)],[t295,t321]) ).
cnf(t334,plain,
meet(top,X1) = X1,
inference(orient,[status(thm)],[t107519]) ).
cnf(t335,plain,
X1 = meet(X1,top),
inference(cp,[status(thm)],[t334,t71]) ).
cnf(t336,plain,
meet(X1,top) = X1,
inference(orient,[status(thm)],[t335]) ).
cnf(t107667,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(step,[status(thm)],[t5211,t336]) ).
cnf(t5260,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(orient,[status(thm)],[t107667]) ).
cnf(t5291,plain,
join(X1,complement(converse(complement(converse(complement(complement(X1))))))) = complement(complement(X1)),
inference(cp,[status(thm)],[t820,t5260]) ).
cnf(t107668,plain,
join(X1,complement(converse(complement(converse(X1))))) = complement(complement(X1)),
inference(step,[status(thm)],[t5291,t321]) ).
cnf(t107669,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t107668,t321]) ).
cnf(t5297,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t107669]) ).
cnf(t5343,plain,
join(X1,converse(complement(converse(complement(converse(converse(X1))))))) = converse(converse(X1)),
inference(cp,[status(thm)],[t117,t5297]) ).
cnf(t107670,plain,
join(X1,converse(complement(converse(complement(X1))))) = converse(converse(X1)),
inference(step,[status(thm)],[t5343,t18]) ).
cnf(t107671,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(step,[status(thm)],[t107670,t18]) ).
cnf(t5351,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(orient,[status(thm)],[t107671]) ).
cnf(t5373,plain,
meet(X1,converse(complement(converse(complement(complement(X1)))))) = meet(X1,complement(X1)),
inference(cp,[status(thm)],[t5192,t5351]) ).
cnf(t107672,plain,
meet(X1,converse(complement(converse(X1)))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t5373,t321]) ).
cnf(t107673,plain,
meet(X1,converse(complement(converse(X1)))) = zero,
inference(step,[status(thm)],[t107672,t60]) ).
cnf(t5392,plain,
meet(X1,converse(complement(converse(X1)))) = zero,
inference(orient,[status(thm)],[t107673]) ).
cnf(t5405,plain,
zero = meet(converse(X1),converse(complement(X1))),
inference(cp,[status(thm)],[t5392,t18]) ).
cnf(t5415,plain,
meet(converse(X1),converse(complement(X1))) = zero,
inference(orient,[status(thm)],[t5405]) ).
cnf(t5766,plain,
join(complement(converse(X1)),converse(complement(X1))) = join(complement(converse(X1)),zero),
inference(cp,[status(thm)],[t5739,t5415]) ).
cnf(t107716,plain,
join(converse(complement(X1)),complement(converse(X1))) = join(complement(converse(X1)),zero),
inference(step,[status(thm)],[t5766,t19]) ).
cnf(t287,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t285,t19]) ).
cnf(t308,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t287]) ).
cnf(t107717,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(step,[status(thm)],[t107716,t308]) ).
cnf(t6756,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(orient,[status(thm)],[t107717]) ).
cnf(t6761,plain,
complement(converse(complement(X1))) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t6756,t321]) ).
cnf(t5310,plain,
converse(X1) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t5297,t18]) ).
cnf(t6175,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(orient,[status(thm)],[t5310]) ).
cnf(t107718,plain,
complement(converse(complement(X1))) = converse(X1),
inference(step,[status(thm)],[t6761,t6175]) ).
cnf(t6795,plain,
complement(converse(complement(X1))) = converse(X1),
inference(orient,[status(thm)],[t107718]) ).
cnf(t6800,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(cp,[status(thm)],[t6795,t321]) ).
cnf(t6840,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(orient,[status(thm)],[t6800]) ).
cnf(t6850,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(cp,[status(thm)],[t6840,t117]) ).
cnf(t7360,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(orient,[status(thm)],[t6850]) ).
cnf(t6861,plain,
complement(meet(converse(X1),X2)) = join(converse(complement(X1)),complement(X2)),
inference(cp,[status(thm)],[t757,t6840]) ).
cnf(t7571,plain,
join(converse(complement(X1)),complement(X2)) = complement(meet(converse(X1),X2)),
inference(orient,[status(thm)],[t6861]) ).
cnf(t7613,plain,
complement(join(complement(X1),converse(complement(X2)))) = converse(complement(complement(meet(converse(X1),X2)))),
inference(cp,[status(thm)],[t7360,t7571]) ).
cnf(t107747,plain,
meet(X1,complement(converse(complement(X2)))) = converse(complement(complement(meet(converse(X1),X2)))),
inference(step,[status(thm)],[t7613,t988]) ).
cnf(t107748,plain,
meet(X1,converse(X2)) = converse(complement(complement(meet(converse(X1),X2)))),
inference(step,[status(thm)],[t107747,t6795]) ).
cnf(t107749,plain,
meet(X1,converse(X2)) = converse(meet(converse(X1),X2)),
inference(step,[status(thm)],[t107748,t321]) ).
cnf(t7621,plain,
converse(meet(converse(X1),X2)) = meet(X1,converse(X2)),
inference(orient,[status(thm)],[t107749]) ).
cnf(t7631,plain,
meet(X1,converse(X2)) = converse(meet(X2,converse(X1))),
inference(cp,[status(thm)],[t7621,t71]) ).
cnf(t7681,plain,
converse(meet(X1,converse(X2))) = meet(X2,converse(X1)),
inference(orient,[status(thm)],[t7631]) ).
cnf(t5225,plain,
meet(complement(X1),X2) = meet(complement(X1),join(X1,X2)),
inference(cp,[status(thm)],[t5192,t321]) ).
cnf(t5986,plain,
meet(complement(X1),join(X1,X2)) = meet(complement(X1),X2),
inference(orient,[status(thm)],[t5225]) ).
cnf(t432,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(cp,[status(thm)],[t425,t19]) ).
cnf(t500,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t432]) ).
fof(f13,conjecture,
! [X0] :
( join(X0,one) = one
=> converse(X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0] :
( join(X0,one) = one
=> converse(X0) = X0 ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0] :
( converse(X0) != X0
& join(X0,one) = one ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( converse(sk0) != sk0
& join(sk0,one) = one ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f13_nnf]) ).
cnf(c13,plain,
join(sk0,one) = one,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t2,plain,
join(sk0,one) = one,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t39,plain,
join(sk0,one) = one,
inference(orient,[status(thm)],[t2]) ).
cnf(t40,plain,
join(sk0,join(one,X1)) = join(one,X1),
inference(cp,[status(thm)],[t21,t39]) ).
cnf(t74,plain,
join(sk0,join(one,X1)) = join(one,X1),
inference(orient,[status(thm)],[t40]) ).
cnf(t507,plain,
join(join(one,X1),sk0) = join(join(one,X1),join(one,X1)),
inference(cp,[status(thm)],[t500,t74]) ).
cnf(t107539,plain,
join(one,join(X1,sk0)) = join(join(one,X1),join(one,X1)),
inference(step,[status(thm)],[t507,t21]) ).
cnf(t107540,plain,
join(one,join(X1,sk0)) = join(one,join(X1,join(one,X1))),
inference(step,[status(thm)],[t107539,t21]) ).
cnf(t107541,plain,
join(one,join(X1,sk0)) = join(one,join(X1,one)),
inference(step,[status(thm)],[t107540,t500]) ).
cnf(t107542,plain,
join(one,join(X1,sk0)) = join(one,X1),
inference(step,[status(thm)],[t107541,t500]) ).
cnf(t512,plain,
join(one,join(X1,sk0)) = join(one,X1),
inference(orient,[status(thm)],[t107542]) ).
cnf(t516,plain,
join(one,X1) = join(one,join(sk0,X1)),
inference(cp,[status(thm)],[t512,t19]) ).
cnf(t519,plain,
join(one,join(sk0,X1)) = join(one,X1),
inference(orient,[status(thm)],[t516]) ).
cnf(t523,plain,
join(one,complement(sk0)) = join(one,top),
inference(cp,[status(thm)],[t519,t24]) ).
cnf(t107543,plain,
join(one,complement(sk0)) = top,
inference(step,[status(thm)],[t523,t435]) ).
cnf(t526,plain,
join(one,complement(sk0)) = top,
inference(orient,[status(thm)],[t107543]) ).
cnf(t529,plain,
join(one,join(complement(sk0),X1)) = join(top,X1),
inference(cp,[status(thm)],[t21,t526]) ).
cnf(t107549,plain,
join(one,join(complement(sk0),X1)) = top,
inference(step,[status(thm)],[t529,t441]) ).
cnf(t549,plain,
join(one,join(complement(sk0),X1)) = top,
inference(orient,[status(thm)],[t107549]) ).
cnf(t4836,plain,
join(join(complement(sk0),X1),complement(one)) = join(join(complement(sk0),X1),complement(top)),
inference(cp,[status(thm)],[t4787,t549]) ).
cnf(t107835,plain,
join(complement(sk0),join(X1,complement(one))) = join(join(complement(sk0),X1),complement(top)),
inference(step,[status(thm)],[t4836,t21]) ).
cnf(t107836,plain,
join(complement(sk0),join(X1,complement(one))) = join(complement(sk0),join(X1,complement(top))),
inference(step,[status(thm)],[t107835,t21]) ).
cnf(t22,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(cp,[status(thm)],[t21,t19]) ).
cnf(t563,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(orient,[status(thm)],[t22]) ).
cnf(t107837,plain,
join(complement(sk0),join(X1,complement(one))) = join(complement(top),join(complement(sk0),X1)),
inference(step,[status(thm)],[t107836,t563]) ).
cnf(t107838,plain,
join(complement(sk0),join(X1,complement(one))) = join(zero,join(complement(sk0),X1)),
inference(step,[status(thm)],[t107837,t62]) ).
cnf(t107839,plain,
join(complement(sk0),join(X1,complement(one))) = join(complement(sk0),X1),
inference(step,[status(thm)],[t107838,t285]) ).
cnf(t15073,plain,
join(complement(sk0),join(X1,complement(one))) = join(complement(sk0),X1),
inference(orient,[status(thm)],[t107839]) ).
cnf(t15082,plain,
meet(complement(complement(sk0)),join(X1,complement(one))) = meet(complement(complement(sk0)),join(complement(sk0),X1)),
inference(cp,[status(thm)],[t5986,t15073]) ).
cnf(t107840,plain,
meet(sk0,join(X1,complement(one))) = meet(complement(complement(sk0)),join(complement(sk0),X1)),
inference(step,[status(thm)],[t15082,t321]) ).
cnf(t107841,plain,
meet(sk0,join(X1,complement(one))) = meet(complement(complement(sk0)),X1),
inference(step,[status(thm)],[t107840,t5986]) ).
cnf(t107842,plain,
meet(sk0,join(X1,complement(one))) = meet(sk0,X1),
inference(step,[status(thm)],[t107841,t321]) ).
cnf(t15114,plain,
meet(sk0,join(X1,complement(one))) = meet(sk0,X1),
inference(orient,[status(thm)],[t107842]) ).
cnf(t15118,plain,
meet(sk0,X1) = meet(sk0,join(complement(one),X1)),
inference(cp,[status(thm)],[t15114,t19]) ).
cnf(t15153,plain,
meet(sk0,join(complement(one),X1)) = meet(sk0,X1),
inference(orient,[status(thm)],[t15118]) ).
cnf(t6862,plain,
complement(meet(X1,converse(X2))) = join(complement(X1),converse(complement(X2))),
inference(cp,[status(thm)],[t757,t6840]) ).
cnf(t8060,plain,
join(complement(X1),converse(complement(X2))) = complement(meet(X1,converse(X2))),
inference(orient,[status(thm)],[t6862]) ).
cnf(t15155,plain,
meet(sk0,converse(complement(X1))) = meet(sk0,complement(meet(one,converse(X1)))),
inference(cp,[status(thm)],[t15153,t8060]) ).
cnf(t575,plain,
join(complement(X1),join(X2,X1)) = join(X2,top),
inference(cp,[status(thm)],[t563,t24]) ).
cnf(t107552,plain,
join(X1,join(complement(X1),X2)) = join(X2,top),
inference(step,[status(thm)],[t575,t563]) ).
cnf(t107553,plain,
join(X1,join(complement(X1),X2)) = top,
inference(step,[status(thm)],[t107552,t435]) ).
cnf(t652,plain,
join(X1,join(complement(X1),X2)) = top,
inference(orient,[status(thm)],[t107553]) ).
cnf(t654,plain,
top = join(X1,join(X2,complement(X1))),
inference(cp,[status(thm)],[t652,t19]) ).
cnf(t744,plain,
join(X1,join(X2,complement(X1))) = top,
inference(orient,[status(thm)],[t654]) ).
cnf(t765,plain,
top = join(X1,complement(meet(X2,X1))),
inference(cp,[status(thm)],[t744,t757]) ).
cnf(t772,plain,
join(X1,complement(meet(X2,X1))) = top,
inference(orient,[status(thm)],[t765]) ).
cnf(t854,plain,
meet(complement(X1),meet(X2,X1)) = complement(top),
inference(cp,[status(thm)],[t852,t772]) ).
cnf(t107568,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(step,[status(thm)],[t854,t62]) ).
cnf(t883,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t107568]) ).
cnf(t662,plain,
X1 = join(meet(X1,join(complement(complement(X1)),X2)),complement(top)),
inference(cp,[status(thm)],[t263,t652]) ).
cnf(t107554,plain,
X1 = join(complement(top),meet(X1,join(complement(complement(X1)),X2))),
inference(step,[status(thm)],[t662,t19]) ).
cnf(t107555,plain,
X1 = join(zero,meet(X1,join(complement(complement(X1)),X2))),
inference(step,[status(thm)],[t107554,t62]) ).
cnf(t107556,plain,
X1 = meet(X1,join(complement(complement(X1)),X2)),
inference(step,[status(thm)],[t107555,t285]) ).
cnf(t107557,plain,
X1 = meet(X1,join(X1,X2)),
inference(step,[status(thm)],[t107556,t321]) ).
cnf(t664,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t107557]) ).
cnf(t892,plain,
zero = meet(complement(join(X1,X2)),X1),
inference(cp,[status(thm)],[t883,t664]) ).
cnf(t107572,plain,
zero = meet(X1,complement(join(X1,X2))),
inference(step,[status(thm)],[t892,t71]) ).
cnf(t935,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(orient,[status(thm)],[t107572]) ).
cnf(t940,plain,
zero = meet(converse(X1),complement(converse(join(X1,X2)))),
inference(cp,[status(thm)],[t935,t34]) ).
cnf(t4145,plain,
meet(converse(X1),complement(converse(join(X1,X2)))) = zero,
inference(orient,[status(thm)],[t940]) ).
cnf(t173,plain,
converse(join(one,X1)) = join(one,converse(X1)),
inference(cp,[status(thm)],[t34,t170]) ).
cnf(t185,plain,
converse(join(one,X1)) = join(one,converse(X1)),
inference(orient,[status(thm)],[t173]) ).
cnf(t186,plain,
join(one,converse(complement(one))) = converse(top),
inference(cp,[status(thm)],[t185,t24]) ).
cnf(t228,plain,
join(one,converse(complement(one))) = converse(top),
inference(orient,[status(thm)],[t186]) ).
cnf(t107535,plain,
join(one,converse(complement(one))) = top,
inference(step,[status(thm)],[t228,t459]) ).
cnf(t460,plain,
join(one,converse(complement(one))) = top,
inference(orient,[status(thm)],[t107535]) ).
cnf(t4845,plain,
join(converse(complement(one)),complement(one)) = join(converse(complement(one)),complement(top)),
inference(cp,[status(thm)],[t4787,t460]) ).
cnf(t107650,plain,
join(complement(one),converse(complement(one))) = join(converse(complement(one)),complement(top)),
inference(step,[status(thm)],[t4845,t19]) ).
cnf(t107651,plain,
join(complement(one),converse(complement(one))) = join(complement(top),converse(complement(one))),
inference(step,[status(thm)],[t107650,t19]) ).
cnf(t107652,plain,
join(complement(one),converse(complement(one))) = join(zero,converse(complement(one))),
inference(step,[status(thm)],[t107651,t62]) ).
cnf(t107653,plain,
join(complement(one),converse(complement(one))) = converse(complement(one)),
inference(step,[status(thm)],[t107652,t285]) ).
cnf(t4893,plain,
join(complement(one),converse(complement(one))) = converse(complement(one)),
inference(orient,[status(thm)],[t107653]) ).
cnf(t4911,plain,
zero = meet(converse(complement(one)),complement(converse(converse(complement(one))))),
inference(cp,[status(thm)],[t4145,t4893]) ).
cnf(t107654,plain,
zero = meet(converse(complement(one)),complement(complement(one))),
inference(step,[status(thm)],[t4911,t18]) ).
cnf(t107655,plain,
zero = meet(converse(complement(one)),one),
inference(step,[status(thm)],[t107654,t321]) ).
cnf(t107656,plain,
zero = meet(one,converse(complement(one))),
inference(step,[status(thm)],[t107655,t71]) ).
cnf(t4915,plain,
meet(one,converse(complement(one))) = zero,
inference(orient,[status(thm)],[t107656]) ).
cnf(t4917,plain,
one = join(zero,meet(one,complement(converse(complement(one))))),
inference(cp,[status(thm)],[t4444,t4915]) ).
cnf(t107657,plain,
one = meet(one,complement(converse(complement(one)))),
inference(step,[status(thm)],[t4917,t285]) ).
cnf(t4920,plain,
meet(one,complement(converse(complement(one)))) = one,
inference(orient,[status(thm)],[t107657]) ).
cnf(t4938,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(cp,[status(thm)],[t836,t4920]) ).
cnf(t107658,plain,
converse(complement(one)) = complement(one),
inference(step,[status(thm)],[t4938,t4893]) ).
cnf(t4941,plain,
converse(complement(one)) = complement(one),
inference(orient,[status(thm)],[t107658]) ).
cnf(t4945,plain,
converse(join(X1,complement(one))) = join(converse(X1),complement(one)),
inference(cp,[status(thm)],[t34,t4941]) ).
cnf(t5056,plain,
converse(join(X1,complement(one))) = join(converse(X1),complement(one)),
inference(orient,[status(thm)],[t4945]) ).
cnf(t6841,plain,
converse(complement(join(X1,complement(one)))) = complement(join(converse(X1),complement(one))),
inference(cp,[status(thm)],[t6840,t5056]) ).
cnf(t107730,plain,
converse(meet(complement(X1),one)) = complement(join(converse(X1),complement(one))),
inference(step,[status(thm)],[t6841,t852]) ).
cnf(t107731,plain,
converse(meet(one,complement(X1))) = complement(join(converse(X1),complement(one))),
inference(step,[status(thm)],[t107730,t71]) ).
cnf(t107732,plain,
converse(meet(one,complement(X1))) = meet(complement(converse(X1)),one),
inference(step,[status(thm)],[t107731,t852]) ).
cnf(t107733,plain,
converse(meet(one,complement(X1))) = meet(one,complement(converse(X1))),
inference(step,[status(thm)],[t107732,t71]) ).
cnf(t107734,plain,
converse(meet(one,complement(X1))) = meet(one,converse(complement(X1))),
inference(step,[status(thm)],[t107733,t6840]) ).
cnf(t6887,plain,
converse(meet(one,complement(X1))) = meet(one,converse(complement(X1))),
inference(orient,[status(thm)],[t107734]) ).
cnf(t6899,plain,
meet(one,converse(complement(complement(X1)))) = converse(meet(one,X1)),
inference(cp,[status(thm)],[t6887,t321]) ).
cnf(t107735,plain,
meet(one,converse(X1)) = converse(meet(one,X1)),
inference(step,[status(thm)],[t6899,t321]) ).
cnf(t6921,plain,
converse(meet(one,X1)) = meet(one,converse(X1)),
inference(orient,[status(thm)],[t107735]) ).
cnf(t6937,plain,
converse(complement(meet(one,X1))) = complement(meet(one,converse(X1))),
inference(cp,[status(thm)],[t6840,t6921]) ).
cnf(t7127,plain,
complement(meet(one,converse(X1))) = converse(complement(meet(one,X1))),
inference(orient,[status(thm)],[t6937]) ).
cnf(t107928,plain,
meet(sk0,converse(complement(X1))) = meet(sk0,converse(complement(meet(one,X1)))),
inference(step,[status(thm)],[t15155,t7127]) ).
cnf(t20977,plain,
meet(sk0,converse(complement(meet(one,X1)))) = meet(sk0,converse(complement(X1))),
inference(orient,[status(thm)],[t107928]) ).
cnf(t21024,plain,
meet(complement(meet(one,X1)),converse(sk0)) = converse(meet(sk0,converse(complement(X1)))),
inference(cp,[status(thm)],[t7681,t20977]) ).
cnf(t107948,plain,
meet(converse(sk0),complement(meet(one,X1))) = converse(meet(sk0,converse(complement(X1)))),
inference(step,[status(thm)],[t21024,t71]) ).
cnf(t107949,plain,
meet(converse(sk0),complement(meet(one,X1))) = meet(complement(X1),converse(sk0)),
inference(step,[status(thm)],[t107948,t7681]) ).
cnf(t107950,plain,
meet(converse(sk0),complement(meet(one,X1))) = meet(converse(sk0),complement(X1)),
inference(step,[status(thm)],[t107949,t71]) ).
cnf(t21656,plain,
meet(converse(sk0),complement(meet(one,X1))) = meet(converse(sk0),complement(X1)),
inference(orient,[status(thm)],[t107950]) ).
cnf(t21657,plain,
meet(converse(sk0),complement(complement(X1))) = meet(converse(sk0),join(complement(one),X1)),
inference(cp,[status(thm)],[t21656,t836]) ).
cnf(t107965,plain,
meet(converse(sk0),X1) = meet(converse(sk0),join(complement(one),X1)),
inference(step,[status(thm)],[t21657,t321]) ).
cnf(t22147,plain,
meet(converse(sk0),join(complement(one),X1)) = meet(converse(sk0),X1),
inference(orient,[status(thm)],[t107965]) ).
cnf(t510,plain,
join(X1,join(join(X2,X1),X3)) = join(join(X1,X2),X3),
inference(cp,[status(thm)],[t21,t500]) ).
cnf(t107901,plain,
join(X1,join(X2,join(X1,X3))) = join(join(X1,X2),X3),
inference(step,[status(thm)],[t510,t21]) ).
cnf(t107902,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t107901,t21]) ).
cnf(t18812,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t107902]) ).
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(t57,plain,
composition(join(converse(X1),X2),converse(X3)) = join(converse(composition(X3,X1)),composition(X2,converse(X3))),
inference(cp,[status(thm)],[t27,t53]) ).
cnf(t32985,plain,
join(converse(composition(X1,X2)),composition(X3,converse(X1))) = composition(join(converse(X2),X3),converse(X1)),
inference(orient,[status(thm)],[t57]) ).
cnf(t32989,plain,
composition(join(converse(one),X1),converse(X2)) = join(converse(X2),composition(X1,converse(X2))),
inference(cp,[status(thm)],[t32985,t17]) ).
cnf(t108451,plain,
composition(join(one,X1),converse(X2)) = join(converse(X2),composition(X1,converse(X2))),
inference(step,[status(thm)],[t32989,t170]) ).
cnf(t76667,plain,
join(converse(X1),composition(X2,converse(X1))) = composition(join(one,X2),converse(X1)),
inference(orient,[status(thm)],[t108451]) ).
cnf(t6938,plain,
converse(composition(X1,meet(one,X2))) = composition(meet(one,converse(X2)),converse(X1)),
inference(cp,[status(thm)],[t53,t6921]) ).
cnf(t70296,plain,
composition(meet(one,converse(X1)),converse(X2)) = converse(composition(X2,meet(one,X1))),
inference(orient,[status(thm)],[t6938]) ).
cnf(t76719,plain,
composition(join(one,meet(one,converse(X1))),converse(X2)) = join(converse(X2),converse(composition(X2,meet(one,X1)))),
inference(cp,[status(thm)],[t76667,t70296]) ).
cnf(t108452,plain,
composition(one,converse(X2)) = join(converse(X2),converse(composition(X2,meet(one,X1)))),
inference(step,[status(thm)],[t76719,t467]) ).
cnf(t108453,plain,
converse(X2) = join(converse(X2),converse(composition(X2,meet(one,X1)))),
inference(step,[status(thm)],[t108452,t181]) ).
cnf(t108454,plain,
converse(X2) = converse(join(X2,composition(X2,meet(one,X1)))),
inference(step,[status(thm)],[t108453,t34]) ).
cnf(t76872,plain,
converse(join(X1,composition(X1,meet(one,X2)))) = converse(X1),
inference(orient,[status(thm)],[t108454]) ).
cnf(t6939,plain,
converse(composition(meet(one,X1),X2)) = composition(converse(X2),meet(one,converse(X1))),
inference(cp,[status(thm)],[t53,t6921]) ).
cnf(t70407,plain,
composition(converse(X1),meet(one,converse(X2))) = converse(composition(meet(one,X2),X1)),
inference(orient,[status(thm)],[t6939]) ).
cnf(t76880,plain,
converse(converse(X1)) = converse(join(converse(X1),converse(composition(meet(one,X2),X1)))),
inference(cp,[status(thm)],[t76872,t70407]) ).
cnf(t108455,plain,
X1 = converse(join(converse(X1),converse(composition(meet(one,X2),X1)))),
inference(step,[status(thm)],[t76880,t18]) ).
cnf(t108456,plain,
X1 = join(X1,converse(converse(composition(meet(one,X2),X1)))),
inference(step,[status(thm)],[t108455,t117]) ).
cnf(t108457,plain,
X1 = join(X1,composition(meet(one,X2),X1)),
inference(step,[status(thm)],[t108456,t18]) ).
cnf(t77040,plain,
join(X1,composition(meet(one,X2),X1)) = X1,
inference(orient,[status(thm)],[t108457]) ).
cnf(t672,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t664,t19]) ).
cnf(t688,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t672]) ).
cnf(t174,plain,
converse(join(X1,one)) = join(converse(X1),one),
inference(cp,[status(thm)],[t34,t170]) ).
cnf(t107488,plain,
converse(join(X1,one)) = join(one,converse(X1)),
inference(step,[status(thm)],[t174,t19]) ).
cnf(t195,plain,
converse(join(X1,one)) = join(one,converse(X1)),
inference(orient,[status(thm)],[t107488]) ).
cnf(t197,plain,
join(one,converse(sk0)) = converse(one),
inference(cp,[status(thm)],[t195,t39]) ).
cnf(t107489,plain,
join(one,converse(sk0)) = one,
inference(step,[status(thm)],[t197,t170]) ).
cnf(t209,plain,
join(one,converse(sk0)) = one,
inference(orient,[status(thm)],[t107489]) ).
cnf(t700,plain,
converse(sk0) = meet(converse(sk0),one),
inference(cp,[status(thm)],[t688,t209]) ).
cnf(t107558,plain,
converse(sk0) = meet(one,converse(sk0)),
inference(step,[status(thm)],[t700,t71]) ).
cnf(t709,plain,
meet(one,converse(sk0)) = converse(sk0),
inference(orient,[status(thm)],[t107558]) ).
cnf(t77051,plain,
X1 = join(X1,composition(converse(sk0),X1)),
inference(cp,[status(thm)],[t77040,t709]) ).
cnf(t77174,plain,
join(X1,composition(converse(sk0),X1)) = X1,
inference(orient,[status(thm)],[t77051]) ).
cnf(t77239,plain,
join(X1,converse(composition(converse(sk0),converse(X1)))) = converse(converse(X1)),
inference(cp,[status(thm)],[t117,t77174]) ).
cnf(t108458,plain,
join(X1,composition(converse(converse(X1)),sk0)) = converse(converse(X1)),
inference(step,[status(thm)],[t77239,t148]) ).
cnf(t108459,plain,
join(X1,composition(X1,sk0)) = converse(converse(X1)),
inference(step,[status(thm)],[t108458,t18]) ).
cnf(t108460,plain,
join(X1,composition(X1,sk0)) = X1,
inference(step,[status(thm)],[t108459,t18]) ).
cnf(t77290,plain,
join(X1,composition(X1,sk0)) = X1,
inference(orient,[status(thm)],[t108460]) ).
cnf(t77326,plain,
join(X1,join(X2,composition(X1,sk0))) = join(X1,join(X2,X1)),
inference(cp,[status(thm)],[t18812,t77290]) ).
cnf(t108608,plain,
join(X1,join(X2,composition(X1,sk0))) = join(X1,X2),
inference(step,[status(thm)],[t77326,t500]) ).
cnf(t86175,plain,
join(X1,join(X2,composition(X1,sk0))) = join(X1,X2),
inference(orient,[status(thm)],[t108608]) ).
cnf(t182,plain,
composition(join(one,X1),X2) = join(X2,composition(X1,X2)),
inference(cp,[status(thm)],[t27,t181]) ).
cnf(t105649,plain,
composition(join(one,X1),X2) = join(X2,composition(X1,X2)),
inference(orient,[status(thm)],[t182]) ).
cnf(t106024,plain,
join(X1,composition(complement(one),X1)) = composition(top,X1),
inference(cp,[status(thm)],[t105649,t24]) ).
cnf(t106470,plain,
join(X1,composition(complement(one),X1)) = composition(top,X1),
inference(orient,[status(thm)],[t106024]) ).
cnf(t106498,plain,
join(complement(one),sk0) = join(complement(one),composition(top,sk0)),
inference(cp,[status(thm)],[t86175,t106470]) ).
cnf(t108785,plain,
join(sk0,complement(one)) = join(complement(one),composition(top,sk0)),
inference(step,[status(thm)],[t106498,t19]) ).
cnf(t107194,plain,
join(complement(one),composition(top,sk0)) = join(sk0,complement(one)),
inference(orient,[status(thm)],[t108785]) ).
cnf(t107220,plain,
meet(converse(sk0),composition(top,sk0)) = meet(converse(sk0),join(sk0,complement(one))),
inference(cp,[status(thm)],[t22147,t107194]) ).
cnf(t521,plain,
join(one,meet(sk0,X1)) = join(one,sk0),
inference(cp,[status(thm)],[t519,t467]) ).
cnf(t107545,plain,
join(one,meet(sk0,X1)) = join(sk0,one),
inference(step,[status(thm)],[t521,t19]) ).
cnf(t107546,plain,
join(one,meet(sk0,X1)) = one,
inference(step,[status(thm)],[t107545,t39]) ).
cnf(t533,plain,
join(one,meet(sk0,X1)) = one,
inference(orient,[status(thm)],[t107546]) ).
cnf(t537,plain,
join(one,converse(meet(sk0,X1))) = converse(one),
inference(cp,[status(thm)],[t185,t533]) ).
cnf(t107550,plain,
join(one,converse(meet(sk0,X1))) = one,
inference(step,[status(thm)],[t537,t170]) ).
cnf(t553,plain,
join(one,converse(meet(sk0,X1))) = one,
inference(orient,[status(thm)],[t107550]) ).
cnf(t694,plain,
converse(meet(sk0,X1)) = meet(converse(meet(sk0,X1)),one),
inference(cp,[status(thm)],[t688,t553]) ).
cnf(t107613,plain,
converse(meet(sk0,X1)) = meet(one,converse(meet(sk0,X1))),
inference(step,[status(thm)],[t694,t71]) ).
cnf(t1582,plain,
meet(one,converse(meet(sk0,X1))) = converse(meet(sk0,X1)),
inference(orient,[status(thm)],[t107613]) ).
cnf(t4478,plain,
X1 = join(meet(X1,X2),meet(complement(X2),X1)),
inference(cp,[status(thm)],[t4444,t71]) ).
cnf(t12109,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(orient,[status(thm)],[t4478]) ).
cnf(t893,plain,
zero = meet(complement(join(X1,X2)),X2),
inference(cp,[status(thm)],[t883,t688]) ).
cnf(t107573,plain,
zero = meet(X2,complement(join(X1,X2))),
inference(step,[status(thm)],[t893,t71]) ).
cnf(t947,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t107573]) ).
cnf(t951,plain,
zero = meet(composition(converse(X1),complement(composition(X1,X2))),complement(complement(X2))),
inference(cp,[status(thm)],[t947,t30]) ).
cnf(t108047,plain,
zero = meet(complement(complement(X2)),composition(converse(X1),complement(composition(X1,X2)))),
inference(step,[status(thm)],[t951,t71]) ).
cnf(t108048,plain,
zero = meet(X2,composition(converse(X1),complement(composition(X1,X2)))),
inference(step,[status(thm)],[t108047,t321]) ).
cnf(t31710,plain,
meet(X1,composition(converse(X2),complement(composition(X2,X1)))) = zero,
inference(orient,[status(thm)],[t108048]) ).
cnf(t77303,plain,
composition(X1,sk0) = meet(composition(X1,sk0),X1),
inference(cp,[status(thm)],[t688,t77290]) ).
cnf(t108461,plain,
composition(X1,sk0) = meet(X1,composition(X1,sk0)),
inference(step,[status(thm)],[t77303,t71]) ).
cnf(t77394,plain,
meet(X1,composition(X1,sk0)) = composition(X1,sk0),
inference(orient,[status(thm)],[t108461]) ).
cnf(t4589,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,join(meet(X3,X1),X2)),
inference(cp,[status(thm)],[t1950,t4551]) ).
cnf(t107988,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,X2),
inference(step,[status(thm)],[t4589,t1950]) ).
cnf(t23367,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,X2),
inference(orient,[status(thm)],[t107988]) ).
cnf(t23382,plain,
join(X1,X2) = join(X1,meet(X2,join(X3,complement(X1)))),
inference(cp,[status(thm)],[t23367,t820]) ).
cnf(t25464,plain,
join(X1,meet(X2,join(X3,complement(X1)))) = join(X1,X2),
inference(orient,[status(thm)],[t23382]) ).
cnf(t25534,plain,
meet(X1,meet(X2,join(X3,complement(complement(X1))))) = meet(X1,join(complement(X1),X2)),
inference(cp,[status(thm)],[t5192,t25464]) ).
cnf(t108019,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,join(complement(X1),X2)),
inference(step,[status(thm)],[t25534,t321]) ).
cnf(t108020,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(step,[status(thm)],[t108019,t5192]) ).
cnf(t25634,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t108020]) ).
cnf(t25678,plain,
meet(X1,X2) = meet(X1,meet(join(X3,X1),X2)),
inference(cp,[status(thm)],[t25634,t71]) ).
cnf(t26062,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t25678]) ).
cnf(t37,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(cp,[status(thm)],[t34,t18]) ).
cnf(t126,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(orient,[status(thm)],[t37]) ).
cnf(t462,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(cp,[status(thm)],[t53,t459]) ).
cnf(t480,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(orient,[status(thm)],[t462]) ).
cnf(t488,plain,
join(converse(X1),composition(X2,top)) = converse(join(X1,composition(top,converse(X2)))),
inference(cp,[status(thm)],[t126,t480]) ).
cnf(t43349,plain,
converse(join(X1,composition(top,converse(X2)))) = join(converse(X1),composition(X2,top)),
inference(orient,[status(thm)],[t488]) ).
cnf(t43350,plain,
join(converse(converse(composition(X1,X2))),composition(X1,top)) = converse(composition(join(converse(X2),top),converse(X1))),
inference(cp,[status(thm)],[t43349,t32985]) ).
cnf(t108233,plain,
join(composition(X1,X2),composition(X1,top)) = converse(composition(join(converse(X2),top),converse(X1))),
inference(step,[status(thm)],[t43350,t18]) ).
cnf(t122,plain,
converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))),
inference(cp,[status(thm)],[t53,t117]) ).
cnf(t42056,plain,
converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))),
inference(orient,[status(thm)],[t122]) ).
cnf(t108234,plain,
join(composition(X1,X2),composition(X1,top)) = composition(converse(converse(X1)),join(X2,converse(top))),
inference(step,[status(thm)],[t108233,t42056]) ).
cnf(t108235,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,join(X2,converse(top))),
inference(step,[status(thm)],[t108234,t18]) ).
cnf(t108236,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,converse(top)),
inference(step,[status(thm)],[t108235,t454]) ).
cnf(t108237,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,top),
inference(step,[status(thm)],[t108236,t459]) ).
cnf(t43479,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,top),
inference(orient,[status(thm)],[t108237]) ).
cnf(t43482,plain,
composition(X1,top) = join(X1,composition(X1,top)),
inference(cp,[status(thm)],[t43479,t17]) ).
cnf(t43524,plain,
join(X1,composition(X1,top)) = composition(X1,top),
inference(orient,[status(thm)],[t43482]) ).
cnf(t43535,plain,
X1 = meet(X1,composition(X1,top)),
inference(cp,[status(thm)],[t664,t43524]) ).
cnf(t43611,plain,
meet(X1,composition(X1,top)) = X1,
inference(orient,[status(thm)],[t43535]) ).
cnf(t43671,plain,
meet(X1,converse(composition(converse(X1),top))) = converse(converse(X1)),
inference(cp,[status(thm)],[t7621,t43611]) ).
cnf(t108238,plain,
meet(X1,composition(converse(top),X1)) = converse(converse(X1)),
inference(step,[status(thm)],[t43671,t148]) ).
cnf(t108239,plain,
meet(X1,composition(top,X1)) = converse(converse(X1)),
inference(step,[status(thm)],[t108238,t459]) ).
cnf(t108240,plain,
meet(X1,composition(top,X1)) = X1,
inference(step,[status(thm)],[t108239,t18]) ).
cnf(t43718,plain,
meet(X1,composition(top,X1)) = X1,
inference(orient,[status(thm)],[t108240]) ).
cnf(t43756,plain,
meet(X1,composition(top,join(X2,X1))) = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t26062,t43718]) ).
cnf(t108262,plain,
meet(X1,composition(top,join(X2,X1))) = X1,
inference(step,[status(thm)],[t43756,t688]) ).
cnf(t45289,plain,
meet(X1,composition(top,join(X2,X1))) = X1,
inference(orient,[status(thm)],[t108262]) ).
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(t48,plain,
composition(composition(X1,X2),X3) = composition(X1,composition(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t52,plain,
complement(X1) = join(complement(X1),composition(converse(composition(X2,X3)),complement(composition(X2,composition(X3,X1))))),
inference(cp,[status(thm)],[t30,t48]) ).
cnf(t21909,plain,
join(complement(X1),composition(converse(composition(X2,X3)),complement(composition(X2,composition(X3,X1))))) = complement(X1),
inference(orient,[status(thm)],[t52]) ).
cnf(t31,plain,
complement(X1) = join(complement(X1),composition(X2,complement(composition(converse(X2),X1)))),
inference(cp,[status(thm)],[t30,t18]) ).
cnf(t6302,plain,
join(complement(X1),composition(X2,complement(composition(converse(X2),X1)))) = complement(X1),
inference(orient,[status(thm)],[t31]) ).
cnf(t6308,plain,
complement(top) = join(zero,composition(X1,complement(composition(converse(X1),top)))),
inference(cp,[status(thm)],[t6302,t62]) ).
cnf(t107689,plain,
zero = join(zero,composition(X1,complement(composition(converse(X1),top)))),
inference(step,[status(thm)],[t6308,t62]) ).
cnf(t107690,plain,
zero = composition(X1,complement(composition(converse(X1),top))),
inference(step,[status(thm)],[t107689,t285]) ).
cnf(t6354,plain,
composition(X1,complement(composition(converse(X1),top))) = zero,
inference(orient,[status(thm)],[t107690]) ).
cnf(t6370,plain,
zero = composition(converse(X1),complement(composition(X1,top))),
inference(cp,[status(thm)],[t6354,t18]) ).
cnf(t6445,plain,
composition(converse(X1),complement(composition(X1,top))) = zero,
inference(orient,[status(thm)],[t6370]) ).
cnf(t21978,plain,
complement(complement(composition(X1,top))) = join(complement(complement(composition(X1,top))),composition(converse(composition(X2,converse(X1))),complement(composition(X2,zero)))),
inference(cp,[status(thm)],[t21909,t6445]) ).
cnf(t108010,plain,
composition(X1,top) = join(complement(complement(composition(X1,top))),composition(converse(composition(X2,converse(X1))),complement(composition(X2,zero)))),
inference(step,[status(thm)],[t21978,t321]) ).
cnf(t108011,plain,
composition(X1,top) = join(composition(X1,top),composition(converse(composition(X2,converse(X1))),complement(composition(X2,zero)))),
inference(step,[status(thm)],[t108010,t321]) ).
cnf(t54,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(cp,[status(thm)],[t53,t18]) ).
cnf(t136,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(orient,[status(thm)],[t54]) ).
cnf(t108012,plain,
composition(X1,top) = join(composition(X1,top),composition(composition(X1,converse(X2)),complement(composition(X2,zero)))),
inference(step,[status(thm)],[t108011,t136]) ).
cnf(t108013,plain,
composition(X1,top) = join(composition(X1,top),composition(X1,composition(converse(X2),complement(composition(X2,zero))))),
inference(step,[status(thm)],[t108012,t48]) ).
cnf(t6363,plain,
zero = composition(top,complement(composition(top,top))),
inference(cp,[status(thm)],[t6354,t459]) ).
cnf(t6383,plain,
composition(top,complement(composition(top,top))) = zero,
inference(orient,[status(thm)],[t6363]) ).
cnf(t6386,plain,
composition(join(top,X1),complement(composition(top,top))) = join(zero,composition(X1,complement(composition(top,top)))),
inference(cp,[status(thm)],[t27,t6383]) ).
cnf(t107691,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(X1,complement(composition(top,top)))),
inference(step,[status(thm)],[t6386,t441]) ).
cnf(t107692,plain,
zero = join(zero,composition(X1,complement(composition(top,top)))),
inference(step,[status(thm)],[t107691,t6383]) ).
cnf(t107693,plain,
zero = composition(X1,complement(composition(top,top))),
inference(step,[status(thm)],[t107692,t285]) ).
cnf(t6393,plain,
composition(X1,complement(composition(top,top))) = zero,
inference(orient,[status(thm)],[t107693]) ).
cnf(t6395,plain,
zero = composition(X1,composition(X2,complement(composition(top,top)))),
inference(cp,[status(thm)],[t6393,t48]) ).
cnf(t107694,plain,
zero = composition(X1,zero),
inference(step,[status(thm)],[t6395,t6393]) ).
cnf(t6401,plain,
composition(X1,zero) = zero,
inference(orient,[status(thm)],[t107694]) ).
cnf(t108014,plain,
composition(X1,top) = join(composition(X1,top),composition(X1,composition(converse(X2),complement(zero)))),
inference(step,[status(thm)],[t108013,t6401]) ).
cnf(t286,plain,
complement(zero) = top,
inference(cp,[status(thm)],[t285,t24]) ).
cnf(t296,plain,
complement(zero) = top,
inference(orient,[status(thm)],[t286]) ).
cnf(t108015,plain,
composition(X1,top) = join(composition(X1,top),composition(X1,composition(converse(X2),top))),
inference(step,[status(thm)],[t108014,t296]) ).
cnf(t51,plain,
composition(join(X1,composition(X2,X3)),Y3) = join(composition(X1,Y3),composition(X2,composition(X3,Y3))),
inference(cp,[status(thm)],[t27,t48]) ).
cnf(t18411,plain,
join(composition(X1,X2),composition(X3,composition(Y3,X2))) = composition(join(X1,composition(X3,Y3)),X2),
inference(orient,[status(thm)],[t51]) ).
cnf(t108016,plain,
composition(X1,top) = composition(join(X1,composition(X1,converse(X2))),top),
inference(step,[status(thm)],[t108015,t18411]) ).
cnf(t25276,plain,
composition(join(X1,composition(X1,converse(X2))),top) = composition(X1,top),
inference(orient,[status(thm)],[t108016]) ).
cnf(t25310,plain,
composition(X1,top) = composition(join(X1,composition(X1,X2)),top),
inference(cp,[status(thm)],[t25276,t18]) ).
cnf(t25334,plain,
composition(join(X1,composition(X1,X2)),top) = composition(X1,top),
inference(orient,[status(thm)],[t25310]) ).
cnf(t42058,plain,
composition(converse(top),join(X1,converse(composition(converse(X1),X2)))) = converse(composition(converse(X1),top)),
inference(cp,[status(thm)],[t42056,t25334]) ).
cnf(t108228,plain,
composition(top,join(X1,converse(composition(converse(X1),X2)))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t42058,t459]) ).
cnf(t108229,plain,
composition(top,join(X1,composition(converse(X2),X1))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t108228,t148]) ).
cnf(t108230,plain,
composition(top,join(X1,composition(converse(X2),X1))) = composition(converse(top),X1),
inference(step,[status(thm)],[t108229,t148]) ).
cnf(t108231,plain,
composition(top,join(X1,composition(converse(X2),X1))) = composition(top,X1),
inference(step,[status(thm)],[t108230,t459]) ).
cnf(t42212,plain,
composition(top,join(X1,composition(converse(X2),X1))) = composition(top,X1),
inference(orient,[status(thm)],[t108231]) ).
cnf(t42249,plain,
composition(top,X1) = composition(top,join(X1,composition(X2,X1))),
inference(cp,[status(thm)],[t42212,t18]) ).
cnf(t42312,plain,
composition(top,join(X1,composition(X2,X1))) = composition(top,X1),
inference(orient,[status(thm)],[t42249]) ).
cnf(t45291,plain,
composition(X1,X2) = meet(composition(X1,X2),composition(top,X2)),
inference(cp,[status(thm)],[t45289,t42312]) ).
cnf(t47614,plain,
meet(composition(X1,X2),composition(top,X2)) = composition(X1,X2),
inference(orient,[status(thm)],[t45291]) ).
cnf(t47638,plain,
zero = meet(complement(composition(top,X1)),composition(X2,X1)),
inference(cp,[status(thm)],[t883,t47614]) ).
cnf(t52836,plain,
meet(complement(composition(top,X1)),composition(X2,X1)) = zero,
inference(orient,[status(thm)],[t47638]) ).
cnf(t77395,plain,
composition(complement(composition(top,sk0)),sk0) = zero,
inference(cp,[status(thm)],[t77394,t52836]) ).
cnf(t78339,plain,
composition(complement(composition(top,sk0)),sk0) = zero,
inference(orient,[status(thm)],[t77395]) ).
cnf(t78353,plain,
zero = meet(sk0,composition(converse(complement(composition(top,sk0))),complement(zero))),
inference(cp,[status(thm)],[t31710,t78339]) ).
cnf(t108519,plain,
zero = meet(sk0,composition(converse(complement(composition(top,sk0))),top)),
inference(step,[status(thm)],[t78353,t296]) ).
cnf(t463,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(cp,[status(thm)],[t53,t459]) ).
cnf(t491,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(orient,[status(thm)],[t463]) ).
cnf(t7643,plain,
meet(composition(top,X1),converse(X2)) = converse(meet(composition(converse(X1),top),X2)),
inference(cp,[status(thm)],[t7621,t491]) ).
cnf(t72015,plain,
converse(meet(composition(converse(X1),top),X2)) = meet(composition(top,X1),converse(X2)),
inference(orient,[status(thm)],[t7643]) ).
cnf(t6382,plain,
composition(converse(complement(composition(converse(converse(X1)),top))),X1) = converse(zero),
inference(cp,[status(thm)],[t148,t6354]) ).
cnf(t107704,plain,
composition(converse(complement(composition(X1,top))),X1) = converse(zero),
inference(step,[status(thm)],[t6382,t18]) ).
cnf(t291,plain,
join(converse(zero),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t126,t285]) ).
cnf(t107521,plain,
join(converse(zero),X1) = X1,
inference(step,[status(thm)],[t291,t18]) ).
cnf(t340,plain,
join(converse(zero),X1) = X1,
inference(orient,[status(thm)],[t107521]) ).
cnf(t342,plain,
zero = converse(zero),
inference(cp,[status(thm)],[t340,t308]) ).
cnf(t345,plain,
converse(zero) = zero,
inference(orient,[status(thm)],[t342]) ).
cnf(t107705,plain,
composition(converse(complement(composition(X1,top))),X1) = zero,
inference(step,[status(thm)],[t107704,t345]) ).
cnf(t6465,plain,
composition(converse(complement(composition(X1,top))),X1) = zero,
inference(orient,[status(thm)],[t107705]) ).
cnf(t31758,plain,
zero = meet(X1,composition(converse(converse(complement(composition(X1,top)))),complement(zero))),
inference(cp,[status(thm)],[t31710,t6465]) ).
cnf(t108049,plain,
zero = meet(X1,composition(complement(composition(X1,top)),complement(zero))),
inference(step,[status(thm)],[t31758,t18]) ).
cnf(t108050,plain,
zero = meet(X1,composition(complement(composition(X1,top)),top)),
inference(step,[status(thm)],[t108049,t296]) ).
cnf(t31860,plain,
meet(X1,composition(complement(composition(X1,top)),top)) = zero,
inference(orient,[status(thm)],[t108050]) ).
cnf(t31878,plain,
X1 = join(zero,meet(complement(composition(complement(composition(X1,top)),top)),X1)),
inference(cp,[status(thm)],[t12109,t31860]) ).
cnf(t108205,plain,
X1 = meet(complement(composition(complement(composition(X1,top)),top)),X1),
inference(step,[status(thm)],[t31878,t285]) ).
cnf(t108206,plain,
X1 = meet(X1,complement(composition(complement(composition(X1,top)),top))),
inference(step,[status(thm)],[t108205,t71]) ).
cnf(t40937,plain,
meet(X1,complement(composition(complement(composition(X1,top)),top))) = X1,
inference(orient,[status(thm)],[t108206]) ).
cnf(t72064,plain,
meet(composition(top,X1),converse(complement(composition(complement(composition(composition(converse(X1),top),top)),top)))) = converse(composition(converse(X1),top)),
inference(cp,[status(thm)],[t72015,t40937]) ).
cnf(t108433,plain,
meet(composition(top,X1),converse(complement(composition(complement(composition(converse(X1),composition(top,top))),top)))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t72064,t48]) ).
cnf(t6394,plain,
zero = complement(composition(top,top)),
inference(cp,[status(thm)],[t6393,t181]) ).
cnf(t6412,plain,
complement(composition(top,top)) = zero,
inference(orient,[status(thm)],[t6394]) ).
cnf(t6419,plain,
composition(top,top) = complement(zero),
inference(cp,[status(thm)],[t321,t6412]) ).
cnf(t107703,plain,
composition(top,top) = top,
inference(step,[status(thm)],[t6419,t296]) ).
cnf(t6437,plain,
composition(top,top) = top,
inference(orient,[status(thm)],[t107703]) ).
cnf(t108434,plain,
meet(composition(top,X1),converse(complement(composition(complement(composition(converse(X1),top)),top)))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t108433,t6437]) ).
cnf(t6845,plain,
converse(complement(composition(top,X1))) = complement(composition(converse(X1),top)),
inference(cp,[status(thm)],[t6840,t491]) ).
cnf(t6979,plain,
complement(composition(converse(X1),top)) = converse(complement(composition(top,X1))),
inference(orient,[status(thm)],[t6845]) ).
cnf(t108435,plain,
meet(composition(top,X1),converse(complement(composition(converse(complement(composition(top,X1))),top)))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t108434,t6979]) ).
cnf(t108436,plain,
meet(composition(top,X1),converse(converse(complement(composition(top,complement(composition(top,X1))))))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t108435,t6979]) ).
cnf(t108437,plain,
meet(composition(top,X1),complement(composition(top,complement(composition(top,X1))))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t108436,t18]) ).
cnf(t43558,plain,
join(X1,converse(composition(converse(X1),top))) = converse(composition(converse(X1),top)),
inference(cp,[status(thm)],[t117,t43524]) ).
cnf(t108241,plain,
join(X1,composition(converse(top),X1)) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t43558,t148]) ).
cnf(t108242,plain,
join(X1,composition(top,X1)) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t108241,t459]) ).
cnf(t108243,plain,
join(X1,composition(top,X1)) = composition(converse(top),X1),
inference(step,[status(thm)],[t108242,t148]) ).
cnf(t108244,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(step,[status(thm)],[t108243,t459]) ).
cnf(t43823,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(orient,[status(thm)],[t108244]) ).
cnf(t43846,plain,
meet(X1,complement(composition(top,complement(X1)))) = complement(composition(top,complement(X1))),
inference(cp,[status(thm)],[t988,t43823]) ).
cnf(t54261,plain,
meet(X1,complement(composition(top,complement(X1)))) = complement(composition(top,complement(X1))),
inference(orient,[status(thm)],[t43846]) ).
cnf(t108438,plain,
complement(composition(top,complement(composition(top,X1)))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t108437,t54261]) ).
cnf(t108439,plain,
complement(composition(top,complement(composition(top,X1)))) = composition(converse(top),X1),
inference(step,[status(thm)],[t108438,t148]) ).
cnf(t108440,plain,
complement(composition(top,complement(composition(top,X1)))) = composition(top,X1),
inference(step,[status(thm)],[t108439,t459]) ).
cnf(t72277,plain,
complement(composition(top,complement(composition(top,X1)))) = composition(top,X1),
inference(orient,[status(thm)],[t108440]) ).
cnf(t72287,plain,
composition(top,complement(composition(top,X1))) = complement(composition(top,X1)),
inference(cp,[status(thm)],[t321,t72277]) ).
cnf(t72419,plain,
composition(top,complement(composition(top,X1))) = complement(composition(top,X1)),
inference(orient,[status(thm)],[t72287]) ).
cnf(t72427,plain,
composition(converse(complement(composition(top,X1))),top) = converse(complement(composition(top,X1))),
inference(cp,[status(thm)],[t491,t72419]) ).
cnf(t72539,plain,
composition(converse(complement(composition(top,X1))),top) = converse(complement(composition(top,X1))),
inference(orient,[status(thm)],[t72427]) ).
cnf(t108520,plain,
zero = meet(sk0,converse(complement(composition(top,sk0)))),
inference(step,[status(thm)],[t108519,t72539]) ).
cnf(t82031,plain,
meet(sk0,converse(complement(composition(top,sk0)))) = zero,
inference(orient,[status(thm)],[t108520]) ).
cnf(t82038,plain,
sk0 = join(zero,meet(complement(converse(complement(composition(top,sk0)))),sk0)),
inference(cp,[status(thm)],[t12109,t82031]) ).
cnf(t108521,plain,
sk0 = meet(complement(converse(complement(composition(top,sk0)))),sk0),
inference(step,[status(thm)],[t82038,t285]) ).
cnf(t108522,plain,
sk0 = meet(sk0,complement(converse(complement(composition(top,sk0))))),
inference(step,[status(thm)],[t108521,t71]) ).
cnf(t108523,plain,
sk0 = meet(sk0,converse(composition(top,sk0))),
inference(step,[status(thm)],[t108522,t6795]) ).
cnf(t108524,plain,
sk0 = meet(sk0,composition(converse(sk0),top)),
inference(step,[status(thm)],[t108523,t491]) ).
cnf(t82052,plain,
meet(sk0,composition(converse(sk0),top)) = sk0,
inference(orient,[status(thm)],[t108524]) ).
cnf(t82115,plain,
converse(meet(sk0,composition(converse(sk0),top))) = meet(one,converse(sk0)),
inference(cp,[status(thm)],[t1582,t82052]) ).
cnf(t7712,plain,
meet(composition(top,X1),converse(X2)) = converse(meet(X2,composition(converse(X1),top))),
inference(cp,[status(thm)],[t7681,t491]) ).
cnf(t73046,plain,
converse(meet(X1,composition(converse(X2),top))) = meet(composition(top,X2),converse(X1)),
inference(orient,[status(thm)],[t7712]) ).
cnf(t108525,plain,
meet(composition(top,sk0),converse(sk0)) = meet(one,converse(sk0)),
inference(step,[status(thm)],[t82115,t73046]) ).
cnf(t108526,plain,
meet(converse(sk0),composition(top,sk0)) = meet(one,converse(sk0)),
inference(step,[status(thm)],[t108525,t71]) ).
cnf(t108527,plain,
meet(converse(sk0),composition(top,sk0)) = converse(sk0),
inference(step,[status(thm)],[t108526,t709]) ).
cnf(t82134,plain,
meet(converse(sk0),composition(top,sk0)) = converse(sk0),
inference(orient,[status(thm)],[t108527]) ).
cnf(t108786,plain,
converse(sk0) = meet(converse(sk0),join(sk0,complement(one))),
inference(step,[status(thm)],[t107220,t82134]) ).
cnf(t4676,plain,
meet(X1,complement(meet(complement(complement(X1)),X2))) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t988,t4636]) ).
cnf(t107681,plain,
meet(X1,join(complement(X1),complement(X2))) = complement(join(complement(X1),X2)),
inference(step,[status(thm)],[t4676,t820]) ).
cnf(t107682,plain,
meet(X1,complement(meet(X1,X2))) = complement(join(complement(X1),X2)),
inference(step,[status(thm)],[t107681,t757]) ).
cnf(t107683,plain,
meet(X1,complement(meet(X1,X2))) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t107682,t988]) ).
cnf(t5808,plain,
meet(X1,complement(meet(X1,X2))) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t107683]) ).
cnf(t21672,plain,
meet(converse(sk0),complement(complement(meet(one,X1)))) = meet(converse(sk0),complement(meet(one,complement(X1)))),
inference(cp,[status(thm)],[t21656,t5808]) ).
cnf(t107954,plain,
meet(converse(sk0),meet(one,X1)) = meet(converse(sk0),complement(meet(one,complement(X1)))),
inference(step,[status(thm)],[t21672,t321]) ).
cnf(t107955,plain,
meet(converse(sk0),meet(one,X1)) = meet(converse(sk0),complement(complement(X1))),
inference(step,[status(thm)],[t107954,t21656]) ).
cnf(t107956,plain,
meet(converse(sk0),meet(one,X1)) = meet(converse(sk0),X1),
inference(step,[status(thm)],[t107955,t321]) ).
cnf(t21781,plain,
meet(converse(sk0),meet(one,X1)) = meet(converse(sk0),X1),
inference(orient,[status(thm)],[t107956]) ).
cnf(t21796,plain,
meet(converse(sk0),join(X1,complement(one))) = meet(converse(sk0),meet(one,X1)),
inference(cp,[status(thm)],[t21781,t5152]) ).
cnf(t107966,plain,
meet(converse(sk0),join(X1,complement(one))) = meet(converse(sk0),X1),
inference(step,[status(thm)],[t21796,t21781]) ).
cnf(t22202,plain,
meet(converse(sk0),join(X1,complement(one))) = meet(converse(sk0),X1),
inference(orient,[status(thm)],[t107966]) ).
cnf(t108787,plain,
converse(sk0) = meet(converse(sk0),sk0),
inference(step,[status(thm)],[t108786,t22202]) ).
cnf(t108788,plain,
converse(sk0) = meet(sk0,converse(sk0)),
inference(step,[status(thm)],[t108787,t71]) ).
cnf(t107257,plain,
meet(sk0,converse(sk0)) = converse(sk0),
inference(orient,[status(thm)],[t108788]) ).
cnf(t107308,plain,
meet(sk0,converse(sk0)) = converse(converse(sk0)),
inference(cp,[status(thm)],[t7681,t107257]) ).
cnf(t108789,plain,
converse(sk0) = converse(converse(sk0)),
inference(step,[status(thm)],[t107308,t107257]) ).
cnf(t108790,plain,
converse(sk0) = sk0,
inference(step,[status(thm)],[t108789,t18]) ).
cnf(t107341,plain,
converse(sk0) = sk0,
inference(orient,[status(thm)],[t108790]) ).
cnf(c14,plain,
converse(sk0) != sk0,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
converse(sk0) != sk0,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
sk0 != sk0,
inference(rw,[status(thm)],[goal_0,t107341]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL025+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.37 % Computer : n005.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 07:20:33 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 38.42/5.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.42/5.46 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------