%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL005+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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:34:37 PM UTC 2026
% Result : Theorem 51.03s 11.93s
% Output : Proof 51.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 109
% Number of leaves : 13
% Syntax : Number of formulae : 259 ( 254 unt; 0 def)
% Number of atoms : 264 ( 263 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 37 ( 32 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 349 ( 32 sgn 61 !; 2 ?)
% 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(t5,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t27,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t5]) ).
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(t47,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t6]) ).
cnf(t49,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t47,t27]) ).
cnf(t4520,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t49,t47]) ).
cnf(t72,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t4520]) ).
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(t30,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
fof(f10,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/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(t4516,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t12,t27]) ).
cnf(t42,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t4516]) ).
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(t24,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(t15,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t26,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t24,t15]) ).
cnf(t132,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t26]) ).
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(t133,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t132,t19]) ).
cnf(t4522,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t133,t15]) ).
cnf(t147,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t4522]) ).
cnf(t148,plain,
one = converse(one),
inference(cp,[status(thm)],[t147,t19]) ).
cnf(t154,plain,
converse(one) = one,
inference(orient,[status(thm)],[t148]) ).
cnf(t4523,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t147,t154]) ).
cnf(t164,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t4523]) ).
cnf(t165,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t164]) ).
cnf(t168,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t42,t165]) ).
cnf(t4525,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t168,t154]) ).
cnf(t4526,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t4525,t165]) ).
cnf(t192,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t4526]) ).
cnf(t202,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t47,t192]) ).
cnf(t209,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t202]) ).
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(t16,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t29,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t16]) ).
cnf(t4538,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t29,t27]) ).
cnf(t4539,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t4538,t47]) ).
cnf(t4540,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t4539,t27]) ).
cnf(t288,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t4540]) ).
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(t60,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t289,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t288,t60]) ).
cnf(t4547,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t289,t47]) ).
cnf(t324,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t4547]) ).
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(t34,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t48,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t47,t34]) ).
cnf(t4518,plain,
zero = complement(top),
inference(step,[status(thm)],[t48,t60]) ).
cnf(t63,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t4518]) ).
cnf(t196,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t192,t63]) ).
cnf(t4527,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t196,t63]) ).
cnf(t4528,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t4527,t63]) ).
cnf(t203,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t4528]) ).
cnf(t204,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t30,t203]) ).
cnf(t219,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t204]) ).
cnf(t326,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t219,t324]) ).
cnf(t4548,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t326,t324]) ).
cnf(t328,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t4548]) ).
cnf(t4549,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t324,t328]) ).
cnf(t335,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t4549]) ).
cnf(t350,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t335]) ).
cnf(t4555,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t209,t350]) ).
cnf(t352,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t4555]) ).
cnf(t359,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t352]) ).
cnf(t361,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t192,t359]) ).
cnf(t4562,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t361,t359]) ).
cnf(t4563,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t4562,t359]) ).
cnf(t370,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t4563]) ).
cnf(t372,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t30,t370]) ).
cnf(t444,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t372]) ).
cnf(t446,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1),
inference(cp,[status(thm)],[t444,t288]) ).
cnf(t4567,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t446,t288]) ).
cnf(t4568,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t4567,t27]) ).
cnf(t450,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t4568]) ).
cnf(t452,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t450,t72]) ).
cnf(t457,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t452]) ).
cnf(t460,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t30,t457]) ).
cnf(t1115,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t460]) ).
cnf(t360,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(cp,[status(thm)],[t359,t47]) ).
cnf(t607,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t360]) ).
cnf(t610,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(cp,[status(thm)],[t607,t359]) ).
cnf(t637,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(orient,[status(thm)],[t610]) ).
cnf(t647,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t359,t637]) ).
cnf(t684,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t647]) ).
cnf(t4590,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(step,[status(thm)],[t288,t684]) ).
cnf(t710,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[t4590]) ).
cnf(t1907,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(orient,[status(thm)],[t710]) ).
cnf(t1947,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(cp,[status(thm)],[t1115,t1907]) ).
cnf(t1957,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t1947]) ).
cnf(t1961,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(cp,[status(thm)],[t1957,t72]) ).
cnf(t1991,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t1961]) ).
cnf(t2000,plain,
join(complement(X1),X2) = join(complement(X1),meet(X1,X2)),
inference(cp,[status(thm)],[t1991,t359]) ).
cnf(t2756,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t2000]) ).
cnf(t448,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(cp,[status(thm)],[t444,t27]) ).
cnf(t463,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t448]) ).
cnf(t36,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(cp,[status(thm)],[t30,t34]) ).
cnf(t252,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(orient,[status(thm)],[t36]) ).
cnf(t214,plain,
top = join(complement(X1),meet(X1,X1)),
inference(cp,[status(thm)],[t34,t209]) ).
cnf(t230,plain,
join(complement(X1),meet(X1,X1)) = top,
inference(orient,[status(thm)],[t214]) ).
cnf(t256,plain,
join(top,meet(X1,X1)) = join(X1,top),
inference(cp,[status(thm)],[t252,t230]) ).
cnf(t258,plain,
join(top,complement(X1)) = join(X1,complement(X1)),
inference(cp,[status(thm)],[t252,t192]) ).
cnf(t4533,plain,
join(top,complement(X1)) = top,
inference(step,[status(thm)],[t258,t34]) ).
cnf(t269,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t4533]) ).
cnf(t270,plain,
top = join(top,meet(X1,X2)),
inference(cp,[status(thm)],[t269,t47]) ).
cnf(t277,plain,
join(top,meet(X1,X2)) = top,
inference(orient,[status(thm)],[t270]) ).
cnf(t4535,plain,
top = join(X1,top),
inference(step,[status(thm)],[t256,t277]) ).
cnf(t282,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t4535]) ).
cnf(t283,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t282,t27]) ).
cnf(t308,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t283]) ).
cnf(t4541,plain,
join(X1,join(complement(X1),X2)) = top,
inference(step,[status(thm)],[t252,t308]) ).
cnf(t309,plain,
join(X1,join(complement(X1),X2)) = top,
inference(orient,[status(thm)],[t4541]) ).
cnf(t465,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),top),
inference(cp,[status(thm)],[t463,t309]) ).
cnf(t4576,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),top),
inference(step,[status(thm)],[t465,t30]) ).
cnf(t4577,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,top)),
inference(step,[status(thm)],[t4576,t30]) ).
cnf(t4578,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),top),
inference(step,[status(thm)],[t4577,t282]) ).
cnf(t4579,plain,
join(complement(X1),join(X2,X1)) = top,
inference(step,[status(thm)],[t4578,t282]) ).
cnf(t521,plain,
join(complement(X1),join(X2,X1)) = top,
inference(orient,[status(thm)],[t4579]) ).
cnf(t528,plain,
top = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t521,t457]) ).
cnf(t4585,plain,
top = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t528,t27]) ).
cnf(t556,plain,
join(X1,complement(meet(X2,X1))) = top,
inference(orient,[status(thm)],[t4585]) ).
cnf(t561,plain,
meet(X1,meet(X2,complement(X1))) = complement(top),
inference(cp,[status(thm)],[t47,t556]) ).
cnf(t4587,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t561,t63]) ).
cnf(t570,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t4587]) ).
cnf(t571,plain,
zero = meet(complement(X1),meet(X2,X1)),
inference(cp,[status(thm)],[t570,t359]) ).
cnf(t581,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t571]) ).
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(t21,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t8]) ).
cnf(t22,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t21,t15]) ).
cnf(t101,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t22]) ).
cnf(t102,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(cp,[status(thm)],[t101,t34]) ).
cnf(t235,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(orient,[status(thm)],[t102]) ).
cnf(t311,plain,
top = converse(top),
inference(cp,[status(thm)],[t308,t235]) ).
cnf(t314,plain,
converse(top) = top,
inference(orient,[status(thm)],[t311]) ).
cnf(t4545,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(step,[status(thm)],[t235,t314]) ).
cnf(t317,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(orient,[status(thm)],[t4545]) ).
cnf(t687,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = complement(top),
inference(cp,[status(thm)],[t684,t317]) ).
cnf(t4616,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(step,[status(thm)],[t687,t63]) ).
cnf(t1902,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(orient,[status(thm)],[t4616]) ).
cnf(t1994,plain,
join(X1,complement(converse(complement(converse(complement(complement(X1))))))) = join(X1,zero),
inference(cp,[status(thm)],[t1991,t1902]) ).
cnf(t4619,plain,
join(X1,complement(converse(complement(converse(X1))))) = join(X1,zero),
inference(step,[status(thm)],[t1994,t359]) ).
cnf(t332,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t328,t27]) ).
cnf(t346,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t332]) ).
cnf(t4620,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t4619,t346]) ).
cnf(t2051,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t4620]) ).
cnf(t2083,plain,
join(X1,converse(complement(converse(complement(converse(converse(X1))))))) = converse(converse(X1)),
inference(cp,[status(thm)],[t101,t2051]) ).
cnf(t4626,plain,
join(X1,converse(complement(converse(complement(X1))))) = converse(converse(X1)),
inference(step,[status(thm)],[t2083,t15]) ).
cnf(t4627,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(step,[status(thm)],[t4626,t15]) ).
cnf(t2393,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(orient,[status(thm)],[t4627]) ).
cnf(t2415,plain,
meet(X1,complement(converse(complement(converse(complement(complement(X1))))))) = complement(complement(X1)),
inference(cp,[status(thm)],[t684,t2393]) ).
cnf(t4628,plain,
meet(X1,complement(converse(complement(converse(X1))))) = complement(complement(X1)),
inference(step,[status(thm)],[t2415,t359]) ).
cnf(t4629,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t4628,t359]) ).
cnf(t2421,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t4629]) ).
cnf(t2443,plain,
zero = meet(complement(complement(converse(complement(converse(X1))))),X1),
inference(cp,[status(thm)],[t581,t2421]) ).
cnf(t4630,plain,
zero = meet(X1,complement(complement(converse(complement(converse(X1)))))),
inference(step,[status(thm)],[t2443,t72]) ).
cnf(t4631,plain,
zero = meet(X1,converse(complement(converse(X1)))),
inference(step,[status(thm)],[t4630,t359]) ).
cnf(t2458,plain,
meet(X1,converse(complement(converse(X1)))) = zero,
inference(orient,[status(thm)],[t4631]) ).
cnf(t2471,plain,
zero = meet(converse(X1),converse(complement(X1))),
inference(cp,[status(thm)],[t2458,t15]) ).
cnf(t2476,plain,
meet(converse(X1),converse(complement(X1))) = zero,
inference(orient,[status(thm)],[t2471]) ).
cnf(t2775,plain,
join(complement(converse(X1)),converse(complement(X1))) = join(complement(converse(X1)),zero),
inference(cp,[status(thm)],[t2756,t2476]) ).
cnf(t4644,plain,
join(converse(complement(X1)),complement(converse(X1))) = join(complement(converse(X1)),zero),
inference(step,[status(thm)],[t2775,t27]) ).
cnf(t4645,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(step,[status(thm)],[t4644,t346]) ).
cnf(t3159,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(orient,[status(thm)],[t4645]) ).
cnf(t3164,plain,
complement(converse(complement(X1))) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t3159,t359]) ).
cnf(t2061,plain,
converse(X1) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t2051,t15]) ).
cnf(t2966,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(orient,[status(thm)],[t2061]) ).
cnf(t4646,plain,
complement(converse(complement(X1))) = converse(X1),
inference(step,[status(thm)],[t3164,t2966]) ).
cnf(t3199,plain,
complement(converse(complement(X1))) = converse(X1),
inference(orient,[status(thm)],[t4646]) ).
cnf(t3204,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(cp,[status(thm)],[t3199,t359]) ).
cnf(t3239,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(orient,[status(thm)],[t3204]) ).
cnf(t3251,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(cp,[status(thm)],[t3239,t101]) ).
cnf(t4080,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(orient,[status(thm)],[t3251]) ).
cnf(t3260,plain,
complement(meet(converse(X1),X2)) = join(converse(complement(X1)),complement(X2)),
inference(cp,[status(thm)],[t607,t3239]) ).
cnf(t4286,plain,
join(converse(complement(X1)),complement(X2)) = complement(meet(converse(X1),X2)),
inference(orient,[status(thm)],[t3260]) ).
cnf(t4328,plain,
complement(join(complement(X1),converse(complement(X2)))) = converse(complement(complement(meet(converse(X1),X2)))),
inference(cp,[status(thm)],[t4080,t4286]) ).
cnf(t4703,plain,
meet(X1,complement(converse(complement(X2)))) = converse(complement(complement(meet(converse(X1),X2)))),
inference(step,[status(thm)],[t4328,t684]) ).
cnf(t4704,plain,
meet(X1,converse(X2)) = converse(complement(complement(meet(converse(X1),X2)))),
inference(step,[status(thm)],[t4703,t3199]) ).
cnf(t4705,plain,
meet(X1,converse(X2)) = converse(meet(converse(X1),X2)),
inference(step,[status(thm)],[t4704,t359]) ).
cnf(t4334,plain,
converse(meet(converse(X1),X2)) = meet(X1,converse(X2)),
inference(orient,[status(thm)],[t4705]) ).
cnf(t4360,plain,
meet(converse(X1),converse(X2)) = converse(meet(X1,X2)),
inference(cp,[status(thm)],[t4334,t15]) ).
cnf(t4455,plain,
meet(converse(X1),converse(X2)) = converse(meet(X1,X2)),
inference(orient,[status(thm)],[t4360]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t20,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
fof(f13,conjecture,
! [X0,X1] :
( join(meet(converse(X0),converse(X1)),converse(meet(X0,X1))) = converse(meet(X0,X1))
& join(converse(meet(X0,X1)),meet(converse(X0),converse(X1))) = meet(converse(X0),converse(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0,X1] :
( join(meet(converse(X0),converse(X1)),converse(meet(X0,X1))) = converse(meet(X0,X1))
& join(converse(meet(X0,X1)),meet(converse(X0),converse(X1))) = meet(converse(X0),converse(X1)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0,X1] :
( join(meet(converse(X0),converse(X1)),converse(meet(X0,X1))) != converse(meet(X0,X1))
| join(converse(meet(X0,X1)),meet(converse(X0),converse(X1))) != meet(converse(X0),converse(X1)) ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( join(meet(converse(sk0),converse(sk1)),converse(meet(sk0,sk1))) != converse(meet(sk0,sk1))
| join(converse(meet(sk0,sk1)),meet(converse(sk0),converse(sk1))) != meet(converse(sk0),converse(sk1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f13_nnf]) ).
cnf(c13,plain,
( join(meet(converse(sk0),converse(sk1)),converse(meet(sk0,sk1))) != converse(meet(sk0,sk1))
| join(converse(meet(sk0,sk1)),meet(converse(sk0),converse(sk1))) != meet(converse(sk0),converse(sk1)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(g0_0,plain,
true != ifeq(join(converse(meet(sk0,sk1)),meet(converse(sk0),converse(sk1))),meet(converse(sk0),converse(sk1)),ifeq(join(converse(meet(sk0,sk1)),meet(converse(sk0),converse(sk1))),converse(meet(sk0,sk1)),false,true),true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(join(meet(converse(sk0),converse(sk1)),converse(meet(sk0,sk1))),meet(converse(sk0),converse(sk1)),ifeq(join(converse(meet(sk0,sk1)),meet(converse(sk0),converse(sk1))),converse(meet(sk0,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_0,t27]) ).
cnf(g0_2,plain,
true != ifeq(join(meet(converse(sk0),converse(sk1)),converse(meet(sk0,sk1))),meet(converse(sk0),converse(sk1)),ifeq(join(converse(meet(sk0,sk1)),meet(converse(sk0),converse(sk1))),converse(meet(sk1,sk0)),false,true),true),
inference(rw,[status(thm)],[g0_1,t72]) ).
cnf(g0_3,plain,
true != ifeq(join(meet(converse(sk1),converse(sk0)),converse(meet(sk0,sk1))),meet(converse(sk0),converse(sk1)),ifeq(join(converse(meet(sk0,sk1)),meet(converse(sk0),converse(sk1))),converse(meet(sk1,sk0)),false,true),true),
inference(rw,[status(thm)],[g0_2,t72]) ).
cnf(g0_4,plain,
true != ifeq(join(meet(converse(sk1),converse(sk0)),converse(meet(sk0,sk1))),converse(meet(sk0,sk1)),ifeq(join(converse(meet(sk0,sk1)),meet(converse(sk0),converse(sk1))),converse(meet(sk1,sk0)),false,true),true),
inference(rw,[status(thm)],[g0_3,t4455]) ).
cnf(g0_5,plain,
true != ifeq(join(meet(converse(sk1),converse(sk0)),converse(meet(sk0,sk1))),converse(meet(sk0,sk1)),ifeq(join(converse(meet(sk0,sk1)),converse(meet(sk0,sk1))),converse(meet(sk1,sk0)),false,true),true),
inference(rw,[status(thm)],[g0_4,t4455]) ).
cnf(g0_6,plain,
true != ifeq(join(meet(converse(sk1),converse(sk0)),converse(meet(sk0,sk1))),converse(meet(sk0,sk1)),ifeq(join(converse(meet(sk0,sk1)),converse(meet(sk0,sk1))),converse(meet(sk0,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_5,t72]) ).
cnf(g0_7,plain,
true != ifeq(join(meet(converse(sk1),converse(sk0)),converse(meet(sk0,sk1))),converse(meet(sk0,sk1)),ifeq(join(converse(meet(sk0,sk1)),converse(meet(sk1,sk0))),converse(meet(sk0,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_6,t72]) ).
cnf(g0_8,plain,
true != ifeq(join(meet(converse(sk1),converse(sk0)),converse(meet(sk0,sk1))),converse(meet(sk0,sk1)),ifeq(join(converse(meet(sk1,sk0)),converse(meet(sk1,sk0))),converse(meet(sk0,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_7,t72]) ).
cnf(g0_9,plain,
true != ifeq(join(meet(converse(sk1),converse(sk0)),converse(meet(sk0,sk1))),converse(meet(sk0,sk1)),ifeq(join(converse(meet(sk1,sk0)),converse(meet(sk1,sk0))),converse(meet(sk1,sk0)),false,true),true),
inference(rw,[status(thm)],[g0_8,t72]) ).
cnf(g0_10,plain,
true != ifeq(join(meet(converse(sk1),converse(sk0)),converse(meet(sk0,sk1))),converse(meet(sk1,sk0)),ifeq(join(converse(meet(sk1,sk0)),converse(meet(sk1,sk0))),converse(meet(sk1,sk0)),false,true),true),
inference(rw,[status(thm)],[g0_9,t72]) ).
cnf(g0_11,plain,
true != ifeq(join(meet(converse(sk1),converse(sk0)),converse(meet(sk0,sk1))),converse(meet(sk1,sk0)),ifeq(join(converse(meet(sk1,sk0)),converse(meet(sk0,sk1))),converse(meet(sk1,sk0)),false,true),true),
inference(rw,[status(thm)],[g0_10,t72]) ).
cnf(g0_12,plain,
true != ifeq(join(meet(converse(sk1),converse(sk0)),converse(meet(sk0,sk1))),converse(meet(sk1,sk0)),ifeq(join(converse(meet(sk1,sk0)),converse(meet(sk0,sk1))),converse(meet(sk0,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_11,t72]) ).
cnf(g0_13,plain,
true != ifeq(join(meet(converse(sk1),converse(sk0)),converse(meet(sk1,sk0))),converse(meet(sk1,sk0)),ifeq(join(converse(meet(sk1,sk0)),converse(meet(sk0,sk1))),converse(meet(sk0,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_12,t72]) ).
cnf(g0_14,plain,
true != ifeq(join(meet(converse(sk1),converse(sk0)),converse(meet(sk1,sk0))),converse(meet(sk1,sk0)),ifeq(join(converse(meet(sk1,sk0)),converse(meet(sk1,sk0))),converse(meet(sk0,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_13,t72]) ).
cnf(g0_15,plain,
true != ifeq(join(meet(converse(sk0),converse(sk1)),converse(meet(sk1,sk0))),converse(meet(sk1,sk0)),ifeq(join(converse(meet(sk1,sk0)),converse(meet(sk1,sk0))),converse(meet(sk0,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_14,t72]) ).
cnf(g0_16,plain,
true != ifeq(join(meet(converse(sk0),converse(sk1)),converse(meet(sk1,sk0))),converse(meet(sk1,sk0)),ifeq(join(converse(meet(sk1,sk0)),converse(meet(sk1,sk0))),converse(meet(sk1,sk0)),false,true),true),
inference(rw,[status(thm)],[g0_15,t72]) ).
cnf(g0_17,plain,
true != ifeq(join(converse(meet(sk1,sk0)),meet(converse(sk0),converse(sk1))),converse(meet(sk1,sk0)),ifeq(join(converse(meet(sk1,sk0)),converse(meet(sk1,sk0))),converse(meet(sk1,sk0)),false,true),true),
inference(rw,[status(thm)],[g0_16,t27]) ).
cnf(g0_18,plain,
true != ifeq(join(converse(meet(sk1,sk0)),meet(converse(sk1),converse(sk0))),converse(meet(sk1,sk0)),ifeq(join(converse(meet(sk1,sk0)),converse(meet(sk1,sk0))),converse(meet(sk1,sk0)),false,true),true),
inference(rw,[status(thm)],[g0_17,t72]) ).
cnf(g0_19,plain,
true != ifeq(join(converse(meet(sk1,sk0)),meet(converse(sk1),converse(sk0))),converse(meet(sk1,sk0)),ifeq(converse(meet(sk1,sk0)),converse(meet(sk1,sk0)),false,true),true),
inference(rw,[status(thm)],[g0_18,t370]) ).
cnf(g0_20,plain,
true != ifeq(join(converse(meet(sk1,sk0)),meet(converse(sk1),converse(sk0))),converse(meet(sk1,sk0)),false,true),
inference(rw,[status(thm)],[g0_19,t20]) ).
cnf(g0_21,plain,
true != ifeq(join(converse(meet(sk1,sk0)),converse(meet(sk1,sk0))),converse(meet(sk1,sk0)),false,true),
inference(rw,[status(thm)],[g0_20,t4455]) ).
cnf(g0_22,plain,
true != ifeq(converse(meet(sk1,sk0)),converse(meet(sk1,sk0)),false,true),
inference(rw,[status(thm)],[g0_21,t370]) ).
cnf(g0_23,plain,
true != false,
inference(rw,[status(thm)],[g0_22,t20]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL005+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.38 % Computer : n004.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 07:06:11 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 51.03/11.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 51.03/11.93 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------