%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL041+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:36:04 PM UTC 2026
% Result : Theorem 23.05s 3.29s
% Output : Proof 23.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 159
% Number of leaves : 15
% Syntax : Number of formulae : 537 ( 533 unt; 0 def)
% Number of atoms : 541 ( 540 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 806 ( 132 sgn 88 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dedekind_law) ).
fof(f13_nnf,plain,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t16,plain,
join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t33,plain,
join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
inference(orient,[status(thm)],[t16]) ).
fof(f3,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/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(t85,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t6]) ).
fof(f0,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f0_nnf,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t43,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t87,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t85,t43]) ).
cnf(t74118,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t87,t85]) ).
cnf(t106,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t74118]) ).
cnf(t108,plain,
composition(meet(X1,composition(X2,converse(X3))),meet(X3,composition(converse(X1),X2))) = join(meet(composition(X1,X3),X2),composition(meet(composition(X2,converse(X3)),X1),meet(X3,composition(converse(X1),X2)))),
inference(cp,[status(thm)],[t33,t106]) ).
cnf(t50689,plain,
join(meet(composition(X1,X2),X3),composition(meet(composition(X3,converse(X2)),X1),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
inference(orient,[status(thm)],[t108]) ).
fof(f10,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f10_nnf,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t12,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t74114,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t12,t43]) ).
cnf(t54,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t74114]) ).
fof(f9,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/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(t27,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/sandbox2/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(t21,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t29,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t27,t21]) ).
cnf(t151,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t29]) ).
fof(f5,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/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(t152,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t151,t17]) ).
cnf(t74120,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t152,t21]) ).
cnf(t164,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t74120]) ).
cnf(t165,plain,
one = converse(one),
inference(cp,[status(thm)],[t164,t17]) ).
cnf(t174,plain,
converse(one) = one,
inference(orient,[status(thm)],[t165]) ).
cnf(t74121,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t164,t174]) ).
cnf(t184,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t74121]) ).
cnf(t185,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t184]) ).
cnf(t188,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t54,t185]) ).
cnf(t74123,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t188,t174]) ).
cnf(t74124,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t74123,t185]) ).
cnf(t214,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t74124]) ).
cnf(t224,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t85,t214]) ).
cnf(t231,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t224]) ).
cnf(t242,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),meet(X2,X2))),
inference(cp,[status(thm)],[t85,t231]) ).
cnf(t1075,plain,
complement(join(complement(X1),meet(X2,X2))) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t242]) ).
fof(f2,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/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(t18,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t45,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t18]) ).
cnf(t74657,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t45,t43]) ).
cnf(t74658,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t74657,t85]) ).
cnf(t74659,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t74658,t43]) ).
cnf(t14892,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t74659]) ).
fof(f12,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).
fof(f12_nnf,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t3,plain,
meet(X1,complement(X1)) = zero,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t92,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t14893,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t14892,t92]) ).
cnf(t74767,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t14893,t85]) ).
cnf(t15562,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t74767]) ).
fof(f1,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/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(t46,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/sandbox2/benchmark/theBenchmark.p',def_top) ).
fof(f11_nnf,plain,
! [X0] : top = join(X0,complement(X0)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X0] : top = join(X0,complement(X0)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
top = join(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t2,plain,
join(X1,complement(X1)) = top,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t51,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t86,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t85,t51]) ).
cnf(t74116,plain,
zero = complement(top),
inference(step,[status(thm)],[t86,t92]) ).
cnf(t97,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t74116]) ).
cnf(t218,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t214,t97]) ).
cnf(t74125,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t218,t97]) ).
cnf(t74126,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t74125,t97]) ).
cnf(t225,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t74126]) ).
cnf(t226,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t46,t225]) ).
cnf(t244,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t226]) ).
cnf(t15567,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t244,t15562]) ).
cnf(t74769,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t15567,t15562]) ).
cnf(t15581,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t74769]) ).
cnf(t74774,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t15562,t15581]) ).
cnf(t15608,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t74774]) ).
cnf(t15633,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t15608]) ).
cnf(t74793,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t1075,t15633]) ).
cnf(t15666,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(rw,[status(thm)],[t74793]) ).
cnf(t16028,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t15666]) ).
fof(f8,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/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(t62,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t8]) ).
cnf(t66,plain,
join(converse(X1),join(converse(X2),X3)) = join(converse(join(X1,X2)),X3),
inference(cp,[status(thm)],[t46,t62]) ).
cnf(t1829,plain,
join(converse(X1),join(converse(X2),X3)) = join(converse(join(X1,X2)),X3),
inference(orient,[status(thm)],[t66]) ).
cnf(t53,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(cp,[status(thm)],[t46,t51]) ).
cnf(t313,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(orient,[status(thm)],[t53]) ).
cnf(t322,plain,
join(top,X1) = join(X2,join(X1,complement(X2))),
inference(cp,[status(thm)],[t313,t43]) ).
cnf(t239,plain,
top = join(complement(X1),meet(X1,X1)),
inference(cp,[status(thm)],[t51,t231]) ).
cnf(t255,plain,
join(complement(X1),meet(X1,X1)) = top,
inference(orient,[status(thm)],[t239]) ).
cnf(t317,plain,
join(top,meet(X1,X1)) = join(X1,top),
inference(cp,[status(thm)],[t313,t255]) ).
cnf(t319,plain,
join(top,complement(X1)) = join(X1,complement(X1)),
inference(cp,[status(thm)],[t313,t214]) ).
cnf(t74131,plain,
join(top,complement(X1)) = top,
inference(step,[status(thm)],[t319,t51]) ).
cnf(t330,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t74131]) ).
cnf(t331,plain,
top = join(top,meet(X1,X2)),
inference(cp,[status(thm)],[t330,t85]) ).
cnf(t347,plain,
join(top,meet(X1,X2)) = top,
inference(orient,[status(thm)],[t331]) ).
cnf(t74133,plain,
top = join(X1,top),
inference(step,[status(thm)],[t317,t347]) ).
cnf(t352,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t74133]) ).
cnf(t353,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t352,t43]) ).
cnf(t358,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t353]) ).
cnf(t74142,plain,
top = join(X2,join(X1,complement(X2))),
inference(step,[status(thm)],[t322,t358]) ).
cnf(t402,plain,
join(X1,join(X2,complement(X1))) = top,
inference(orient,[status(thm)],[t74142]) ).
cnf(t1833,plain,
join(converse(join(X1,X2)),complement(converse(X1))) = top,
inference(cp,[status(thm)],[t1829,t402]) ).
cnf(t74227,plain,
join(complement(converse(X1)),converse(join(X1,X2))) = top,
inference(step,[status(thm)],[t1833,t43]) ).
cnf(t1884,plain,
join(complement(converse(X1)),converse(join(X1,X2))) = top,
inference(orient,[status(thm)],[t74227]) ).
cnf(t1917,plain,
top = join(complement(converse(converse(X1))),converse(converse(join(X1,X2)))),
inference(cp,[status(thm)],[t1884,t62]) ).
cnf(t74228,plain,
top = join(complement(X1),converse(converse(join(X1,X2)))),
inference(step,[status(thm)],[t1917,t21]) ).
cnf(t74229,plain,
top = join(complement(X1),join(X1,X2)),
inference(step,[status(thm)],[t74228,t21]) ).
cnf(t1931,plain,
join(complement(X1),join(X1,X2)) = top,
inference(orient,[status(thm)],[t74229]) ).
cnf(t1962,plain,
top = join(complement(X1),join(X2,X1)),
inference(cp,[status(thm)],[t1931,t43]) ).
cnf(t1965,plain,
join(complement(X1),join(X2,X1)) = top,
inference(orient,[status(thm)],[t1962]) ).
cnf(t16037,plain,
meet(X1,complement(join(X2,X1))) = complement(top),
inference(cp,[status(thm)],[t16028,t1965]) ).
cnf(t74826,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(step,[status(thm)],[t16037,t97]) ).
cnf(t16154,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t74826]) ).
cnf(t215,plain,
complement(join(complement(X1),complement(X2))) = join(meet(X1,X2),complement(join(complement(X1),complement(X2)))),
inference(cp,[status(thm)],[t214,t85]) ).
cnf(t74144,plain,
meet(X1,X2) = join(meet(X1,X2),complement(join(complement(X1),complement(X2)))),
inference(step,[status(thm)],[t215,t85]) ).
cnf(t74145,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X1,X2)),
inference(step,[status(thm)],[t74144,t85]) ).
cnf(t438,plain,
join(meet(X1,X2),meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t74145]) ).
cnf(t439,plain,
meet(X1,X2) = join(meet(X2,X1),meet(X1,X2)),
inference(cp,[status(thm)],[t438,t106]) ).
cnf(t459,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X2,X1),
inference(orient,[status(thm)],[t439]) ).
cnf(t15634,plain,
meet(X1,X1) = join(X1,meet(X1,X1)),
inference(cp,[status(thm)],[t459,t15633]) ).
cnf(t74809,plain,
X1 = join(X1,meet(X1,X1)),
inference(step,[status(thm)],[t15634,t15633]) ).
cnf(t74810,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t74809,t15633]) ).
cnf(t15700,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t74810]) ).
cnf(t15704,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t46,t15700]) ).
cnf(t15746,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t15704]) ).
cnf(t15762,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1),
inference(cp,[status(thm)],[t15746,t14892]) ).
cnf(t74814,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t15762,t14892]) ).
cnf(t74815,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t74814,t43]) ).
cnf(t15770,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t74815]) ).
cnf(t15776,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t46,t15770]) ).
cnf(t18085,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t15776]) ).
cnf(t15772,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t15770,t106]) ).
cnf(t15796,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t15772]) ).
cnf(t18099,plain,
join(X1,meet(X2,meet(X1,X3))) = join(X1,meet(X1,X3)),
inference(cp,[status(thm)],[t18085,t15796]) ).
cnf(t74883,plain,
join(X1,meet(X2,meet(X1,X3))) = X1,
inference(step,[status(thm)],[t18099,t15770]) ).
cnf(t18188,plain,
join(X1,meet(X2,meet(X1,X3))) = X1,
inference(orient,[status(thm)],[t74883]) ).
cnf(t100,plain,
meet(top,X1) = complement(join(zero,complement(X1))),
inference(cp,[status(thm)],[t85,t97]) ).
cnf(t118,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(orient,[status(thm)],[t100]) ).
cnf(t65,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(cp,[status(thm)],[t62,t21]) ).
cnf(t277,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(orient,[status(thm)],[t65]) ).
cnf(t64,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t62,t21]) ).
cnf(t260,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t64]) ).
cnf(t262,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(cp,[status(thm)],[t260,t51]) ).
cnf(t296,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(orient,[status(thm)],[t262]) ).
cnf(t361,plain,
top = converse(top),
inference(cp,[status(thm)],[t358,t296]) ).
cnf(t364,plain,
converse(top) = top,
inference(orient,[status(thm)],[t361]) ).
cnf(t369,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(cp,[status(thm)],[t27,t364]) ).
cnf(t376,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(orient,[status(thm)],[t369]) ).
cnf(t382,plain,
join(converse(X1),composition(X2,top)) = converse(join(X1,composition(top,converse(X2)))),
inference(cp,[status(thm)],[t277,t376]) ).
cnf(t10178,plain,
converse(join(X1,composition(top,converse(X2)))) = join(converse(X1),composition(X2,top)),
inference(orient,[status(thm)],[t382]) ).
fof(f6,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/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(t24,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(orient,[status(thm)],[t11]) ).
cnf(t30,plain,
composition(join(converse(X1),X2),converse(X3)) = join(converse(composition(X3,X1)),composition(X2,converse(X3))),
inference(cp,[status(thm)],[t24,t27]) ).
cnf(t1715,plain,
join(converse(composition(X1,X2)),composition(X3,converse(X1))) = composition(join(converse(X2),X3),converse(X1)),
inference(orient,[status(thm)],[t30]) ).
cnf(t10179,plain,
join(converse(converse(composition(X1,X2))),composition(X1,top)) = converse(composition(join(converse(X2),top),converse(X1))),
inference(cp,[status(thm)],[t10178,t1715]) ).
cnf(t74556,plain,
join(composition(X1,X2),composition(X1,top)) = converse(composition(join(converse(X2),top),converse(X1))),
inference(step,[status(thm)],[t10179,t21]) ).
cnf(t28,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(cp,[status(thm)],[t27,t21]) ).
cnf(t141,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(orient,[status(thm)],[t28]) ).
cnf(t74557,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,converse(join(converse(X2),top))),
inference(step,[status(thm)],[t74556,t141]) ).
cnf(t74558,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,join(X2,converse(top))),
inference(step,[status(thm)],[t74557,t260]) ).
cnf(t74559,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,join(X2,top)),
inference(step,[status(thm)],[t74558,t364]) ).
cnf(t74560,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,top),
inference(step,[status(thm)],[t74559,t352]) ).
cnf(t10258,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,top),
inference(orient,[status(thm)],[t74560]) ).
cnf(t370,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(cp,[status(thm)],[t27,t364]) ).
cnf(t390,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(orient,[status(thm)],[t370]) ).
cnf(t378,plain,
converse(join(composition(X1,top),X2)) = join(composition(top,converse(X1)),converse(X2)),
inference(cp,[status(thm)],[t62,t376]) ).
cnf(t4193,plain,
join(composition(top,converse(X1)),converse(X2)) = converse(join(composition(X1,top),X2)),
inference(orient,[status(thm)],[t378]) ).
cnf(t4206,plain,
converse(join(composition(top,top),X1)) = join(composition(top,top),converse(X1)),
inference(cp,[status(thm)],[t4193,t364]) ).
cnf(t4240,plain,
converse(join(composition(top,top),X1)) = join(composition(top,top),converse(X1)),
inference(orient,[status(thm)],[t4206]) ).
cnf(t4244,plain,
join(composition(top,top),converse(composition(X1,top))) = converse(composition(join(top,X1),top)),
inference(cp,[status(thm)],[t4240,t24]) ).
cnf(t74328,plain,
join(composition(top,top),composition(top,converse(X1))) = converse(composition(join(top,X1),top)),
inference(step,[status(thm)],[t4244,t376]) ).
cnf(t74329,plain,
join(composition(top,top),composition(top,converse(X1))) = composition(top,converse(join(top,X1))),
inference(step,[status(thm)],[t74328,t376]) ).
cnf(t74330,plain,
join(composition(top,top),composition(top,converse(X1))) = composition(top,converse(top)),
inference(step,[status(thm)],[t74329,t358]) ).
cnf(t74331,plain,
join(composition(top,top),composition(top,converse(X1))) = composition(top,top),
inference(step,[status(thm)],[t74330,t364]) ).
cnf(t4447,plain,
join(composition(top,top),composition(top,converse(X1))) = composition(top,top),
inference(orient,[status(thm)],[t74331]) ).
cnf(t4463,plain,
composition(top,top) = join(composition(top,top),composition(top,one)),
inference(cp,[status(thm)],[t4447,t174]) ).
cnf(t74332,plain,
composition(top,top) = join(composition(top,top),top),
inference(step,[status(thm)],[t4463,t17]) ).
cnf(t74333,plain,
composition(top,top) = top,
inference(step,[status(thm)],[t74332,t352]) ).
cnf(t4476,plain,
composition(top,top) = top,
inference(orient,[status(thm)],[t74333]) ).
cnf(t4481,plain,
complement(top) = join(complement(top),composition(converse(top),complement(top))),
inference(cp,[status(thm)],[t54,t4476]) ).
cnf(t74341,plain,
zero = join(complement(top),composition(converse(top),complement(top))),
inference(step,[status(thm)],[t4481,t97]) ).
cnf(t74342,plain,
zero = join(zero,composition(converse(top),complement(top))),
inference(step,[status(thm)],[t74341,t97]) ).
cnf(t74343,plain,
zero = join(zero,composition(top,complement(top))),
inference(step,[status(thm)],[t74342,t364]) ).
cnf(t74344,plain,
zero = join(zero,composition(top,zero)),
inference(step,[status(thm)],[t74343,t97]) ).
cnf(t56,plain,
complement(one) = join(complement(one),composition(converse(X1),complement(X1))),
inference(cp,[status(thm)],[t54,t17]) ).
cnf(t1148,plain,
join(complement(one),composition(converse(X1),complement(X1))) = complement(one),
inference(orient,[status(thm)],[t56]) ).
cnf(t1158,plain,
complement(one) = join(complement(one),composition(X1,complement(converse(X1)))),
inference(cp,[status(thm)],[t1148,t21]) ).
cnf(t1176,plain,
join(complement(one),composition(X1,complement(converse(X1)))) = complement(one),
inference(orient,[status(thm)],[t1158]) ).
cnf(t1976,plain,
top = join(complement(composition(X1,complement(converse(X1)))),complement(one)),
inference(cp,[status(thm)],[t1965,t1176]) ).
cnf(t74240,plain,
top = join(complement(one),complement(composition(X1,complement(converse(X1))))),
inference(step,[status(thm)],[t1976,t43]) ).
cnf(t2329,plain,
join(complement(one),complement(composition(X1,complement(converse(X1))))) = top,
inference(orient,[status(thm)],[t74240]) ).
cnf(t2347,plain,
meet(one,composition(X1,complement(converse(X1)))) = complement(top),
inference(cp,[status(thm)],[t85,t2329]) ).
cnf(t74241,plain,
meet(one,composition(X1,complement(converse(X1)))) = zero,
inference(step,[status(thm)],[t2347,t97]) ).
cnf(t2350,plain,
meet(one,composition(X1,complement(converse(X1)))) = zero,
inference(orient,[status(thm)],[t74241]) ).
cnf(t2371,plain,
composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),meet(one,composition(converse(X1),complement(converse(converse(X1)))))) = join(meet(composition(X1,one),complement(converse(converse(X1)))),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(cp,[status(thm)],[t33,t2350]) ).
cnf(t74242,plain,
composition(meet(X1,composition(complement(X1),converse(one))),meet(one,composition(converse(X1),complement(converse(converse(X1)))))) = join(meet(composition(X1,one),complement(converse(converse(X1)))),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t2371,t21]) ).
cnf(t74243,plain,
composition(meet(X1,composition(complement(X1),one)),meet(one,composition(converse(X1),complement(converse(converse(X1)))))) = join(meet(composition(X1,one),complement(converse(converse(X1)))),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t74242,t174]) ).
cnf(t74244,plain,
composition(meet(X1,complement(X1)),meet(one,composition(converse(X1),complement(converse(converse(X1)))))) = join(meet(composition(X1,one),complement(converse(converse(X1)))),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t74243,t17]) ).
cnf(t74245,plain,
composition(zero,meet(one,composition(converse(X1),complement(converse(converse(X1)))))) = join(meet(composition(X1,one),complement(converse(converse(X1)))),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t74244,t92]) ).
cnf(t74246,plain,
composition(zero,zero) = join(meet(composition(X1,one),complement(converse(converse(X1)))),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t74245,t2350]) ).
cnf(t74247,plain,
composition(zero,zero) = join(meet(X1,complement(converse(converse(X1)))),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t74246,t17]) ).
cnf(t74248,plain,
composition(zero,zero) = join(meet(X1,complement(X1)),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t74247,t21]) ).
cnf(t74249,plain,
composition(zero,zero) = join(zero,composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t74248,t92]) ).
cnf(t74250,plain,
composition(zero,zero) = join(zero,composition(meet(X1,composition(complement(X1),converse(one))),zero)),
inference(step,[status(thm)],[t74249,t21]) ).
cnf(t74251,plain,
composition(zero,zero) = join(zero,composition(meet(X1,composition(complement(X1),one)),zero)),
inference(step,[status(thm)],[t74250,t174]) ).
cnf(t74252,plain,
composition(zero,zero) = join(zero,composition(meet(X1,complement(X1)),zero)),
inference(step,[status(thm)],[t74251,t17]) ).
cnf(t74253,plain,
composition(zero,zero) = join(zero,composition(zero,zero)),
inference(step,[status(thm)],[t74252,t92]) ).
cnf(t2372,plain,
join(zero,composition(zero,zero)) = composition(zero,zero),
inference(orient,[status(thm)],[t74253]) ).
cnf(t2375,plain,
join(zero,join(composition(zero,zero),X1)) = join(composition(zero,zero),X1),
inference(cp,[status(thm)],[t46,t2372]) ).
cnf(t2507,plain,
join(zero,join(composition(zero,zero),X1)) = join(composition(zero,zero),X1),
inference(orient,[status(thm)],[t2375]) ).
cnf(t2515,plain,
join(composition(zero,zero),composition(X1,zero)) = join(zero,composition(join(zero,X1),zero)),
inference(cp,[status(thm)],[t2507,t24]) ).
cnf(t74262,plain,
composition(join(zero,X1),zero) = join(zero,composition(join(zero,X1),zero)),
inference(step,[status(thm)],[t2515,t24]) ).
cnf(t2578,plain,
join(zero,composition(join(zero,X1),zero)) = composition(join(zero,X1),zero),
inference(orient,[status(thm)],[t74262]) ).
cnf(t52,plain,
top = join(X1,join(X2,complement(join(X1,X2)))),
inference(cp,[status(thm)],[t51,t46]) ).
cnf(t471,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(orient,[status(thm)],[t52]) ).
cnf(t488,plain,
top = join(X1,join(X2,complement(join(X2,X1)))),
inference(cp,[status(thm)],[t471,t43]) ).
cnf(t572,plain,
join(X1,join(X2,complement(join(X2,X1)))) = top,
inference(orient,[status(thm)],[t488]) ).
cnf(t584,plain,
top = join(complement(X1),join(X1,complement(top))),
inference(cp,[status(thm)],[t572,t51]) ).
cnf(t74153,plain,
top = join(complement(X1),join(X1,zero)),
inference(step,[status(thm)],[t584,t97]) ).
cnf(t604,plain,
join(complement(X1),join(X1,zero)) = top,
inference(orient,[status(thm)],[t74153]) ).
cnf(t611,plain,
top = join(complement(X1),join(zero,X1)),
inference(cp,[status(thm)],[t604,t43]) ).
cnf(t613,plain,
join(complement(X1),join(zero,X1)) = top,
inference(orient,[status(thm)],[t611]) ).
cnf(t102,plain,
complement(top) = join(zero,composition(converse(X1),complement(composition(X1,top)))),
inference(cp,[status(thm)],[t54,t97]) ).
cnf(t74184,plain,
zero = join(zero,composition(converse(X1),complement(composition(X1,top)))),
inference(step,[status(thm)],[t102,t97]) ).
cnf(t1397,plain,
join(zero,composition(converse(X1),complement(composition(X1,top)))) = zero,
inference(orient,[status(thm)],[t74184]) ).
cnf(t1402,plain,
zero = join(zero,composition(top,complement(composition(top,top)))),
inference(cp,[status(thm)],[t1397,t364]) ).
cnf(t1419,plain,
join(zero,composition(top,complement(composition(top,top)))) = zero,
inference(orient,[status(thm)],[t1402]) ).
cnf(t1421,plain,
top = join(complement(composition(top,complement(composition(top,top)))),zero),
inference(cp,[status(thm)],[t613,t1419]) ).
cnf(t74207,plain,
top = join(zero,complement(composition(top,complement(composition(top,top))))),
inference(step,[status(thm)],[t1421,t43]) ).
cnf(t1679,plain,
join(zero,complement(composition(top,complement(composition(top,top))))) = top,
inference(orient,[status(thm)],[t74207]) ).
cnf(t2581,plain,
composition(join(zero,complement(composition(top,complement(composition(top,top))))),zero) = join(zero,composition(top,zero)),
inference(cp,[status(thm)],[t2578,t1679]) ).
cnf(t74263,plain,
composition(top,zero) = join(zero,composition(top,zero)),
inference(step,[status(thm)],[t2581,t1679]) ).
cnf(t2607,plain,
join(zero,composition(top,zero)) = composition(top,zero),
inference(orient,[status(thm)],[t74263]) ).
cnf(t74345,plain,
zero = composition(top,zero),
inference(step,[status(thm)],[t74344,t2607]) ).
cnf(t4490,plain,
composition(top,zero) = zero,
inference(orient,[status(thm)],[t74345]) ).
cnf(t4491,plain,
composition(converse(zero),top) = converse(zero),
inference(cp,[status(thm)],[t390,t4490]) ).
cnf(t4510,plain,
composition(converse(zero),top) = converse(zero),
inference(orient,[status(thm)],[t4491]) ).
cnf(t10310,plain,
composition(converse(zero),top) = join(composition(converse(zero),X1),converse(zero)),
inference(cp,[status(thm)],[t10258,t4510]) ).
cnf(t74589,plain,
converse(zero) = join(composition(converse(zero),X1),converse(zero)),
inference(step,[status(thm)],[t10310,t4510]) ).
cnf(t74590,plain,
converse(zero) = join(converse(zero),composition(converse(zero),X1)),
inference(step,[status(thm)],[t74589,t43]) ).
cnf(t11289,plain,
join(converse(zero),composition(converse(zero),X1)) = converse(zero),
inference(orient,[status(thm)],[t74590]) ).
cnf(t2597,plain,
composition(join(zero,X1),zero) = join(zero,composition(join(X1,zero),zero)),
inference(cp,[status(thm)],[t2578,t43]) ).
cnf(t2658,plain,
join(zero,composition(join(X1,zero),zero)) = composition(join(zero,X1),zero),
inference(orient,[status(thm)],[t2597]) ).
cnf(t4492,plain,
composition(join(top,X1),zero) = join(zero,composition(X1,zero)),
inference(cp,[status(thm)],[t24,t4490]) ).
cnf(t74351,plain,
composition(top,zero) = join(zero,composition(X1,zero)),
inference(step,[status(thm)],[t4492,t358]) ).
cnf(t74352,plain,
zero = join(zero,composition(X1,zero)),
inference(step,[status(thm)],[t74351,t4490]) ).
cnf(t4532,plain,
join(zero,composition(X1,zero)) = zero,
inference(orient,[status(thm)],[t74352]) ).
cnf(t74355,plain,
zero = composition(join(zero,X1),zero),
inference(step,[status(thm)],[t2658,t4532]) ).
cnf(t4550,plain,
zero = composition(join(zero,X1),zero),
inference(rw,[status(thm)],[t74355]) ).
cnf(t4588,plain,
composition(join(zero,X1),zero) = zero,
inference(orient,[status(thm)],[t4550]) ).
cnf(t4591,plain,
zero = composition(join(X1,zero),zero),
inference(cp,[status(thm)],[t4588,t43]) ).
cnf(t4608,plain,
composition(join(X1,zero),zero) = zero,
inference(orient,[status(thm)],[t4591]) ).
cnf(t4610,plain,
composition(join(join(X1,zero),X2),zero) = join(zero,composition(X2,zero)),
inference(cp,[status(thm)],[t24,t4608]) ).
cnf(t74377,plain,
composition(join(X1,join(zero,X2)),zero) = join(zero,composition(X2,zero)),
inference(step,[status(thm)],[t4610,t46]) ).
cnf(t74378,plain,
composition(join(X1,join(zero,X2)),zero) = zero,
inference(step,[status(thm)],[t74377,t4532]) ).
cnf(t4791,plain,
composition(join(X1,join(zero,X2)),zero) = zero,
inference(orient,[status(thm)],[t74378]) ).
cnf(t175,plain,
converse(join(one,X1)) = join(one,converse(X1)),
inference(cp,[status(thm)],[t62,t174]) ).
cnf(t191,plain,
converse(join(one,X1)) = join(one,converse(X1)),
inference(orient,[status(thm)],[t175]) ).
cnf(t197,plain,
composition(converse(X1),join(one,X2)) = converse(composition(join(one,converse(X2)),X1)),
inference(cp,[status(thm)],[t151,t191]) ).
cnf(t3963,plain,
converse(composition(join(one,converse(X1)),X2)) = composition(converse(X2),join(one,X1)),
inference(orient,[status(thm)],[t197]) ).
fof(f4,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/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(t22,plain,
composition(composition(X1,X2),X3) = composition(X1,composition(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t26,plain,
composition(join(X1,composition(X2,X3)),Y3) = join(composition(X1,Y3),composition(X2,composition(X3,Y3))),
inference(cp,[status(thm)],[t24,t22]) ).
cnf(t835,plain,
join(composition(X1,X2),composition(X3,composition(Y3,X2))) = composition(join(X1,composition(X3,Y3)),X2),
inference(orient,[status(thm)],[t26]) ).
cnf(t4479,plain,
composition(join(X1,composition(X2,top)),top) = join(composition(X1,top),composition(X2,top)),
inference(cp,[status(thm)],[t835,t4476]) ).
cnf(t74466,plain,
composition(join(X1,composition(X2,top)),top) = composition(join(X1,X2),top),
inference(step,[status(thm)],[t4479,t24]) ).
cnf(t6516,plain,
composition(join(X1,composition(X2,top)),top) = composition(join(X1,X2),top),
inference(orient,[status(thm)],[t74466]) ).
cnf(t6528,plain,
composition(join(X1,one),top) = composition(join(X1,top),top),
inference(cp,[status(thm)],[t6516,t185]) ).
cnf(t74467,plain,
composition(join(X1,one),top) = composition(top,top),
inference(step,[status(thm)],[t6528,t352]) ).
cnf(t74468,plain,
composition(join(X1,one),top) = top,
inference(step,[status(thm)],[t74467,t4476]) ).
cnf(t6554,plain,
composition(join(X1,one),top) = top,
inference(orient,[status(thm)],[t74468]) ).
cnf(t6556,plain,
top = composition(join(one,X1),top),
inference(cp,[status(thm)],[t6554,t43]) ).
cnf(t6580,plain,
composition(join(one,X1),top) = top,
inference(orient,[status(thm)],[t6556]) ).
cnf(t6595,plain,
composition(converse(top),join(one,X1)) = converse(top),
inference(cp,[status(thm)],[t3963,t6580]) ).
cnf(t74471,plain,
composition(top,join(one,X1)) = converse(top),
inference(step,[status(thm)],[t6595,t364]) ).
cnf(t74472,plain,
composition(top,join(one,X1)) = top,
inference(step,[status(thm)],[t74471,t364]) ).
cnf(t6620,plain,
composition(top,join(one,X1)) = top,
inference(orient,[status(thm)],[t74472]) ).
cnf(t6621,plain,
top = composition(top,join(X1,one)),
inference(cp,[status(thm)],[t6620,t43]) ).
cnf(t6638,plain,
composition(top,join(X1,one)) = top,
inference(orient,[status(thm)],[t6621]) ).
cnf(t6645,plain,
complement(join(X1,one)) = join(complement(join(X1,one)),composition(converse(top),complement(top))),
inference(cp,[status(thm)],[t54,t6638]) ).
cnf(t74491,plain,
complement(join(X1,one)) = join(complement(join(X1,one)),composition(top,complement(top))),
inference(step,[status(thm)],[t6645,t364]) ).
cnf(t74492,plain,
complement(join(X1,one)) = join(composition(top,complement(top)),complement(join(X1,one))),
inference(step,[status(thm)],[t74491,t43]) ).
cnf(t74493,plain,
complement(join(X1,one)) = join(composition(top,zero),complement(join(X1,one))),
inference(step,[status(thm)],[t74492,t97]) ).
cnf(t74494,plain,
complement(join(X1,one)) = join(zero,complement(join(X1,one))),
inference(step,[status(thm)],[t74493,t4490]) ).
cnf(t7235,plain,
join(zero,complement(join(X1,one))) = complement(join(X1,one)),
inference(orient,[status(thm)],[t74494]) ).
cnf(t7244,plain,
zero = composition(join(X1,complement(join(X2,one))),zero),
inference(cp,[status(thm)],[t4791,t7235]) ).
cnf(t7504,plain,
composition(join(X1,complement(join(X2,one))),zero) = zero,
inference(orient,[status(thm)],[t7244]) ).
cnf(t15106,plain,
zero = composition(X1,zero),
inference(cp,[status(thm)],[t7504,t14892]) ).
cnf(t15111,plain,
composition(X1,zero) = zero,
inference(orient,[status(thm)],[t15106]) ).
cnf(t15118,plain,
converse(zero) = join(converse(zero),zero),
inference(cp,[status(thm)],[t11289,t15111]) ).
cnf(t74703,plain,
converse(zero) = join(zero,converse(zero)),
inference(step,[status(thm)],[t15118,t43]) ).
cnf(t15272,plain,
join(zero,converse(zero)) = converse(zero),
inference(orient,[status(thm)],[t74703]) ).
cnf(t15281,plain,
join(converse(zero),zero) = converse(converse(zero)),
inference(cp,[status(thm)],[t277,t15272]) ).
cnf(t74704,plain,
join(zero,converse(zero)) = converse(converse(zero)),
inference(step,[status(thm)],[t15281,t43]) ).
cnf(t74705,plain,
converse(zero) = converse(converse(zero)),
inference(step,[status(thm)],[t74704,t15272]) ).
cnf(t74706,plain,
converse(zero) = zero,
inference(step,[status(thm)],[t74705,t21]) ).
cnf(t15284,plain,
converse(zero) = zero,
inference(orient,[status(thm)],[t74706]) ).
cnf(t15287,plain,
converse(composition(X1,zero)) = composition(zero,converse(X1)),
inference(cp,[status(thm)],[t27,t15284]) ).
cnf(t74738,plain,
converse(zero) = composition(zero,converse(X1)),
inference(step,[status(thm)],[t15287,t15111]) ).
cnf(t74739,plain,
zero = composition(zero,converse(X1)),
inference(step,[status(thm)],[t74738,t15284]) ).
cnf(t15368,plain,
composition(zero,converse(X1)) = zero,
inference(orient,[status(thm)],[t74739]) ).
cnf(t15385,plain,
zero = composition(zero,X1),
inference(cp,[status(thm)],[t15368,t21]) ).
cnf(t15406,plain,
composition(zero,X1) = zero,
inference(orient,[status(thm)],[t15385]) ).
cnf(t15417,plain,
complement(X1) = join(complement(X1),composition(converse(zero),complement(zero))),
inference(cp,[status(thm)],[t54,t15406]) ).
cnf(t74740,plain,
complement(X1) = join(complement(X1),composition(zero,complement(zero))),
inference(step,[status(thm)],[t15417,t15284]) ).
cnf(t74741,plain,
complement(X1) = join(complement(X1),zero),
inference(step,[status(thm)],[t74740,t15406]) ).
cnf(t74742,plain,
complement(X1) = join(zero,complement(X1)),
inference(step,[status(thm)],[t74741,t43]) ).
cnf(t15419,plain,
join(zero,complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t74742]) ).
cnf(t74755,plain,
complement(complement(X1)) = meet(top,X1),
inference(step,[status(thm)],[t118,t15419]) ).
cnf(t15459,plain,
complement(complement(X1)) = meet(top,X1),
inference(rw,[status(thm)],[t74755]) ).
cnf(t15460,plain,
complement(complement(X1)) = meet(top,X1),
inference(orient,[status(thm)],[t15459]) ).
cnf(t15587,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t15581,t43]) ).
cnf(t15620,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t15587]) ).
cnf(t15628,plain,
X1 = join(meet(X1,zero),complement(complement(X1))),
inference(cp,[status(thm)],[t14892,t15620]) ).
cnf(t2005,plain,
join(complement(X1),join(join(X2,X1),X3)) = join(top,X3),
inference(cp,[status(thm)],[t46,t1965]) ).
cnf(t74237,plain,
join(complement(X1),join(X2,join(X1,X3))) = join(top,X3),
inference(step,[status(thm)],[t2005,t46]) ).
cnf(t74238,plain,
join(complement(X1),join(X2,join(X1,X3))) = top,
inference(step,[status(thm)],[t74237,t358]) ).
cnf(t2232,plain,
join(complement(X1),join(X2,join(X1,X3))) = top,
inference(orient,[status(thm)],[t74238]) ).
cnf(t7245,plain,
top = join(complement(zero),join(X1,complement(join(X2,one)))),
inference(cp,[status(thm)],[t2232,t7235]) ).
cnf(t9425,plain,
join(complement(zero),join(X1,complement(join(X2,one)))) = top,
inference(orient,[status(thm)],[t7245]) ).
cnf(t15105,plain,
top = join(complement(zero),X1),
inference(cp,[status(thm)],[t9425,t14892]) ).
cnf(t15170,plain,
join(complement(zero),X1) = top,
inference(orient,[status(thm)],[t15105]) ).
cnf(t15171,plain,
top = complement(zero),
inference(cp,[status(thm)],[t15170,t54]) ).
cnf(t15213,plain,
complement(zero) = top,
inference(orient,[status(thm)],[t15171]) ).
cnf(t15235,plain,
meet(X1,zero) = complement(join(complement(X1),top)),
inference(cp,[status(thm)],[t85,t15213]) ).
cnf(t74700,plain,
meet(X1,zero) = complement(top),
inference(step,[status(thm)],[t15235,t352]) ).
cnf(t74701,plain,
meet(X1,zero) = zero,
inference(step,[status(thm)],[t74700,t97]) ).
cnf(t15261,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t74701]) ).
cnf(t74796,plain,
X1 = join(zero,complement(complement(X1))),
inference(step,[status(thm)],[t15628,t15261]) ).
cnf(t74797,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t74796,t15419]) ).
cnf(t74798,plain,
X1 = meet(top,X1),
inference(step,[status(thm)],[t74797,t15460]) ).
cnf(t15669,plain,
meet(top,X1) = X1,
inference(orient,[status(thm)],[t74798]) ).
cnf(t74799,plain,
complement(complement(X1)) = X1,
inference(step,[status(thm)],[t15460,t15669]) ).
cnf(t15670,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t74799]) ).
cnf(t16081,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(cp,[status(thm)],[t16028,t15670]) ).
cnf(t16352,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(orient,[status(thm)],[t16081]) ).
cnf(t16359,plain,
complement(X1) = join(complement(X1),complement(join(X2,X1))),
inference(cp,[status(thm)],[t15796,t16352]) ).
cnf(t120,plain,
meet(top,join(complement(X1),complement(X2))) = complement(join(zero,meet(X1,X2))),
inference(cp,[status(thm)],[t118,t85]) ).
cnf(t3514,plain,
meet(top,join(complement(X1),complement(X2))) = complement(join(zero,meet(X1,X2))),
inference(orient,[status(thm)],[t120]) ).
cnf(t74770,plain,
meet(top,join(complement(X1),complement(X2))) = complement(meet(X1,X2)),
inference(step,[status(thm)],[t3514,t15581]) ).
cnf(t15582,plain,
meet(top,join(complement(X1),complement(X2))) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t74770]) ).
cnf(t74805,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(step,[status(thm)],[t15582,t15669]) ).
cnf(t15697,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(rw,[status(thm)],[t74805]) ).
cnf(t16299,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t15697]) ).
cnf(t74830,plain,
complement(X1) = complement(meet(X1,join(X2,X1))),
inference(step,[status(thm)],[t16359,t16299]) ).
cnf(t16498,plain,
complement(meet(X1,join(X2,X1))) = complement(X1),
inference(orient,[status(thm)],[t74830]) ).
cnf(t16531,plain,
meet(X1,join(X2,X1)) = complement(complement(X1)),
inference(cp,[status(thm)],[t15670,t16498]) ).
cnf(t74831,plain,
meet(X1,join(X2,X1)) = X1,
inference(step,[status(thm)],[t16531,t15670]) ).
cnf(t16586,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t74831]) ).
cnf(t16589,plain,
meet(X1,X2) = meet(meet(X1,X2),X2),
inference(cp,[status(thm)],[t16586,t15796]) ).
cnf(t74833,plain,
meet(X1,X2) = meet(X2,meet(X1,X2)),
inference(step,[status(thm)],[t16589,t106]) ).
cnf(t16733,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(orient,[status(thm)],[t74833]) ).
cnf(t18190,plain,
X1 = join(X1,meet(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t18188,t16733]) ).
cnf(t18260,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(orient,[status(thm)],[t18190]) ).
cnf(t18283,plain,
zero = meet(meet(X1,meet(X2,X3)),complement(X3)),
inference(cp,[status(thm)],[t16154,t18260]) ).
cnf(t75006,plain,
zero = meet(complement(X3),meet(X1,meet(X2,X3))),
inference(step,[status(thm)],[t18283,t106]) ).
cnf(t28032,plain,
meet(complement(X1),meet(X2,meet(X3,X1))) = zero,
inference(orient,[status(thm)],[t75006]) ).
cnf(t16050,plain,
meet(one,complement(composition(converse(X1),complement(X1)))) = complement(complement(one)),
inference(cp,[status(thm)],[t16028,t1148]) ).
cnf(t74914,plain,
meet(one,complement(composition(converse(X1),complement(X1)))) = one,
inference(step,[status(thm)],[t16050,t15670]) ).
cnf(t21569,plain,
meet(one,complement(composition(converse(X1),complement(X1)))) = one,
inference(orient,[status(thm)],[t74914]) ).
cnf(t21589,plain,
one = meet(one,complement(composition(converse(complement(X1)),X1))),
inference(cp,[status(thm)],[t21569,t15670]) ).
cnf(t30052,plain,
meet(one,complement(composition(converse(complement(X1)),X1))) = one,
inference(orient,[status(thm)],[t21589]) ).
cnf(t30111,plain,
zero = meet(complement(complement(composition(converse(complement(X1)),X1))),meet(X2,one)),
inference(cp,[status(thm)],[t28032,t30052]) ).
cnf(t75295,plain,
zero = meet(composition(converse(complement(X1)),X1),meet(X2,one)),
inference(step,[status(thm)],[t30111,t15670]) ).
cnf(t52005,plain,
meet(composition(converse(complement(X1)),X1),meet(X2,one)) = zero,
inference(orient,[status(thm)],[t75295]) ).
cnf(t52050,plain,
composition(meet(meet(X1,one),composition(converse(complement(converse(X2))),converse(X2))),meet(X2,composition(converse(meet(X1,one)),converse(complement(converse(X2)))))) = join(meet(composition(meet(X1,one),X2),converse(complement(converse(X2)))),composition(zero,meet(X2,composition(converse(meet(X1,one)),converse(complement(converse(X2))))))),
inference(cp,[status(thm)],[t50689,t52005]) ).
cnf(t15801,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t46,t15796]) ).
cnf(t18299,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t15801]) ).
cnf(t74824,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(step,[status(thm)],[t14892,t16028]) ).
cnf(t16143,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[t74824]) ).
cnf(t21805,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(orient,[status(thm)],[t16143]) ).
cnf(t21860,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(cp,[status(thm)],[t18299,t21805]) ).
cnf(t22012,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t21860]) ).
cnf(t22026,plain,
join(X1,complement(X2)) = join(X1,complement(join(X2,X1))),
inference(cp,[status(thm)],[t22012,t16352]) ).
cnf(t22932,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t22026]) ).
cnf(t23046,plain,
meet(X1,complement(complement(join(X2,complement(X1))))) = complement(join(complement(X1),complement(X2))),
inference(cp,[status(thm)],[t16028,t22932]) ).
cnf(t74932,plain,
meet(X1,join(X2,complement(X1))) = complement(join(complement(X1),complement(X2))),
inference(step,[status(thm)],[t23046,t15670]) ).
cnf(t74933,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(step,[status(thm)],[t74932,t85]) ).
cnf(t23064,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t74933]) ).
cnf(t23077,plain,
meet(X1,X2) = meet(X1,join(complement(X1),X2)),
inference(cp,[status(thm)],[t23064,t43]) ).
cnf(t23120,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t23077]) ).
cnf(t22045,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,join(meet(X3,X1),X2)),
inference(cp,[status(thm)],[t18299,t22012]) ).
cnf(t75108,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,X2),
inference(step,[status(thm)],[t22045,t18299]) ).
cnf(t35341,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,X2),
inference(orient,[status(thm)],[t75108]) ).
cnf(t241,plain,
meet(complement(X1),X2) = complement(join(meet(X1,X1),complement(X2))),
inference(cp,[status(thm)],[t85,t231]) ).
cnf(t1025,plain,
complement(join(meet(X1,X1),complement(X2))) = meet(complement(X1),X2),
inference(orient,[status(thm)],[t241]) ).
cnf(t74794,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(step,[status(thm)],[t1025,t15633]) ).
cnf(t15667,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(rw,[status(thm)],[t74794]) ).
cnf(t16228,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(orient,[status(thm)],[t15667]) ).
cnf(t16239,plain,
join(X1,complement(X2)) = complement(meet(complement(X1),X2)),
inference(cp,[status(thm)],[t15670,t16228]) ).
cnf(t16433,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t16239]) ).
cnf(t35353,plain,
join(X1,X2) = join(X1,meet(X2,join(X3,complement(X1)))),
inference(cp,[status(thm)],[t35341,t16433]) ).
cnf(t36433,plain,
join(X1,meet(X2,join(X3,complement(X1)))) = join(X1,X2),
inference(orient,[status(thm)],[t35353]) ).
cnf(t36483,plain,
meet(X1,meet(X2,join(X3,complement(complement(X1))))) = meet(X1,join(complement(X1),X2)),
inference(cp,[status(thm)],[t23120,t36433]) ).
cnf(t75116,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,join(complement(X1),X2)),
inference(step,[status(thm)],[t36483,t15670]) ).
cnf(t75117,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(step,[status(thm)],[t75116,t23120]) ).
cnf(t36515,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t75117]) ).
cnf(t36563,plain,
meet(meet(X1,X2),X3) = meet(meet(X1,X2),meet(X3,X1)),
inference(cp,[status(thm)],[t36515,t15770]) ).
cnf(t37808,plain,
meet(meet(X1,X2),meet(X3,X1)) = meet(meet(X1,X2),X3),
inference(orient,[status(thm)],[t36563]) ).
cnf(t37821,plain,
meet(meet(X1,X2),X3) = meet(meet(X3,X1),meet(X1,X2)),
inference(cp,[status(thm)],[t37808,t106]) ).
cnf(t36538,plain,
meet(X1,X2) = meet(X1,meet(join(X3,X1),X2)),
inference(cp,[status(thm)],[t36515,t106]) ).
cnf(t36724,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t36538]) ).
cnf(t36807,plain,
meet(meet(X1,X2),X3) = meet(meet(X1,X2),meet(X2,X3)),
inference(cp,[status(thm)],[t36724,t15796]) ).
cnf(t38611,plain,
meet(meet(X1,X2),meet(X2,X3)) = meet(meet(X1,X2),X3),
inference(orient,[status(thm)],[t36807]) ).
cnf(t75119,plain,
meet(meet(X1,X2),X3) = meet(meet(X3,X1),X2),
inference(step,[status(thm)],[t37821,t38611]) ).
cnf(t38886,plain,
meet(meet(X1,X2),X3) = meet(meet(X3,X1),X2),
inference(orient,[status(thm)],[t75119]) ).
cnf(t38902,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(cp,[status(thm)],[t38886,t106]) ).
cnf(t39587,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t38902]) ).
cnf(t75296,plain,
composition(meet(X1,meet(one,composition(converse(complement(converse(X2))),converse(X2)))),meet(X2,composition(converse(meet(X1,one)),converse(complement(converse(X2)))))) = join(meet(composition(meet(X1,one),X2),converse(complement(converse(X2)))),composition(zero,meet(X2,composition(converse(meet(X1,one)),converse(complement(converse(X2))))))),
inference(step,[status(thm)],[t52050,t39587]) ).
cnf(t2360,plain,
zero = meet(one,composition(converse(X1),complement(X1))),
inference(cp,[status(thm)],[t2350,t21]) ).
cnf(t2384,plain,
meet(one,composition(converse(X1),complement(X1))) = zero,
inference(orient,[status(thm)],[t2360]) ).
cnf(t2403,plain,
zero = meet(one,composition(converse(complement(X1)),meet(X1,X1))),
inference(cp,[status(thm)],[t2384,t231]) ).
cnf(t3254,plain,
meet(one,composition(converse(complement(X1)),meet(X1,X1))) = zero,
inference(orient,[status(thm)],[t2403]) ).
cnf(t74795,plain,
meet(one,composition(converse(complement(X1)),X1)) = zero,
inference(step,[status(thm)],[t3254,t15633]) ).
cnf(t15668,plain,
meet(one,composition(converse(complement(X1)),X1)) = zero,
inference(rw,[status(thm)],[t74795]) ).
cnf(t17187,plain,
meet(one,composition(converse(complement(X1)),X1)) = zero,
inference(orient,[status(thm)],[t15668]) ).
cnf(t75297,plain,
composition(meet(X1,zero),meet(X2,composition(converse(meet(X1,one)),converse(complement(converse(X2)))))) = join(meet(composition(meet(X1,one),X2),converse(complement(converse(X2)))),composition(zero,meet(X2,composition(converse(meet(X1,one)),converse(complement(converse(X2))))))),
inference(step,[status(thm)],[t75296,t17187]) ).
cnf(t75298,plain,
composition(zero,meet(X2,composition(converse(meet(X1,one)),converse(complement(converse(X2)))))) = join(meet(composition(meet(X1,one),X2),converse(complement(converse(X2)))),composition(zero,meet(X2,composition(converse(meet(X1,one)),converse(complement(converse(X2))))))),
inference(step,[status(thm)],[t75297,t15261]) ).
cnf(t75299,plain,
zero = join(meet(composition(meet(X1,one),X2),converse(complement(converse(X2)))),composition(zero,meet(X2,composition(converse(meet(X1,one)),converse(complement(converse(X2))))))),
inference(step,[status(thm)],[t75298,t15406]) ).
cnf(t75300,plain,
zero = join(meet(converse(complement(converse(X2))),composition(meet(X1,one),X2)),composition(zero,meet(X2,composition(converse(meet(X1,one)),converse(complement(converse(X2))))))),
inference(step,[status(thm)],[t75299,t106]) ).
cnf(t22027,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(cp,[status(thm)],[t22012,t106]) ).
cnf(t22519,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t22027]) ).
cnf(t22543,plain,
join(complement(X1),X2) = join(complement(X1),meet(X1,X2)),
inference(cp,[status(thm)],[t22519,t15670]) ).
cnf(t23384,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t22543]) ).
cnf(t39,plain,
composition(meet(X1,composition(X2,converse(converse(X3)))),meet(converse(X3),composition(converse(X1),X2))) = join(meet(composition(X1,converse(X3)),X2),composition(meet(X1,composition(X2,X3)),meet(converse(X3),composition(converse(X1),X2)))),
inference(cp,[status(thm)],[t33,t21]) ).
cnf(t74542,plain,
composition(meet(X1,composition(X2,X3)),meet(converse(X3),composition(converse(X1),X2))) = join(meet(composition(X1,converse(X3)),X2),composition(meet(X1,composition(X2,X3)),meet(converse(X3),composition(converse(X1),X2)))),
inference(step,[status(thm)],[t39,t21]) ).
cnf(t9035,plain,
join(meet(composition(X1,converse(X2)),X3),composition(meet(X1,composition(X3,X2)),meet(converse(X2),composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,X2)),meet(converse(X2),composition(converse(X1),X3))),
inference(orient,[status(thm)],[t74542]) ).
cnf(t17202,plain,
composition(meet(one,composition(converse(complement(X1)),X1)),meet(converse(X1),composition(converse(one),converse(complement(X1))))) = join(meet(composition(one,converse(X1)),converse(complement(X1))),composition(zero,meet(converse(X1),composition(converse(one),converse(complement(X1)))))),
inference(cp,[status(thm)],[t9035,t17187]) ).
cnf(t74839,plain,
composition(zero,meet(converse(X1),composition(converse(one),converse(complement(X1))))) = join(meet(composition(one,converse(X1)),converse(complement(X1))),composition(zero,meet(converse(X1),composition(converse(one),converse(complement(X1)))))),
inference(step,[status(thm)],[t17202,t17187]) ).
cnf(t74840,plain,
zero = join(meet(composition(one,converse(X1)),converse(complement(X1))),composition(zero,meet(converse(X1),composition(converse(one),converse(complement(X1)))))),
inference(step,[status(thm)],[t74839,t15406]) ).
cnf(t74841,plain,
zero = join(meet(converse(complement(X1)),composition(one,converse(X1))),composition(zero,meet(converse(X1),composition(converse(one),converse(complement(X1)))))),
inference(step,[status(thm)],[t74840,t106]) ).
cnf(t74842,plain,
zero = join(meet(converse(complement(X1)),converse(X1)),composition(zero,meet(converse(X1),composition(converse(one),converse(complement(X1)))))),
inference(step,[status(thm)],[t74841,t185]) ).
cnf(t74843,plain,
zero = join(meet(converse(X1),converse(complement(X1))),composition(zero,meet(converse(X1),composition(converse(one),converse(complement(X1)))))),
inference(step,[status(thm)],[t74842,t106]) ).
cnf(t74844,plain,
zero = join(meet(converse(X1),converse(complement(X1))),zero),
inference(step,[status(thm)],[t74843,t15406]) ).
cnf(t74845,plain,
zero = meet(converse(X1),converse(complement(X1))),
inference(step,[status(thm)],[t74844,t15620]) ).
cnf(t17233,plain,
meet(converse(X1),converse(complement(X1))) = zero,
inference(orient,[status(thm)],[t74845]) ).
cnf(t23423,plain,
join(complement(converse(X1)),converse(complement(X1))) = join(complement(converse(X1)),zero),
inference(cp,[status(thm)],[t23384,t17233]) ).
cnf(t74946,plain,
join(converse(complement(X1)),complement(converse(X1))) = join(complement(converse(X1)),zero),
inference(step,[status(thm)],[t23423,t43]) ).
cnf(t74947,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(step,[status(thm)],[t74946,t15620]) ).
cnf(t24144,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(orient,[status(thm)],[t74947]) ).
cnf(t24149,plain,
complement(converse(complement(X1))) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t24144,t15670]) ).
cnf(t74140,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(step,[status(thm)],[t296,t364]) ).
cnf(t367,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(orient,[status(thm)],[t74140]) ).
cnf(t16077,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = complement(top),
inference(cp,[status(thm)],[t16028,t367]) ).
cnf(t74915,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(step,[status(thm)],[t16077,t97]) ).
cnf(t21625,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(orient,[status(thm)],[t74915]) ).
cnf(t22524,plain,
join(X1,complement(converse(complement(converse(complement(complement(X1))))))) = join(X1,zero),
inference(cp,[status(thm)],[t22519,t21625]) ).
cnf(t74928,plain,
join(X1,complement(converse(complement(converse(X1))))) = join(X1,zero),
inference(step,[status(thm)],[t22524,t15670]) ).
cnf(t74929,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t74928,t15620]) ).
cnf(t22756,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t74929]) ).
cnf(t22775,plain,
converse(X1) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t22756,t21]) ).
cnf(t23979,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(orient,[status(thm)],[t22775]) ).
cnf(t74948,plain,
complement(converse(complement(X1))) = converse(X1),
inference(step,[status(thm)],[t24149,t23979]) ).
cnf(t24196,plain,
complement(converse(complement(X1))) = converse(X1),
inference(orient,[status(thm)],[t74948]) ).
cnf(t24201,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(cp,[status(thm)],[t24196,t15670]) ).
cnf(t24267,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(orient,[status(thm)],[t24201]) ).
cnf(t75301,plain,
zero = join(meet(converse(converse(complement(X2))),composition(meet(X1,one),X2)),composition(zero,meet(X2,composition(converse(meet(X1,one)),converse(complement(converse(X2))))))),
inference(step,[status(thm)],[t75300,t24267]) ).
cnf(t75302,plain,
zero = join(meet(complement(X2),composition(meet(X1,one),X2)),composition(zero,meet(X2,composition(converse(meet(X1,one)),converse(complement(converse(X2))))))),
inference(step,[status(thm)],[t75301,t21]) ).
cnf(t75303,plain,
zero = join(meet(complement(X2),composition(meet(X1,one),X2)),zero),
inference(step,[status(thm)],[t75302,t15406]) ).
cnf(t75304,plain,
zero = meet(complement(X2),composition(meet(X1,one),X2)),
inference(step,[status(thm)],[t75303,t15620]) ).
cnf(t52052,plain,
meet(complement(X1),composition(meet(X2,one),X1)) = zero,
inference(orient,[status(thm)],[t75304]) ).
cnf(t52073,plain,
zero = meet(complement(X1),composition(meet(one,X2),X1)),
inference(cp,[status(thm)],[t52052,t106]) ).
cnf(t52287,plain,
meet(complement(X1),composition(meet(one,X2),X1)) = zero,
inference(orient,[status(thm)],[t52073]) ).
fof(f16,conjecture,
! [X0] :
( join(composition(converse(X0),X0),one) = one
=> ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0] :
( join(composition(converse(X0),X0),one) = one
=> ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0] :
( ? [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) != zero
& join(composition(converse(X0),X0),one) = one ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( meet(composition(sk0,sk1),composition(sk0,complement(sk1))) != zero
& join(composition(converse(sk0),sk0),one) = one ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f16_nnf]) ).
cnf(c16,plain,
join(composition(converse(sk0),sk0),one) = one,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t5,plain,
join(composition(converse(sk0),sk0),one) = one,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t74115,plain,
join(one,composition(converse(sk0),sk0)) = one,
inference(step,[status(thm)],[t5,t43]) ).
cnf(t60,plain,
join(one,composition(converse(sk0),sk0)) = one,
inference(orient,[status(thm)],[t74115]) ).
cnf(t16606,plain,
composition(converse(sk0),sk0) = meet(composition(converse(sk0),sk0),one),
inference(cp,[status(thm)],[t16586,t60]) ).
cnf(t74881,plain,
composition(converse(sk0),sk0) = meet(one,composition(converse(sk0),sk0)),
inference(step,[status(thm)],[t16606,t106]) ).
cnf(t17954,plain,
meet(one,composition(converse(sk0),sk0)) = composition(converse(sk0),sk0),
inference(orient,[status(thm)],[t74881]) ).
cnf(t52309,plain,
zero = meet(complement(X1),composition(composition(converse(sk0),sk0),X1)),
inference(cp,[status(thm)],[t52287,t17954]) ).
cnf(t75753,plain,
zero = meet(complement(X1),composition(converse(sk0),composition(sk0,X1))),
inference(step,[status(thm)],[t52309,t22]) ).
cnf(t74014,plain,
meet(complement(X1),composition(converse(sk0),composition(sk0,X1))) = zero,
inference(orient,[status(thm)],[t75753]) ).
cnf(t74059,plain,
composition(meet(sk0,composition(composition(sk0,X1),converse(complement(X1)))),meet(complement(X1),composition(converse(sk0),composition(sk0,X1)))) = join(meet(composition(sk0,complement(X1)),composition(sk0,X1)),composition(meet(sk0,composition(composition(sk0,X1),converse(complement(X1)))),zero)),
inference(cp,[status(thm)],[t33,t74014]) ).
cnf(t75754,plain,
composition(meet(sk0,composition(sk0,composition(X1,converse(complement(X1))))),meet(complement(X1),composition(converse(sk0),composition(sk0,X1)))) = join(meet(composition(sk0,complement(X1)),composition(sk0,X1)),composition(meet(sk0,composition(composition(sk0,X1),converse(complement(X1)))),zero)),
inference(step,[status(thm)],[t74059,t22]) ).
cnf(t75755,plain,
composition(meet(sk0,composition(sk0,composition(X1,converse(complement(X1))))),zero) = join(meet(composition(sk0,complement(X1)),composition(sk0,X1)),composition(meet(sk0,composition(composition(sk0,X1),converse(complement(X1)))),zero)),
inference(step,[status(thm)],[t75754,t74014]) ).
cnf(t75756,plain,
zero = join(meet(composition(sk0,complement(X1)),composition(sk0,X1)),composition(meet(sk0,composition(composition(sk0,X1),converse(complement(X1)))),zero)),
inference(step,[status(thm)],[t75755,t15111]) ).
cnf(t75757,plain,
zero = join(meet(composition(sk0,X1),composition(sk0,complement(X1))),composition(meet(sk0,composition(composition(sk0,X1),converse(complement(X1)))),zero)),
inference(step,[status(thm)],[t75756,t106]) ).
cnf(t75758,plain,
zero = join(meet(composition(sk0,X1),composition(sk0,complement(X1))),zero),
inference(step,[status(thm)],[t75757,t15111]) ).
cnf(t75759,plain,
zero = meet(composition(sk0,X1),composition(sk0,complement(X1))),
inference(step,[status(thm)],[t75758,t15620]) ).
cnf(t74068,plain,
meet(composition(sk0,X1),composition(sk0,complement(X1))) = zero,
inference(orient,[status(thm)],[t75759]) ).
cnf(c17,plain,
meet(composition(sk0,sk1),composition(sk0,complement(sk1))) != zero,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
meet(composition(sk0,sk1),composition(sk0,complement(sk1))) != zero,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(g0_0,plain,
zero != zero,
inference(rw,[status(thm)],[goal_0,t74068]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : REL041+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Thu Sep 24 07:34:31 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 23.05/3.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.05/3.29 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------