%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL047+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 02:36:12 PM UTC 2026
% Result : Theorem 13.42s 7.34s
% Output : Proof 13.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 76
% Number of leaves : 11
% Syntax : Number of formulae : 204 ( 200 unt; 0 def)
% Number of atoms : 212 ( 211 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Maximal term depth : 6 ( 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 : 276 ( 19 sgn 57 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f3_nnf,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t7,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t44,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t7]) ).
fof(f0,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f0_nnf,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t6,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t20,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t46,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t44,t20]) ).
cnf(t26176,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t46,t44]) ).
cnf(t74,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t26176]) ).
fof(f1,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
fof(f1_nnf,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t11,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t22,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
fof(f10,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f10_nnf,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t13,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t26171,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t13,t20]) ).
cnf(t31,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t26171]) ).
fof(f9,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f9_nnf,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t8,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t56,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(orient,[status(thm)],[t8]) ).
fof(f7,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f7_nnf,plain,
! [X0] : converse(converse(X0)) = X0,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X0] : converse(converse(X0)) = X0,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
converse(converse(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t1,plain,
converse(converse(X1)) = X1,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t19,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t58,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t56,t19]) ).
cnf(t149,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t58]) ).
fof(f5,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
fof(f5_nnf,plain,
! [X0] : composition(X0,one) = X0,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X0] : composition(X0,one) = X0,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
composition(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t0,plain,
composition(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t18,plain,
composition(X1,one) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t150,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t149,t18]) ).
cnf(t26180,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t150,t19]) ).
cnf(t164,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t26180]) ).
cnf(t165,plain,
one = converse(one),
inference(cp,[status(thm)],[t164,t18]) ).
cnf(t171,plain,
converse(one) = one,
inference(orient,[status(thm)],[t165]) ).
cnf(t26181,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t164,t171]) ).
cnf(t181,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t26181]) ).
cnf(t182,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t181]) ).
cnf(t185,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t31,t182]) ).
cnf(t26183,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t185,t171]) ).
cnf(t26184,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t26183,t182]) ).
cnf(t209,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t26184]) ).
cnf(t219,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t44,t209]) ).
cnf(t226,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t219]) ).
fof(f2,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(f2_nnf,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t14,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t15,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t14]) ).
cnf(t21,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t15]) ).
cnf(t26189,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t21,t20]) ).
cnf(t26190,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t26189,t44]) ).
cnf(t26191,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t26190,t20]) ).
cnf(t268,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t26191]) ).
fof(f12,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
fof(f12_nnf,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t5,plain,
meet(X1,complement(X1)) = zero,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t63,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t5]) ).
cnf(t269,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t268,t63]) ).
cnf(t26194,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t269,t44]) ).
cnf(t290,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t26194]) ).
fof(f11,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
fof(f11_nnf,plain,
! [X0] : top = join(X0,complement(X0)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X0] : top = join(X0,complement(X0)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
top = join(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t4,plain,
join(X1,complement(X1)) = top,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t25,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t4]) ).
cnf(t45,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t44,t25]) ).
cnf(t26174,plain,
zero = complement(top),
inference(step,[status(thm)],[t45,t63]) ).
cnf(t65,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t26174]) ).
cnf(t213,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t209,t65]) ).
cnf(t26185,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t213,t65]) ).
cnf(t26186,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t26185,t65]) ).
cnf(t220,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t26186]) ).
cnf(t221,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t22,t220]) ).
cnf(t236,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t221]) ).
cnf(t292,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t236,t290]) ).
cnf(t26195,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t292,t290]) ).
cnf(t294,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t26195]) ).
cnf(t26196,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t290,t294]) ).
cnf(t302,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t26196]) ).
cnf(t322,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t302]) ).
cnf(t26203,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t226,t322]) ).
cnf(t324,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t26203]) ).
cnf(t329,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t324]) ).
cnf(t331,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t209,t329]) ).
cnf(t26208,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t331,t329]) ).
cnf(t26209,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t26208,t329]) ).
cnf(t339,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t26209]) ).
cnf(t341,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t22,t339]) ).
cnf(t434,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t341]) ).
cnf(t438,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1),
inference(cp,[status(thm)],[t434,t268]) ).
cnf(t26230,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t438,t268]) ).
cnf(t26231,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t26230,t20]) ).
cnf(t478,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t26231]) ).
cnf(t480,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t478,t74]) ).
cnf(t487,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t480]) ).
cnf(t330,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(cp,[status(thm)],[t329,t44]) ).
cnf(t545,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t330]) ).
cnf(t548,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(cp,[status(thm)],[t545,t329]) ).
cnf(t563,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(orient,[status(thm)],[t548]) ).
cnf(t569,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t329,t563]) ).
cnf(t606,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t569]) ).
cnf(t492,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t22,t487]) ).
cnf(t1846,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t492]) ).
cnf(t26248,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(step,[status(thm)],[t268,t606]) ).
cnf(t627,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[t26248]) ).
cnf(t4493,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(orient,[status(thm)],[t627]) ).
cnf(t4572,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(cp,[status(thm)],[t1846,t4493]) ).
cnf(t4685,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t4572]) ).
cnf(t547,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(cp,[status(thm)],[t545,t329]) ).
cnf(t553,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t547]) ).
cnf(t557,plain,
meet(complement(X1),X2) = complement(join(X1,complement(X2))),
inference(cp,[status(thm)],[t329,t553]) ).
cnf(t576,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(orient,[status(thm)],[t557]) ).
cnf(t585,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(cp,[status(thm)],[t576,t329]) ).
cnf(t1013,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(orient,[status(thm)],[t585]) ).
cnf(t4688,plain,
join(X1,complement(X2)) = join(X1,complement(join(X2,X1))),
inference(cp,[status(thm)],[t4685,t1013]) ).
cnf(t5476,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t4688]) ).
cnf(t5558,plain,
meet(X1,complement(complement(join(X2,complement(X1))))) = complement(join(complement(X1),complement(X2))),
inference(cp,[status(thm)],[t606,t5476]) ).
cnf(t26343,plain,
meet(X1,join(X2,complement(X1))) = complement(join(complement(X1),complement(X2))),
inference(step,[status(thm)],[t5558,t329]) ).
cnf(t26344,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(step,[status(thm)],[t26343,t44]) ).
cnf(t5564,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t26344]) ).
cnf(t5592,plain,
meet(X1,X2) = meet(X1,join(complement(X1),X2)),
inference(cp,[status(thm)],[t5564,t20]) ).
cnf(t5608,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t5592]) ).
cnf(t4723,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,join(meet(X3,X1),X2)),
inference(cp,[status(thm)],[t1846,t4685]) ).
cnf(t26634,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,X2),
inference(step,[status(thm)],[t4723,t1846]) ).
cnf(t21321,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,X2),
inference(orient,[status(thm)],[t26634]) ).
cnf(t21333,plain,
join(X1,X2) = join(X1,meet(X2,join(X3,complement(X1)))),
inference(cp,[status(thm)],[t21321,t553]) ).
cnf(t22870,plain,
join(X1,meet(X2,join(X3,complement(X1)))) = join(X1,X2),
inference(orient,[status(thm)],[t21333]) ).
cnf(t22945,plain,
meet(X1,meet(X2,join(X3,complement(complement(X1))))) = meet(X1,join(complement(X1),X2)),
inference(cp,[status(thm)],[t5608,t22870]) ).
cnf(t26653,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,join(complement(X1),X2)),
inference(step,[status(thm)],[t22945,t329]) ).
cnf(t26654,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(step,[status(thm)],[t26653,t5608]) ).
cnf(t22974,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t26654]) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( join(X0,X2) = X2
& join(X0,X1) = X1 )
=> join(X0,meet(X1,X2)) = meet(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( join(X0,X2) = X2
& join(X0,X1) = X1 )
=> join(X0,meet(X1,X2)) = meet(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0,X1,X2] :
( join(X0,meet(X1,X2)) != meet(X1,X2)
& join(X0,X2) = X2
& join(X0,X1) = X1 ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( join(sk0,meet(sk1,sk2)) != meet(sk1,sk2)
& join(sk0,sk2) = sk2
& join(sk0,sk1) = sk1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f13_nnf]) ).
cnf(c14,plain,
join(sk0,sk2) = sk2,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t3,plain,
join(sk0,sk2) = sk2,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t26173,plain,
join(sk2,sk0) = sk2,
inference(step,[status(thm)],[t3,t20]) ).
cnf(t42,plain,
join(sk2,sk0) = sk2,
inference(orient,[status(thm)],[t26173]) ).
cnf(t23108,plain,
meet(sk0,X1) = meet(sk0,meet(X1,sk2)),
inference(cp,[status(thm)],[t22974,t42]) ).
cnf(t23212,plain,
meet(sk0,meet(X1,sk2)) = meet(sk0,X1),
inference(orient,[status(thm)],[t23108]) ).
cnf(t23230,plain,
meet(X1,sk2) = join(meet(X1,sk2),meet(sk0,X1)),
inference(cp,[status(thm)],[t487,t23212]) ).
cnf(t24708,plain,
join(meet(X1,sk2),meet(sk0,X1)) = meet(X1,sk2),
inference(orient,[status(thm)],[t23230]) ).
cnf(t24753,plain,
meet(X1,sk2) = join(meet(X1,sk2),meet(X1,sk0)),
inference(cp,[status(thm)],[t24708,t74]) ).
cnf(t26094,plain,
join(meet(X1,sk2),meet(X1,sk0)) = meet(X1,sk2),
inference(orient,[status(thm)],[t24753]) ).
cnf(c13,plain,
join(sk0,sk1) = sk1,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t2,plain,
join(sk0,sk1) = sk1,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t26172,plain,
join(sk1,sk0) = sk1,
inference(step,[status(thm)],[t2,t20]) ).
cnf(t40,plain,
join(sk1,sk0) = sk1,
inference(orient,[status(thm)],[t26172]) ).
cnf(t41,plain,
join(sk1,join(sk0,X1)) = join(sk1,X1),
inference(cp,[status(thm)],[t22,t40]) ).
cnf(t77,plain,
join(sk1,join(sk0,X1)) = join(sk1,X1),
inference(orient,[status(thm)],[t41]) ).
cnf(t78,plain,
join(sk1,complement(sk0)) = join(sk1,top),
inference(cp,[status(thm)],[t77,t25]) ).
cnf(t26178,plain,
join(sk1,complement(sk0)) = join(top,sk1),
inference(step,[status(thm)],[t78,t20]) ).
cnf(t80,plain,
join(sk1,complement(sk0)) = join(top,sk1),
inference(orient,[status(thm)],[t26178]) ).
cnf(t436,plain,
join(X1,complement(X1)) = join(X1,top),
inference(cp,[status(thm)],[t434,t25]) ).
cnf(t26217,plain,
top = join(X1,top),
inference(step,[status(thm)],[t436,t25]) ).
cnf(t446,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t26217]) ).
cnf(t447,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t446,t20]) ).
cnf(t452,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t447]) ).
cnf(t26220,plain,
join(sk1,complement(sk0)) = top,
inference(step,[status(thm)],[t80,t452]) ).
cnf(t453,plain,
join(sk1,complement(sk0)) = top,
inference(orient,[status(thm)],[t26220]) ).
cnf(t580,plain,
meet(complement(sk1),sk0) = complement(top),
inference(cp,[status(thm)],[t576,t453]) ).
cnf(t26243,plain,
meet(sk0,complement(sk1)) = complement(top),
inference(step,[status(thm)],[t580,t74]) ).
cnf(t26244,plain,
meet(sk0,complement(sk1)) = zero,
inference(step,[status(thm)],[t26243,t65]) ).
cnf(t601,plain,
meet(sk0,complement(sk1)) = zero,
inference(orient,[status(thm)],[t26244]) ).
cnf(t603,plain,
sk0 = join(zero,complement(join(complement(sk0),complement(sk1)))),
inference(cp,[status(thm)],[t268,t601]) ).
cnf(t26245,plain,
sk0 = complement(join(complement(sk0),complement(sk1))),
inference(step,[status(thm)],[t603,t294]) ).
cnf(t26246,plain,
sk0 = meet(sk0,sk1),
inference(step,[status(thm)],[t26245,t44]) ).
cnf(t26247,plain,
sk0 = meet(sk1,sk0),
inference(step,[status(thm)],[t26246,t74]) ).
cnf(t604,plain,
meet(sk1,sk0) = sk0,
inference(orient,[status(thm)],[t26247]) ).
cnf(t26097,plain,
meet(sk1,sk2) = join(meet(sk1,sk2),sk0),
inference(cp,[status(thm)],[t26094,t604]) ).
cnf(t26678,plain,
meet(sk2,sk1) = join(meet(sk1,sk2),sk0),
inference(step,[status(thm)],[t26097,t74]) ).
cnf(t26679,plain,
meet(sk2,sk1) = join(sk0,meet(sk1,sk2)),
inference(step,[status(thm)],[t26678,t20]) ).
cnf(t26680,plain,
meet(sk2,sk1) = join(sk0,meet(sk2,sk1)),
inference(step,[status(thm)],[t26679,t74]) ).
cnf(t26136,plain,
join(sk0,meet(sk2,sk1)) = meet(sk2,sk1),
inference(orient,[status(thm)],[t26680]) ).
cnf(c15,plain,
join(sk0,meet(sk1,sk2)) != meet(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
join(sk0,meet(sk1,sk2)) != meet(sk1,sk2),
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(g0_0,plain,
join(sk0,meet(sk2,sk1)) != meet(sk1,sk2),
inference(rw,[status(thm)],[goal_0,t74]) ).
cnf(g0_1,plain,
meet(sk2,sk1) != meet(sk1,sk2),
inference(rw,[status(thm)],[g0_0,t26136]) ).
cnf(g0_2,plain,
meet(sk2,sk1) != meet(sk2,sk1),
inference(rw,[status(thm)],[g0_1,t74]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL047+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.60 % Computer : n010.cluster.edu
% 0.11/5.60 % Model : x86_64 x86_64
% 0.11/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.60 % Memory : 8046.5625MB
% 0.11/5.60 % OS : Linux 6.8.0-71-generic
% 0.11/5.60 % CPULimit : 300
% 0.11/5.60 % WCLimit : 300
% 0.11/5.60 % DateTime : Thu Sep 24 07:38:05 UTC 2026
% 0.11/5.60 % CPUTime :
% 0.11/5.60 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 13.42/7.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.42/7.34 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------