%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL043+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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:36:08 PM UTC 2026
% Result : Theorem 21.14s 8.39s
% Output : Proof 21.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 116
% Number of leaves : 15
% Syntax : Number of formulae : 389 ( 385 unt; 0 def)
% Number of atoms : 393 ( 392 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 8 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 508 ( 84 sgn 90 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
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(t23228,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t45,t43]) ).
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]) ).
cnf(t23229,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t23228,t85]) ).
cnf(t23230,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t23229,t43]) ).
cnf(t14809,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t23230]) ).
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(t22684,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)],[t22684]) ).
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(t22690,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t152,t21]) ).
cnf(t164,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t22690]) ).
cnf(t165,plain,
one = converse(one),
inference(cp,[status(thm)],[t164,t17]) ).
cnf(t174,plain,
converse(one) = one,
inference(orient,[status(thm)],[t165]) ).
cnf(t22691,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t164,t174]) ).
cnf(t184,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t22691]) ).
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(t22693,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t188,t174]) ).
cnf(t22694,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t22693,t185]) ).
cnf(t214,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t22694]) ).
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(t1074,plain,
complement(join(complement(X1),meet(X2,X2))) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t242]) ).
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(t14810,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t14809,t92]) ).
cnf(t23339,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t14810,t85]) ).
cnf(t15477,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t23339]) ).
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(t22686,plain,
zero = complement(top),
inference(step,[status(thm)],[t86,t92]) ).
cnf(t97,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t22686]) ).
cnf(t218,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t214,t97]) ).
cnf(t22695,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t218,t97]) ).
cnf(t22696,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t22695,t97]) ).
cnf(t225,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t22696]) ).
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(t15482,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t244,t15477]) ).
cnf(t23341,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t15482,t15477]) ).
cnf(t15496,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t23341]) ).
cnf(t23346,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t15477,t15496]) ).
cnf(t15522,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t23346]) ).
cnf(t15547,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t15522]) ).
cnf(t23365,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t1074,t15547]) ).
cnf(t15580,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(rw,[status(thm)],[t23365]) ).
cnf(t15940,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t15580]) ).
cnf(t23396,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(step,[status(thm)],[t14809,t15940]) ).
cnf(t16054,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[t23396]) ).
cnf(t21733,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(orient,[status(thm)],[t16054]) ).
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(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(t1814,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(t22701,plain,
join(top,complement(X1)) = top,
inference(step,[status(thm)],[t319,t51]) ).
cnf(t330,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t22701]) ).
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(t22703,plain,
top = join(X1,top),
inference(step,[status(thm)],[t317,t347]) ).
cnf(t352,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t22703]) ).
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(t22712,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)],[t22712]) ).
cnf(t1818,plain,
join(converse(join(X1,X2)),complement(converse(X1))) = top,
inference(cp,[status(thm)],[t1814,t402]) ).
cnf(t22798,plain,
join(complement(converse(X1)),converse(join(X1,X2))) = top,
inference(step,[status(thm)],[t1818,t43]) ).
cnf(t1870,plain,
join(complement(converse(X1)),converse(join(X1,X2))) = top,
inference(orient,[status(thm)],[t22798]) ).
cnf(t1903,plain,
top = join(complement(converse(converse(X1))),converse(converse(join(X1,X2)))),
inference(cp,[status(thm)],[t1870,t62]) ).
cnf(t22799,plain,
top = join(complement(X1),converse(converse(join(X1,X2)))),
inference(step,[status(thm)],[t1903,t21]) ).
cnf(t22800,plain,
top = join(complement(X1),join(X1,X2)),
inference(step,[status(thm)],[t22799,t21]) ).
cnf(t1917,plain,
join(complement(X1),join(X1,X2)) = top,
inference(orient,[status(thm)],[t22800]) ).
cnf(t1948,plain,
top = join(complement(X1),join(X2,X1)),
inference(cp,[status(thm)],[t1917,t43]) ).
cnf(t1951,plain,
join(complement(X1),join(X2,X1)) = top,
inference(orient,[status(thm)],[t1948]) ).
cnf(t15949,plain,
meet(X1,complement(join(X2,X1))) = complement(top),
inference(cp,[status(thm)],[t15940,t1951]) ).
cnf(t23398,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(step,[status(thm)],[t15949,t97]) ).
cnf(t16065,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t23398]) ).
fof(f16,conjecture,
! [X0,X1,X2] :
( join(composition(X0,converse(X1)),X2) = X2
=> join(composition(complement(X2),X1),complement(X0)) = complement(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( join(composition(X0,converse(X1)),X2) = X2
=> join(composition(complement(X2),X1),complement(X0)) = complement(X0) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0,X1,X2] :
( join(composition(complement(X2),X1),complement(X0)) != complement(X0)
& join(composition(X0,converse(X1)),X2) = X2 ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( join(composition(complement(sk2),sk1),complement(sk0)) != complement(sk0)
& join(composition(sk0,converse(sk1)),sk2) = sk2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f16_nnf]) ).
cnf(c16,plain,
join(composition(sk0,converse(sk1)),sk2) = sk2,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t5,plain,
join(composition(sk0,converse(sk1)),sk2) = sk2,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t22685,plain,
join(sk2,composition(sk0,converse(sk1))) = sk2,
inference(step,[status(thm)],[t5,t43]) ).
cnf(t60,plain,
join(sk2,composition(sk0,converse(sk1))) = sk2,
inference(orient,[status(thm)],[t22685]) ).
cnf(t16081,plain,
zero = meet(composition(sk0,converse(sk1)),complement(sk2)),
inference(cp,[status(thm)],[t16065,t60]) ).
cnf(t87,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t85,t43]) ).
cnf(t22688,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)],[t22688]) ).
cnf(t23424,plain,
zero = meet(complement(sk2),composition(sk0,converse(sk1))),
inference(step,[status(thm)],[t16081,t106]) ).
cnf(t17281,plain,
meet(complement(sk2),composition(sk0,converse(sk1))) = zero,
inference(orient,[status(thm)],[t23424]) ).
cnf(t17285,plain,
composition(meet(complement(sk2),composition(sk0,converse(sk1))),meet(sk1,composition(converse(complement(sk2)),sk0))) = join(meet(composition(complement(sk2),sk1),sk0),composition(zero,meet(sk1,composition(converse(complement(sk2)),sk0)))),
inference(cp,[status(thm)],[t33,t17281]) ).
cnf(t23425,plain,
composition(zero,meet(sk1,composition(converse(complement(sk2)),sk0))) = join(meet(composition(complement(sk2),sk1),sk0),composition(zero,meet(sk1,composition(converse(complement(sk2)),sk0)))),
inference(step,[status(thm)],[t17285,t17281]) ).
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(t10112,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(t1697,plain,
join(converse(composition(X1,X2)),composition(X3,converse(X1))) = composition(join(converse(X2),X3),converse(X1)),
inference(orient,[status(thm)],[t30]) ).
cnf(t10113,plain,
join(converse(converse(composition(X1,X2))),composition(X1,top)) = converse(composition(join(converse(X2),top),converse(X1))),
inference(cp,[status(thm)],[t10112,t1697]) ).
cnf(t23127,plain,
join(composition(X1,X2),composition(X1,top)) = converse(composition(join(converse(X2),top),converse(X1))),
inference(step,[status(thm)],[t10113,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(t23128,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,converse(join(converse(X2),top))),
inference(step,[status(thm)],[t23127,t141]) ).
cnf(t23129,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,join(X2,converse(top))),
inference(step,[status(thm)],[t23128,t260]) ).
cnf(t23130,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,join(X2,top)),
inference(step,[status(thm)],[t23129,t364]) ).
cnf(t23131,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,top),
inference(step,[status(thm)],[t23130,t352]) ).
cnf(t10192,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,top),
inference(orient,[status(thm)],[t23131]) ).
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(t4178,plain,
join(composition(top,converse(X1)),converse(X2)) = converse(join(composition(X1,top),X2)),
inference(orient,[status(thm)],[t378]) ).
cnf(t4191,plain,
converse(join(composition(top,top),X1)) = join(composition(top,top),converse(X1)),
inference(cp,[status(thm)],[t4178,t364]) ).
cnf(t4225,plain,
converse(join(composition(top,top),X1)) = join(composition(top,top),converse(X1)),
inference(orient,[status(thm)],[t4191]) ).
cnf(t4229,plain,
join(composition(top,top),converse(composition(X1,top))) = converse(composition(join(top,X1),top)),
inference(cp,[status(thm)],[t4225,t24]) ).
cnf(t22899,plain,
join(composition(top,top),composition(top,converse(X1))) = converse(composition(join(top,X1),top)),
inference(step,[status(thm)],[t4229,t376]) ).
cnf(t22900,plain,
join(composition(top,top),composition(top,converse(X1))) = composition(top,converse(join(top,X1))),
inference(step,[status(thm)],[t22899,t376]) ).
cnf(t22901,plain,
join(composition(top,top),composition(top,converse(X1))) = composition(top,converse(top)),
inference(step,[status(thm)],[t22900,t358]) ).
cnf(t22902,plain,
join(composition(top,top),composition(top,converse(X1))) = composition(top,top),
inference(step,[status(thm)],[t22901,t364]) ).
cnf(t4432,plain,
join(composition(top,top),composition(top,converse(X1))) = composition(top,top),
inference(orient,[status(thm)],[t22902]) ).
cnf(t4448,plain,
composition(top,top) = join(composition(top,top),composition(top,one)),
inference(cp,[status(thm)],[t4432,t174]) ).
cnf(t22903,plain,
composition(top,top) = join(composition(top,top),top),
inference(step,[status(thm)],[t4448,t17]) ).
cnf(t22904,plain,
composition(top,top) = top,
inference(step,[status(thm)],[t22903,t352]) ).
cnf(t4461,plain,
composition(top,top) = top,
inference(orient,[status(thm)],[t22904]) ).
cnf(t4466,plain,
complement(top) = join(complement(top),composition(converse(top),complement(top))),
inference(cp,[status(thm)],[t54,t4461]) ).
cnf(t22912,plain,
zero = join(complement(top),composition(converse(top),complement(top))),
inference(step,[status(thm)],[t4466,t97]) ).
cnf(t22913,plain,
zero = join(zero,composition(converse(top),complement(top))),
inference(step,[status(thm)],[t22912,t97]) ).
cnf(t22914,plain,
zero = join(zero,composition(top,complement(top))),
inference(step,[status(thm)],[t22913,t364]) ).
cnf(t22915,plain,
zero = join(zero,composition(top,zero)),
inference(step,[status(thm)],[t22914,t97]) ).
cnf(t56,plain,
complement(one) = join(complement(one),composition(converse(X1),complement(X1))),
inference(cp,[status(thm)],[t54,t17]) ).
cnf(t1147,plain,
join(complement(one),composition(converse(X1),complement(X1))) = complement(one),
inference(orient,[status(thm)],[t56]) ).
cnf(t1157,plain,
complement(one) = join(complement(one),composition(X1,complement(converse(X1)))),
inference(cp,[status(thm)],[t1147,t21]) ).
cnf(t1175,plain,
join(complement(one),composition(X1,complement(converse(X1)))) = complement(one),
inference(orient,[status(thm)],[t1157]) ).
cnf(t1962,plain,
top = join(complement(composition(X1,complement(converse(X1)))),complement(one)),
inference(cp,[status(thm)],[t1951,t1175]) ).
cnf(t22811,plain,
top = join(complement(one),complement(composition(X1,complement(converse(X1))))),
inference(step,[status(thm)],[t1962,t43]) ).
cnf(t2314,plain,
join(complement(one),complement(composition(X1,complement(converse(X1))))) = top,
inference(orient,[status(thm)],[t22811]) ).
cnf(t2332,plain,
meet(one,composition(X1,complement(converse(X1)))) = complement(top),
inference(cp,[status(thm)],[t85,t2314]) ).
cnf(t22812,plain,
meet(one,composition(X1,complement(converse(X1)))) = zero,
inference(step,[status(thm)],[t2332,t97]) ).
cnf(t2335,plain,
meet(one,composition(X1,complement(converse(X1)))) = zero,
inference(orient,[status(thm)],[t22812]) ).
cnf(t2356,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,t2335]) ).
cnf(t22813,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)],[t2356,t21]) ).
cnf(t22814,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)],[t22813,t174]) ).
cnf(t22815,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)],[t22814,t17]) ).
cnf(t22816,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)],[t22815,t92]) ).
cnf(t22817,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)],[t22816,t2335]) ).
cnf(t22818,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)],[t22817,t17]) ).
cnf(t22819,plain,
composition(zero,zero) = join(meet(X1,complement(X1)),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t22818,t21]) ).
cnf(t22820,plain,
composition(zero,zero) = join(zero,composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t22819,t92]) ).
cnf(t22821,plain,
composition(zero,zero) = join(zero,composition(meet(X1,composition(complement(X1),converse(one))),zero)),
inference(step,[status(thm)],[t22820,t21]) ).
cnf(t22822,plain,
composition(zero,zero) = join(zero,composition(meet(X1,composition(complement(X1),one)),zero)),
inference(step,[status(thm)],[t22821,t174]) ).
cnf(t22823,plain,
composition(zero,zero) = join(zero,composition(meet(X1,complement(X1)),zero)),
inference(step,[status(thm)],[t22822,t17]) ).
cnf(t22824,plain,
composition(zero,zero) = join(zero,composition(zero,zero)),
inference(step,[status(thm)],[t22823,t92]) ).
cnf(t2357,plain,
join(zero,composition(zero,zero)) = composition(zero,zero),
inference(orient,[status(thm)],[t22824]) ).
cnf(t2360,plain,
join(zero,join(composition(zero,zero),X1)) = join(composition(zero,zero),X1),
inference(cp,[status(thm)],[t46,t2357]) ).
cnf(t2493,plain,
join(zero,join(composition(zero,zero),X1)) = join(composition(zero,zero),X1),
inference(orient,[status(thm)],[t2360]) ).
cnf(t2501,plain,
join(composition(zero,zero),composition(X1,zero)) = join(zero,composition(join(zero,X1),zero)),
inference(cp,[status(thm)],[t2493,t24]) ).
cnf(t22833,plain,
composition(join(zero,X1),zero) = join(zero,composition(join(zero,X1),zero)),
inference(step,[status(thm)],[t2501,t24]) ).
cnf(t2564,plain,
join(zero,composition(join(zero,X1),zero)) = composition(join(zero,X1),zero),
inference(orient,[status(thm)],[t22833]) ).
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(t22723,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)],[t22723]) ).
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(t22755,plain,
zero = join(zero,composition(converse(X1),complement(composition(X1,top)))),
inference(step,[status(thm)],[t102,t97]) ).
cnf(t1395,plain,
join(zero,composition(converse(X1),complement(composition(X1,top)))) = zero,
inference(orient,[status(thm)],[t22755]) ).
cnf(t1400,plain,
zero = join(zero,composition(top,complement(composition(top,top)))),
inference(cp,[status(thm)],[t1395,t364]) ).
cnf(t1417,plain,
join(zero,composition(top,complement(composition(top,top)))) = zero,
inference(orient,[status(thm)],[t1400]) ).
cnf(t1419,plain,
top = join(complement(composition(top,complement(composition(top,top)))),zero),
inference(cp,[status(thm)],[t613,t1417]) ).
cnf(t22778,plain,
top = join(zero,complement(composition(top,complement(composition(top,top))))),
inference(step,[status(thm)],[t1419,t43]) ).
cnf(t1667,plain,
join(zero,complement(composition(top,complement(composition(top,top))))) = top,
inference(orient,[status(thm)],[t22778]) ).
cnf(t2567,plain,
composition(join(zero,complement(composition(top,complement(composition(top,top))))),zero) = join(zero,composition(top,zero)),
inference(cp,[status(thm)],[t2564,t1667]) ).
cnf(t22834,plain,
composition(top,zero) = join(zero,composition(top,zero)),
inference(step,[status(thm)],[t2567,t1667]) ).
cnf(t2593,plain,
join(zero,composition(top,zero)) = composition(top,zero),
inference(orient,[status(thm)],[t22834]) ).
cnf(t22916,plain,
zero = composition(top,zero),
inference(step,[status(thm)],[t22915,t2593]) ).
cnf(t4475,plain,
composition(top,zero) = zero,
inference(orient,[status(thm)],[t22916]) ).
cnf(t4476,plain,
composition(converse(zero),top) = converse(zero),
inference(cp,[status(thm)],[t390,t4475]) ).
cnf(t4495,plain,
composition(converse(zero),top) = converse(zero),
inference(orient,[status(thm)],[t4476]) ).
cnf(t10244,plain,
composition(converse(zero),top) = join(composition(converse(zero),X1),converse(zero)),
inference(cp,[status(thm)],[t10192,t4495]) ).
cnf(t23160,plain,
converse(zero) = join(composition(converse(zero),X1),converse(zero)),
inference(step,[status(thm)],[t10244,t4495]) ).
cnf(t23161,plain,
converse(zero) = join(converse(zero),composition(converse(zero),X1)),
inference(step,[status(thm)],[t23160,t43]) ).
cnf(t11225,plain,
join(converse(zero),composition(converse(zero),X1)) = converse(zero),
inference(orient,[status(thm)],[t23161]) ).
cnf(t2583,plain,
composition(join(zero,X1),zero) = join(zero,composition(join(X1,zero),zero)),
inference(cp,[status(thm)],[t2564,t43]) ).
cnf(t2644,plain,
join(zero,composition(join(X1,zero),zero)) = composition(join(zero,X1),zero),
inference(orient,[status(thm)],[t2583]) ).
cnf(t4477,plain,
composition(join(top,X1),zero) = join(zero,composition(X1,zero)),
inference(cp,[status(thm)],[t24,t4475]) ).
cnf(t22922,plain,
composition(top,zero) = join(zero,composition(X1,zero)),
inference(step,[status(thm)],[t4477,t358]) ).
cnf(t22923,plain,
zero = join(zero,composition(X1,zero)),
inference(step,[status(thm)],[t22922,t4475]) ).
cnf(t4517,plain,
join(zero,composition(X1,zero)) = zero,
inference(orient,[status(thm)],[t22923]) ).
cnf(t22926,plain,
zero = composition(join(zero,X1),zero),
inference(step,[status(thm)],[t2644,t4517]) ).
cnf(t4535,plain,
zero = composition(join(zero,X1),zero),
inference(rw,[status(thm)],[t22926]) ).
cnf(t4573,plain,
composition(join(zero,X1),zero) = zero,
inference(orient,[status(thm)],[t4535]) ).
cnf(t4576,plain,
zero = composition(join(X1,zero),zero),
inference(cp,[status(thm)],[t4573,t43]) ).
cnf(t4593,plain,
composition(join(X1,zero),zero) = zero,
inference(orient,[status(thm)],[t4576]) ).
cnf(t4595,plain,
composition(join(join(X1,zero),X2),zero) = join(zero,composition(X2,zero)),
inference(cp,[status(thm)],[t24,t4593]) ).
cnf(t22948,plain,
composition(join(X1,join(zero,X2)),zero) = join(zero,composition(X2,zero)),
inference(step,[status(thm)],[t4595,t46]) ).
cnf(t22949,plain,
composition(join(X1,join(zero,X2)),zero) = zero,
inference(step,[status(thm)],[t22948,t4517]) ).
cnf(t4776,plain,
composition(join(X1,join(zero,X2)),zero) = zero,
inference(orient,[status(thm)],[t22949]) ).
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(t3946,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(t4464,plain,
composition(join(X1,composition(X2,top)),top) = join(composition(X1,top),composition(X2,top)),
inference(cp,[status(thm)],[t835,t4461]) ).
cnf(t23037,plain,
composition(join(X1,composition(X2,top)),top) = composition(join(X1,X2),top),
inference(step,[status(thm)],[t4464,t24]) ).
cnf(t6497,plain,
composition(join(X1,composition(X2,top)),top) = composition(join(X1,X2),top),
inference(orient,[status(thm)],[t23037]) ).
cnf(t6509,plain,
composition(join(X1,one),top) = composition(join(X1,top),top),
inference(cp,[status(thm)],[t6497,t185]) ).
cnf(t23038,plain,
composition(join(X1,one),top) = composition(top,top),
inference(step,[status(thm)],[t6509,t352]) ).
cnf(t23039,plain,
composition(join(X1,one),top) = top,
inference(step,[status(thm)],[t23038,t4461]) ).
cnf(t6535,plain,
composition(join(X1,one),top) = top,
inference(orient,[status(thm)],[t23039]) ).
cnf(t6537,plain,
top = composition(join(one,X1),top),
inference(cp,[status(thm)],[t6535,t43]) ).
cnf(t6561,plain,
composition(join(one,X1),top) = top,
inference(orient,[status(thm)],[t6537]) ).
cnf(t6576,plain,
composition(converse(top),join(one,X1)) = converse(top),
inference(cp,[status(thm)],[t3946,t6561]) ).
cnf(t23042,plain,
composition(top,join(one,X1)) = converse(top),
inference(step,[status(thm)],[t6576,t364]) ).
cnf(t23043,plain,
composition(top,join(one,X1)) = top,
inference(step,[status(thm)],[t23042,t364]) ).
cnf(t6601,plain,
composition(top,join(one,X1)) = top,
inference(orient,[status(thm)],[t23043]) ).
cnf(t6602,plain,
top = composition(top,join(X1,one)),
inference(cp,[status(thm)],[t6601,t43]) ).
cnf(t6619,plain,
composition(top,join(X1,one)) = top,
inference(orient,[status(thm)],[t6602]) ).
cnf(t6626,plain,
complement(join(X1,one)) = join(complement(join(X1,one)),composition(converse(top),complement(top))),
inference(cp,[status(thm)],[t54,t6619]) ).
cnf(t23062,plain,
complement(join(X1,one)) = join(complement(join(X1,one)),composition(top,complement(top))),
inference(step,[status(thm)],[t6626,t364]) ).
cnf(t23063,plain,
complement(join(X1,one)) = join(composition(top,complement(top)),complement(join(X1,one))),
inference(step,[status(thm)],[t23062,t43]) ).
cnf(t23064,plain,
complement(join(X1,one)) = join(composition(top,zero),complement(join(X1,one))),
inference(step,[status(thm)],[t23063,t97]) ).
cnf(t23065,plain,
complement(join(X1,one)) = join(zero,complement(join(X1,one))),
inference(step,[status(thm)],[t23064,t4475]) ).
cnf(t7211,plain,
join(zero,complement(join(X1,one))) = complement(join(X1,one)),
inference(orient,[status(thm)],[t23065]) ).
cnf(t7220,plain,
zero = composition(join(X1,complement(join(X2,one))),zero),
inference(cp,[status(thm)],[t4776,t7211]) ).
cnf(t7480,plain,
composition(join(X1,complement(join(X2,one))),zero) = zero,
inference(orient,[status(thm)],[t7220]) ).
cnf(t15022,plain,
zero = composition(X1,zero),
inference(cp,[status(thm)],[t7480,t14809]) ).
cnf(t15027,plain,
composition(X1,zero) = zero,
inference(orient,[status(thm)],[t15022]) ).
cnf(t15034,plain,
converse(zero) = join(converse(zero),zero),
inference(cp,[status(thm)],[t11225,t15027]) ).
cnf(t23274,plain,
converse(zero) = join(zero,converse(zero)),
inference(step,[status(thm)],[t15034,t43]) ).
cnf(t15188,plain,
join(zero,converse(zero)) = converse(zero),
inference(orient,[status(thm)],[t23274]) ).
cnf(t15197,plain,
join(converse(zero),zero) = converse(converse(zero)),
inference(cp,[status(thm)],[t277,t15188]) ).
cnf(t23275,plain,
join(zero,converse(zero)) = converse(converse(zero)),
inference(step,[status(thm)],[t15197,t43]) ).
cnf(t23276,plain,
converse(zero) = converse(converse(zero)),
inference(step,[status(thm)],[t23275,t15188]) ).
cnf(t23277,plain,
converse(zero) = zero,
inference(step,[status(thm)],[t23276,t21]) ).
cnf(t15200,plain,
converse(zero) = zero,
inference(orient,[status(thm)],[t23277]) ).
cnf(t15203,plain,
converse(composition(X1,zero)) = composition(zero,converse(X1)),
inference(cp,[status(thm)],[t27,t15200]) ).
cnf(t23309,plain,
converse(zero) = composition(zero,converse(X1)),
inference(step,[status(thm)],[t15203,t15027]) ).
cnf(t23310,plain,
zero = composition(zero,converse(X1)),
inference(step,[status(thm)],[t23309,t15200]) ).
cnf(t15284,plain,
composition(zero,converse(X1)) = zero,
inference(orient,[status(thm)],[t23310]) ).
cnf(t15301,plain,
zero = composition(zero,X1),
inference(cp,[status(thm)],[t15284,t21]) ).
cnf(t15322,plain,
composition(zero,X1) = zero,
inference(orient,[status(thm)],[t15301]) ).
cnf(t23426,plain,
zero = join(meet(composition(complement(sk2),sk1),sk0),composition(zero,meet(sk1,composition(converse(complement(sk2)),sk0)))),
inference(step,[status(thm)],[t23425,t15322]) ).
cnf(t23427,plain,
zero = join(meet(sk0,composition(complement(sk2),sk1)),composition(zero,meet(sk1,composition(converse(complement(sk2)),sk0)))),
inference(step,[status(thm)],[t23426,t106]) ).
cnf(t23428,plain,
zero = join(meet(sk0,composition(complement(sk2),sk1)),zero),
inference(step,[status(thm)],[t23427,t15322]) ).
cnf(t15502,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t15496,t43]) ).
cnf(t15534,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t15502]) ).
cnf(t23429,plain,
zero = meet(sk0,composition(complement(sk2),sk1)),
inference(step,[status(thm)],[t23428,t15534]) ).
cnf(t17288,plain,
meet(sk0,composition(complement(sk2),sk1)) = zero,
inference(orient,[status(thm)],[t23429]) ).
cnf(t21752,plain,
sk0 = join(zero,meet(sk0,complement(composition(complement(sk2),sk1)))),
inference(cp,[status(thm)],[t21733,t17288]) ).
cnf(t23499,plain,
sk0 = meet(sk0,complement(composition(complement(sk2),sk1))),
inference(step,[status(thm)],[t21752,t15496]) ).
cnf(t22641,plain,
meet(sk0,complement(composition(complement(sk2),sk1))) = sk0,
inference(orient,[status(thm)],[t23499]) ).
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(t15333,plain,
complement(X1) = join(complement(X1),composition(converse(zero),complement(zero))),
inference(cp,[status(thm)],[t54,t15322]) ).
cnf(t23311,plain,
complement(X1) = join(complement(X1),composition(zero,complement(zero))),
inference(step,[status(thm)],[t15333,t15200]) ).
cnf(t23312,plain,
complement(X1) = join(complement(X1),zero),
inference(step,[status(thm)],[t23311,t15322]) ).
cnf(t23313,plain,
complement(X1) = join(zero,complement(X1)),
inference(step,[status(thm)],[t23312,t43]) ).
cnf(t15335,plain,
join(zero,complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t23313]) ).
cnf(t23327,plain,
complement(complement(X1)) = meet(top,X1),
inference(step,[status(thm)],[t118,t15335]) ).
cnf(t15375,plain,
complement(complement(X1)) = meet(top,X1),
inference(rw,[status(thm)],[t23327]) ).
cnf(t15376,plain,
complement(complement(X1)) = meet(top,X1),
inference(orient,[status(thm)],[t15375]) ).
cnf(t15542,plain,
X1 = join(meet(X1,zero),complement(complement(X1))),
inference(cp,[status(thm)],[t14809,t15534]) ).
cnf(t1991,plain,
join(complement(X1),join(join(X2,X1),X3)) = join(top,X3),
inference(cp,[status(thm)],[t46,t1951]) ).
cnf(t22808,plain,
join(complement(X1),join(X2,join(X1,X3))) = join(top,X3),
inference(step,[status(thm)],[t1991,t46]) ).
cnf(t22809,plain,
join(complement(X1),join(X2,join(X1,X3))) = top,
inference(step,[status(thm)],[t22808,t358]) ).
cnf(t2217,plain,
join(complement(X1),join(X2,join(X1,X3))) = top,
inference(orient,[status(thm)],[t22809]) ).
cnf(t7221,plain,
top = join(complement(zero),join(X1,complement(join(X2,one)))),
inference(cp,[status(thm)],[t2217,t7211]) ).
cnf(t9375,plain,
join(complement(zero),join(X1,complement(join(X2,one)))) = top,
inference(orient,[status(thm)],[t7221]) ).
cnf(t15021,plain,
top = join(complement(zero),X1),
inference(cp,[status(thm)],[t9375,t14809]) ).
cnf(t15086,plain,
join(complement(zero),X1) = top,
inference(orient,[status(thm)],[t15021]) ).
cnf(t15087,plain,
top = complement(zero),
inference(cp,[status(thm)],[t15086,t54]) ).
cnf(t15129,plain,
complement(zero) = top,
inference(orient,[status(thm)],[t15087]) ).
cnf(t15151,plain,
meet(X1,zero) = complement(join(complement(X1),top)),
inference(cp,[status(thm)],[t85,t15129]) ).
cnf(t23271,plain,
meet(X1,zero) = complement(top),
inference(step,[status(thm)],[t15151,t352]) ).
cnf(t23272,plain,
meet(X1,zero) = zero,
inference(step,[status(thm)],[t23271,t97]) ).
cnf(t15177,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t23272]) ).
cnf(t23368,plain,
X1 = join(zero,complement(complement(X1))),
inference(step,[status(thm)],[t15542,t15177]) ).
cnf(t23369,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t23368,t15335]) ).
cnf(t23370,plain,
X1 = meet(top,X1),
inference(step,[status(thm)],[t23369,t15376]) ).
cnf(t15583,plain,
meet(top,X1) = X1,
inference(orient,[status(thm)],[t23370]) ).
cnf(t23371,plain,
complement(complement(X1)) = X1,
inference(step,[status(thm)],[t15376,t15583]) ).
cnf(t15584,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t23371]) ).
cnf(t15996,plain,
join(complement(X1),X2) = complement(meet(X1,complement(X2))),
inference(cp,[status(thm)],[t15584,t15940]) ).
cnf(t16279,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(orient,[status(thm)],[t15996]) ).
cnf(c17,plain,
join(composition(complement(sk2),sk1),complement(sk0)) != complement(sk0),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
join(composition(complement(sk2),sk1),complement(sk0)) != complement(sk0),
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(g0_0,plain,
join(composition(complement(sk2),sk1),complement(sk0)) != join(complement(sk0),composition(complement(sk2),sk1)),
inference(rw,[status(thm)],[goal_0,t43]) ).
cnf(g0_1,plain,
complement(meet(sk0,complement(composition(complement(sk2),sk1)))) != join(complement(sk0),composition(complement(sk2),sk1)),
inference(rw,[status(thm)],[g0_0,t22641]) ).
cnf(g0_2,plain,
join(complement(sk0),composition(complement(sk2),sk1)) != join(complement(sk0),composition(complement(sk2),sk1)),
inference(rw,[status(thm)],[g0_1,t16279]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL043+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/5.64 % Computer : n009.cluster.edu
% 0.17/5.64 % Model : x86_64 x86_64
% 0.17/5.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.64 % Memory : 8046.5625MB
% 0.17/5.64 % OS : Linux 6.8.0-71-generic
% 0.17/5.64 % CPULimit : 300
% 0.17/5.64 % WCLimit : 300
% 0.17/5.64 % DateTime : Thu Sep 24 07:35:35 UTC 2026
% 0.17/5.65 % CPUTime :
% 0.17/5.65 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 21.14/8.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.14/8.39 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------