%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL046+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 5.48s 1.28s
% Output : Proof 5.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 12
% Syntax : Number of formulae : 183 ( 178 unt; 0 def)
% Number of atoms : 192 ( 191 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 23 ~; 3 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 231 ( 30 sgn 57 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,conjecture,
! [X0,X1,X2] :
( join(X0,meet(X1,X2)) = meet(X1,X2)
=> ( join(X0,X2) = X2
& join(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( join(X0,meet(X1,X2)) = meet(X1,X2)
=> ( join(X0,X2) = X2
& join(X0,X1) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0,X1,X2] :
( ( join(X0,X2) != X2
| join(X0,X1) != X1 )
& join(X0,meet(X1,X2)) = meet(X1,X2) ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( ( join(sk0,sk2) != sk2
| join(sk0,sk1) != sk1 )
& join(sk0,meet(sk1,sk2)) = meet(sk1,sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f13_nnf]) ).
cnf(c14,plain,
( join(sk0,sk2) != sk2
| join(sk0,sk1) != sk1 ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t15,plain,
ifeq(join(sk0,sk1),sk1,ifeq(join(sk0,sk2),sk2,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
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(t5,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t22,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t988,plain,
ifeq(join(sk1,sk0),sk1,ifeq(join(sk0,sk2),sk2,false,true),true) = true,
inference(step,[status(thm)],[t15,t22]) ).
cnf(t989,plain,
ifeq(join(sk1,sk0),sk1,ifeq(join(sk2,sk0),sk2,false,true),true) = true,
inference(step,[status(thm)],[t988,t22]) ).
cnf(t65,plain,
ifeq(join(sk1,sk0),sk1,ifeq(join(sk2,sk0),sk2,false,true),true) = true,
inference(orient,[status(thm)],[t989]) ).
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(t14,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t16,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t14]) ).
cnf(t23,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t16]) ).
cnf(t1009,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t23,t22]) ).
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(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]) ).
cnf(t1010,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t1009,t44]) ).
cnf(t1011,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t1010,t22]) ).
cnf(t282,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t1011]) ).
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(t11,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t24,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
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(t27,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t29,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(cp,[status(thm)],[t24,t27]) ).
cnf(t257,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(orient,[status(thm)],[t29]) ).
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(t13,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t987,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t13,t22]) ).
cnf(t33,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t987]) ).
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(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/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(t20,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,t20]) ).
cnf(t137,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/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(t19,plain,
composition(X1,one) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t138,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t137,t19]) ).
cnf(t996,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t138,t20]) ).
cnf(t152,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t996]) ).
cnf(t153,plain,
one = converse(one),
inference(cp,[status(thm)],[t152,t19]) ).
cnf(t159,plain,
converse(one) = one,
inference(orient,[status(thm)],[t153]) ).
cnf(t997,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t152,t159]) ).
cnf(t169,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t997]) ).
cnf(t170,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t169]) ).
cnf(t173,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t33,t170]) ).
cnf(t999,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t173,t159]) ).
cnf(t1000,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t999,t170]) ).
cnf(t197,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t1000]) ).
cnf(t263,plain,
join(top,complement(X1)) = join(X1,complement(X1)),
inference(cp,[status(thm)],[t257,t197]) ).
cnf(t1007,plain,
join(top,complement(X1)) = top,
inference(step,[status(thm)],[t263,t27]) ).
cnf(t274,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t1007]) ).
cnf(t275,plain,
top = join(top,meet(X1,X2)),
inference(cp,[status(thm)],[t274,t44]) ).
cnf(t302,plain,
join(top,meet(X1,X2)) = top,
inference(orient,[status(thm)],[t275]) ).
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(t63,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t283,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t282,t63]) ).
cnf(t1012,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t283,t44]) ).
cnf(t307,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t1012]) ).
cnf(t45,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t44,t27]) ).
cnf(t990,plain,
zero = complement(top),
inference(step,[status(thm)],[t45,t63]) ).
cnf(t66,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t990]) ).
cnf(t201,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t197,t66]) ).
cnf(t1001,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t201,t66]) ).
cnf(t1002,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t1001,t66]) ).
cnf(t208,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t1002]) ).
cnf(t209,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t24,t208]) ).
cnf(t224,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t209]) ).
cnf(t309,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t224,t307]) ).
cnf(t1013,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t309,t307]) ).
cnf(t311,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t1013]) ).
cnf(t1014,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t307,t311]) ).
cnf(t318,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t1014]) ).
cnf(t335,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t318]) ).
cnf(t336,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t302,t335]) ).
cnf(t344,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t336]) ).
cnf(t1026,plain,
join(X1,join(complement(X1),X2)) = top,
inference(step,[status(thm)],[t257,t344]) ).
cnf(t345,plain,
join(X1,join(complement(X1),X2)) = top,
inference(orient,[status(thm)],[t1026]) ).
cnf(t207,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t44,t197]) ).
cnf(t214,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t207]) ).
cnf(t1021,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t214,t335]) ).
cnf(t338,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t1021]) ).
cnf(t363,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t338]) ).
cnf(t371,plain,
top = join(complement(X1),join(X1,X2)),
inference(cp,[status(thm)],[t345,t363]) ).
cnf(t470,plain,
join(complement(X1),join(X1,X2)) = top,
inference(orient,[status(thm)],[t371]) ).
cnf(t484,plain,
X1 = join(meet(X1,join(X1,X2)),complement(top)),
inference(cp,[status(thm)],[t282,t470]) ).
cnf(t1041,plain,
X1 = join(complement(top),meet(X1,join(X1,X2))),
inference(step,[status(thm)],[t484,t22]) ).
cnf(t1042,plain,
X1 = join(zero,meet(X1,join(X1,X2))),
inference(step,[status(thm)],[t1041,t66]) ).
cnf(t1043,plain,
X1 = meet(X1,join(X1,X2)),
inference(step,[status(thm)],[t1042,t311]) ).
cnf(t485,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t1043]) ).
cnf(t25,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(cp,[status(thm)],[t24,t22]) ).
cnf(t696,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(orient,[status(thm)],[t25]) ).
cnf(t727,plain,
X1 = meet(X1,join(X2,join(X1,X3))),
inference(cp,[status(thm)],[t485,t696]) ).
cnf(t925,plain,
meet(X1,join(X2,join(X1,X3))) = X1,
inference(orient,[status(thm)],[t727]) ).
cnf(c13,plain,
join(sk0,meet(sk1,sk2)) = meet(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t6,plain,
join(sk0,meet(sk1,sk2)) = meet(sk1,sk2),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t42,plain,
join(sk0,meet(sk1,sk2)) = meet(sk1,sk2),
inference(orient,[status(thm)],[t6]) ).
cnf(t77,plain,
join(sk0,meet(sk1,sk2)) = meet(sk1,sk2),
inference(rw,[status(thm)],[t42]) ).
cnf(t46,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t44,t22]) ).
cnf(t992,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t46,t44]) ).
cnf(t75,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t992]) ).
cnf(t994,plain,
join(sk0,meet(sk2,sk1)) = meet(sk1,sk2),
inference(step,[status(thm)],[t77,t75]) ).
cnf(t995,plain,
join(sk0,meet(sk2,sk1)) = meet(sk2,sk1),
inference(step,[status(thm)],[t994,t75]) ).
cnf(t100,plain,
join(sk0,meet(sk2,sk1)) = meet(sk2,sk1),
inference(orient,[status(thm)],[t995]) ).
cnf(t928,plain,
sk0 = meet(sk0,join(X1,meet(sk2,sk1))),
inference(cp,[status(thm)],[t925,t100]) ).
cnf(t967,plain,
meet(sk0,join(X1,meet(sk2,sk1))) = sk0,
inference(orient,[status(thm)],[t928]) ).
cnf(t365,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t197,t363]) ).
cnf(t1032,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t365,t363]) ).
cnf(t1033,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t1032,t363]) ).
cnf(t377,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t1033]) ).
cnf(t379,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t24,t377]) ).
cnf(t440,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t379]) ).
cnf(t442,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1),
inference(cp,[status(thm)],[t440,t282]) ).
cnf(t1039,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t442,t282]) ).
cnf(t1040,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t1039,t22]) ).
cnf(t446,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t1040]) ).
cnf(t448,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t446,t75]) ).
cnf(t453,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t448]) ).
cnf(t968,plain,
sk0 = meet(sk0,sk1),
inference(cp,[status(thm)],[t967,t453]) ).
cnf(t1075,plain,
sk0 = meet(sk1,sk0),
inference(step,[status(thm)],[t968,t75]) ).
cnf(t977,plain,
meet(sk1,sk0) = sk0,
inference(orient,[status(thm)],[t1075]) ).
cnf(t969,plain,
sk0 = meet(sk0,sk2),
inference(cp,[status(thm)],[t967,t446]) ).
cnf(t1076,plain,
sk0 = meet(sk2,sk0),
inference(step,[status(thm)],[t969,t75]) ).
cnf(t982,plain,
meet(sk2,sk0) = sk0,
inference(orient,[status(thm)],[t1076]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t21,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
true != ifeq(join(sk1,sk0),sk1,ifeq(join(sk2,sk0),sk2,false,true),true),
inference(rw,[status(thm)],[goal_0,t65]) ).
cnf(g0_1,plain,
true != ifeq(join(sk0,sk1),sk1,ifeq(join(sk2,sk0),sk2,false,true),true),
inference(rw,[status(thm)],[g0_0,t22]) ).
cnf(g0_2,plain,
true != ifeq(join(meet(sk1,sk0),sk1),sk1,ifeq(join(sk2,sk0),sk2,false,true),true),
inference(rw,[status(thm)],[g0_1,t977]) ).
cnf(g0_3,plain,
true != ifeq(join(meet(sk0,sk1),sk1),sk1,ifeq(join(sk2,sk0),sk2,false,true),true),
inference(rw,[status(thm)],[g0_2,t75]) ).
cnf(g0_4,plain,
true != ifeq(join(meet(sk0,sk1),sk1),sk1,ifeq(join(sk2,meet(sk2,sk0)),sk2,false,true),true),
inference(rw,[status(thm)],[g0_3,t982]) ).
cnf(g0_5,plain,
true != ifeq(join(meet(sk0,sk1),sk1),sk1,ifeq(join(sk2,meet(sk0,sk2)),sk2,false,true),true),
inference(rw,[status(thm)],[g0_4,t75]) ).
cnf(g0_6,plain,
true != ifeq(join(meet(sk0,sk1),sk1),sk1,ifeq(join(meet(sk0,sk2),sk2),sk2,false,true),true),
inference(rw,[status(thm)],[g0_5,t22]) ).
cnf(g0_7,plain,
true != ifeq(join(meet(sk1,sk0),sk1),sk1,ifeq(join(meet(sk0,sk2),sk2),sk2,false,true),true),
inference(rw,[status(thm)],[g0_6,t75]) ).
cnf(g0_8,plain,
true != ifeq(join(sk1,meet(sk1,sk0)),sk1,ifeq(join(meet(sk0,sk2),sk2),sk2,false,true),true),
inference(rw,[status(thm)],[g0_7,t22]) ).
cnf(g0_9,plain,
true != ifeq(join(sk1,meet(sk1,sk0)),sk1,ifeq(join(sk2,meet(sk0,sk2)),sk2,false,true),true),
inference(rw,[status(thm)],[g0_8,t22]) ).
cnf(g0_10,plain,
true != ifeq(join(sk1,meet(sk1,sk0)),sk1,ifeq(sk2,sk2,false,true),true),
inference(rw,[status(thm)],[g0_9,t453]) ).
cnf(g0_11,plain,
true != ifeq(join(sk1,meet(sk0,sk1)),sk1,ifeq(sk2,sk2,false,true),true),
inference(rw,[status(thm)],[g0_10,t75]) ).
cnf(g0_12,plain,
true != ifeq(join(sk1,meet(sk0,sk1)),sk1,false,true),
inference(rw,[status(thm)],[g0_11,t21]) ).
cnf(g0_13,plain,
true != ifeq(sk1,sk1,false,true),
inference(rw,[status(thm)],[g0_12,t453]) ).
cnf(g0_14,plain,
true != false,
inference(rw,[status(thm)],[g0_13,t21]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL046+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 07:37:28 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.48/1.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.48/1.28 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------