%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL007+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 02:34:39 PM UTC 2026
% Result : Theorem 4.09s 1.01s
% Output : Proof 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 79
% Number of leaves : 12
% Syntax : Number of formulae : 246 ( 242 unt; 0 def)
% Number of atoms : 250 ( 249 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 331 ( 51 sgn 61 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(t39,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t6]) ).
fof(f0,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f0_nnf,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t5,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t19,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t41,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t39,t19]) ).
cnf(t2234,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t41,t39]) ).
cnf(t70,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t2234]) ).
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(t21,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(t2231,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t12,t19]) ).
cnf(t30,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t2231]) ).
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(t51,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(t18,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t53,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t51,t18]) ).
cnf(t129,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t53]) ).
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(t130,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t129,t17]) ).
cnf(t2236,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t130,t18]) ).
cnf(t144,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t2236]) ).
cnf(t145,plain,
one = converse(one),
inference(cp,[status(thm)],[t144,t17]) ).
cnf(t151,plain,
converse(one) = one,
inference(orient,[status(thm)],[t145]) ).
cnf(t2237,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t144,t151]) ).
cnf(t161,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t2237]) ).
cnf(t162,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t161]) ).
cnf(t165,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t30,t162]) ).
cnf(t2239,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t165,t151]) ).
cnf(t2240,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t2239,t162]) ).
cnf(t189,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t2240]) ).
cnf(t199,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t39,t189]) ).
cnf(t206,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t199]) ).
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(t14,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t20,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t14]) ).
cnf(t2254,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t20,t19]) ).
cnf(t2255,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t2254,t39]) ).
cnf(t2256,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t2255,t19]) ).
cnf(t292,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t2256]) ).
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(t58,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t293,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t292,t58]) ).
cnf(t2261,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t293,t39]) ).
cnf(t323,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t2261]) ).
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(t24,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t40,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t39,t24]) ).
cnf(t2232,plain,
zero = complement(top),
inference(step,[status(thm)],[t40,t58]) ).
cnf(t61,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t2232]) ).
cnf(t193,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t189,t61]) ).
cnf(t2241,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t193,t61]) ).
cnf(t2242,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t2241,t61]) ).
cnf(t200,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t2242]) ).
cnf(t201,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t21,t200]) ).
cnf(t216,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t201]) ).
cnf(t325,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t216,t323]) ).
cnf(t2262,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t325,t323]) ).
cnf(t327,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t2262]) ).
cnf(t2263,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t323,t327]) ).
cnf(t334,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t2263]) ).
cnf(t349,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t334]) ).
cnf(t2269,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t206,t349]) ).
cnf(t351,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t2269]) ).
cnf(t358,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t351]) ).
cnf(t360,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t189,t358]) ).
cnf(t2276,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t360,t358]) ).
cnf(t2277,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t2276,t358]) ).
cnf(t369,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t2277]) ).
cnf(t371,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t21,t369]) ).
cnf(t443,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t371]) ).
cnf(t447,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(cp,[status(thm)],[t443,t19]) ).
cnf(t462,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t447]) ).
cnf(t26,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(cp,[status(thm)],[t21,t24]) ).
cnf(t249,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(orient,[status(thm)],[t26]) ).
cnf(t211,plain,
top = join(complement(X1),meet(X1,X1)),
inference(cp,[status(thm)],[t24,t206]) ).
cnf(t227,plain,
join(complement(X1),meet(X1,X1)) = top,
inference(orient,[status(thm)],[t211]) ).
cnf(t253,plain,
join(top,meet(X1,X1)) = join(X1,top),
inference(cp,[status(thm)],[t249,t227]) ).
cnf(t255,plain,
join(top,complement(X1)) = join(X1,complement(X1)),
inference(cp,[status(thm)],[t249,t189]) ).
cnf(t2247,plain,
join(top,complement(X1)) = top,
inference(step,[status(thm)],[t255,t24]) ).
cnf(t266,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t2247]) ).
cnf(t267,plain,
top = join(top,meet(X1,X2)),
inference(cp,[status(thm)],[t266,t39]) ).
cnf(t274,plain,
join(top,meet(X1,X2)) = top,
inference(orient,[status(thm)],[t267]) ).
cnf(t2249,plain,
top = join(X1,top),
inference(step,[status(thm)],[t253,t274]) ).
cnf(t280,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t2249]) ).
cnf(t281,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t280,t19]) ).
cnf(t286,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t281]) ).
cnf(t2252,plain,
join(X1,join(complement(X1),X2)) = top,
inference(step,[status(thm)],[t249,t286]) ).
cnf(t287,plain,
join(X1,join(complement(X1),X2)) = top,
inference(orient,[status(thm)],[t2252]) ).
cnf(t464,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),top),
inference(cp,[status(thm)],[t462,t287]) ).
cnf(t2290,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),top),
inference(step,[status(thm)],[t464,t21]) ).
cnf(t2291,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,top)),
inference(step,[status(thm)],[t2290,t21]) ).
cnf(t2292,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),top),
inference(step,[status(thm)],[t2291,t280]) ).
cnf(t2293,plain,
join(complement(X1),join(X2,X1)) = top,
inference(step,[status(thm)],[t2292,t280]) ).
cnf(t520,plain,
join(complement(X1),join(X2,X1)) = top,
inference(orient,[status(thm)],[t2293]) ).
cnf(t445,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1),
inference(cp,[status(thm)],[t443,t292]) ).
cnf(t2281,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t445,t292]) ).
cnf(t2282,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t2281,t19]) ).
cnf(t449,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t2282]) ).
cnf(t451,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t449,t70]) ).
cnf(t456,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t451]) ).
cnf(t527,plain,
top = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t520,t456]) ).
cnf(t2299,plain,
top = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t527,t19]) ).
cnf(t555,plain,
join(X1,complement(meet(X2,X1))) = top,
inference(orient,[status(thm)],[t2299]) ).
cnf(t560,plain,
meet(X1,meet(X2,complement(X1))) = complement(top),
inference(cp,[status(thm)],[t39,t555]) ).
cnf(t2301,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t560,t61]) ).
cnf(t569,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t2301]) ).
cnf(t570,plain,
zero = meet(complement(X1),meet(X2,X1)),
inference(cp,[status(thm)],[t569,t358]) ).
cnf(t580,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t570]) ).
cnf(t366,plain,
top = join(complement(X1),join(X1,X2)),
inference(cp,[status(thm)],[t287,t358]) ).
cnf(t472,plain,
join(complement(X1),join(X1,X2)) = top,
inference(orient,[status(thm)],[t366]) ).
cnf(t485,plain,
X1 = join(meet(X1,join(X1,X2)),complement(top)),
inference(cp,[status(thm)],[t292,t472]) ).
cnf(t2283,plain,
X1 = join(complement(top),meet(X1,join(X1,X2))),
inference(step,[status(thm)],[t485,t19]) ).
cnf(t2284,plain,
X1 = join(zero,meet(X1,join(X1,X2))),
inference(step,[status(thm)],[t2283,t61]) ).
cnf(t2285,plain,
X1 = meet(X1,join(X1,X2)),
inference(step,[status(thm)],[t2284,t327]) ).
cnf(t486,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t2285]) ).
cnf(t586,plain,
zero = meet(complement(join(X1,X2)),X1),
inference(cp,[status(thm)],[t580,t486]) ).
cnf(t2302,plain,
zero = meet(X1,complement(join(X1,X2))),
inference(step,[status(thm)],[t586,t70]) ).
cnf(t589,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(orient,[status(thm)],[t2302]) ).
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(t34,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t8]) ).
cnf(t36,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t34,t18]) ).
cnf(t98,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t36]) ).
cnf(t460,plain,
join(X1,converse(meet(X2,converse(X1)))) = converse(converse(X1)),
inference(cp,[status(thm)],[t98,t456]) ).
cnf(t2306,plain,
join(X1,converse(meet(X2,converse(X1)))) = X1,
inference(step,[status(thm)],[t460,t18]) ).
cnf(t742,plain,
join(X1,converse(meet(X2,converse(X1)))) = X1,
inference(orient,[status(thm)],[t2306]) ).
cnf(t359,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(cp,[status(thm)],[t358,t39]) ).
cnf(t606,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t359]) ).
cnf(t609,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(cp,[status(thm)],[t606,t358]) ).
cnf(t636,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(orient,[status(thm)],[t609]) ).
cnf(t646,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t358,t636]) ).
cnf(t683,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t646]) ).
cnf(t2304,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(step,[status(thm)],[t292,t683]) ).
cnf(t709,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[t2304]) ).
cnf(t1906,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(orient,[status(thm)],[t709]) ).
cnf(t491,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t486,t19]) ).
cnf(t492,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t491]) ).
cnf(t587,plain,
zero = meet(complement(join(X1,X2)),X2),
inference(cp,[status(thm)],[t580,t492]) ).
cnf(t2303,plain,
zero = meet(X2,complement(join(X1,X2))),
inference(step,[status(thm)],[t587,t70]) ).
cnf(t595,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t2303]) ).
cnf(t596,plain,
zero = meet(join(X1,X2),complement(join(X2,X1))),
inference(cp,[status(thm)],[t595,t462]) ).
cnf(t1783,plain,
meet(join(X1,X2),complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t596]) ).
cnf(t561,plain,
join(X1,converse(complement(meet(X2,converse(X1))))) = converse(top),
inference(cp,[status(thm)],[t98,t555]) ).
cnf(t99,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(cp,[status(thm)],[t98,t24]) ).
cnf(t232,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(orient,[status(thm)],[t99]) ).
cnf(t289,plain,
top = converse(top),
inference(cp,[status(thm)],[t286,t232]) ).
cnf(t313,plain,
converse(top) = top,
inference(orient,[status(thm)],[t289]) ).
cnf(t2328,plain,
join(X1,converse(complement(meet(X2,converse(X1))))) = top,
inference(step,[status(thm)],[t561,t313]) ).
cnf(t1744,plain,
join(X1,converse(complement(meet(X2,converse(X1))))) = top,
inference(orient,[status(thm)],[t2328]) ).
cnf(t488,plain,
converse(X1) = meet(converse(X1),converse(join(X1,X2))),
inference(cp,[status(thm)],[t486,t34]) ).
cnf(t957,plain,
meet(converse(X1),converse(join(X1,X2))) = converse(X1),
inference(orient,[status(thm)],[t488]) ).
fof(f13,conjecture,
! [X0,X1] :
( meet(X0,converse(X1)) = zero
=> meet(converse(X0),X1) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0,X1] :
( meet(X0,converse(X1)) = zero
=> meet(converse(X0),X1) = zero ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0,X1] :
( meet(converse(X0),X1) != zero
& meet(X0,converse(X1)) = zero ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( meet(converse(sk0),sk1) != zero
& meet(sk0,converse(sk1)) = zero ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f13_nnf]) ).
cnf(c13,plain,
meet(sk0,converse(sk1)) = zero,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t4,plain,
meet(sk0,converse(sk1)) = zero,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t60,plain,
meet(sk0,converse(sk1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t1917,plain,
sk0 = join(zero,meet(sk0,complement(converse(sk1)))),
inference(cp,[status(thm)],[t1906,t60]) ).
cnf(t2330,plain,
sk0 = meet(sk0,complement(converse(sk1))),
inference(step,[status(thm)],[t1917,t327]) ).
cnf(t1957,plain,
meet(sk0,complement(converse(sk1))) = sk0,
inference(orient,[status(thm)],[t2330]) ).
cnf(t1972,plain,
join(complement(sk0),converse(sk1)) = complement(sk0),
inference(cp,[status(thm)],[t636,t1957]) ).
cnf(t2331,plain,
join(converse(sk1),complement(sk0)) = complement(sk0),
inference(step,[status(thm)],[t1972,t19]) ).
cnf(t1976,plain,
join(converse(sk1),complement(sk0)) = complement(sk0),
inference(orient,[status(thm)],[t2331]) ).
cnf(t1989,plain,
converse(converse(sk1)) = meet(converse(converse(sk1)),converse(complement(sk0))),
inference(cp,[status(thm)],[t957,t1976]) ).
cnf(t2332,plain,
sk1 = meet(converse(converse(sk1)),converse(complement(sk0))),
inference(step,[status(thm)],[t1989,t18]) ).
cnf(t2333,plain,
sk1 = meet(sk1,converse(complement(sk0))),
inference(step,[status(thm)],[t2332,t18]) ).
cnf(t1998,plain,
meet(sk1,converse(complement(sk0))) = sk1,
inference(orient,[status(thm)],[t2333]) ).
cnf(t2016,plain,
top = join(complement(sk0),converse(complement(sk1))),
inference(cp,[status(thm)],[t1744,t1998]) ).
cnf(t2177,plain,
join(complement(sk0),converse(complement(sk1))) = top,
inference(orient,[status(thm)],[t2016]) ).
cnf(t2181,plain,
zero = meet(top,complement(join(converse(complement(sk1)),complement(sk0)))),
inference(cp,[status(thm)],[t1783,t2177]) ).
cnf(t64,plain,
meet(top,X1) = complement(join(zero,complement(X1))),
inference(cp,[status(thm)],[t39,t61]) ).
cnf(t75,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(orient,[status(thm)],[t64]) ).
cnf(t2266,plain,
complement(complement(X1)) = meet(top,X1),
inference(step,[status(thm)],[t75,t327]) ).
cnf(t336,plain,
complement(complement(X1)) = meet(top,X1),
inference(rw,[status(thm)],[t2266]) ).
cnf(t2278,plain,
X1 = meet(top,X1),
inference(step,[status(thm)],[t336,t358]) ).
cnf(t372,plain,
meet(top,X1) = X1,
inference(orient,[status(thm)],[t2278]) ).
cnf(t2338,plain,
zero = complement(join(converse(complement(sk1)),complement(sk0))),
inference(step,[status(thm)],[t2181,t372]) ).
cnf(t608,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(cp,[status(thm)],[t606,t358]) ).
cnf(t615,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t608]) ).
cnf(t626,plain,
meet(complement(X1),X2) = complement(join(X1,complement(X2))),
inference(cp,[status(thm)],[t358,t615]) ).
cnf(t657,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(orient,[status(thm)],[t626]) ).
cnf(t2339,plain,
zero = meet(complement(converse(complement(sk1))),sk0),
inference(step,[status(thm)],[t2338,t657]) ).
cnf(t2340,plain,
zero = meet(sk0,complement(converse(complement(sk1)))),
inference(step,[status(thm)],[t2339,t70]) ).
cnf(t2187,plain,
meet(sk0,complement(converse(complement(sk1)))) = zero,
inference(orient,[status(thm)],[t2340]) ).
cnf(t2188,plain,
sk0 = join(zero,meet(sk0,complement(complement(converse(complement(sk1)))))),
inference(cp,[status(thm)],[t1906,t2187]) ).
cnf(t2341,plain,
sk0 = meet(sk0,complement(complement(converse(complement(sk1))))),
inference(step,[status(thm)],[t2188,t327]) ).
cnf(t2342,plain,
sk0 = meet(sk0,converse(complement(sk1))),
inference(step,[status(thm)],[t2341,t358]) ).
cnf(t2190,plain,
meet(sk0,converse(complement(sk1))) = sk0,
inference(orient,[status(thm)],[t2342]) ).
cnf(t2207,plain,
complement(sk1) = join(complement(sk1),converse(sk0)),
inference(cp,[status(thm)],[t742,t2190]) ).
cnf(t2343,plain,
complement(sk1) = join(converse(sk0),complement(sk1)),
inference(step,[status(thm)],[t2207,t19]) ).
cnf(t2208,plain,
join(converse(sk0),complement(sk1)) = complement(sk1),
inference(orient,[status(thm)],[t2343]) ).
cnf(t2223,plain,
zero = meet(converse(sk0),complement(complement(sk1))),
inference(cp,[status(thm)],[t589,t2208]) ).
cnf(t2344,plain,
zero = meet(converse(sk0),sk1),
inference(step,[status(thm)],[t2223,t358]) ).
cnf(t2345,plain,
zero = meet(sk1,converse(sk0)),
inference(step,[status(thm)],[t2344,t70]) ).
cnf(t2229,plain,
meet(sk1,converse(sk0)) = zero,
inference(orient,[status(thm)],[t2345]) ).
cnf(c14,plain,
meet(converse(sk0),sk1) != zero,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
meet(converse(sk0),sk1) != zero,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
meet(sk1,converse(sk0)) != zero,
inference(rw,[status(thm)],[goal_0,t70]) ).
cnf(g0_1,plain,
zero != zero,
inference(rw,[status(thm)],[g0_0,t2229]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL007+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 07:10:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.09/1.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.09/1.01 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------