%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL005+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 02:34:38 PM UTC 2026
% Result : Theorem 68.06s 20.59s
% Output : Proof 68.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 106
% Number of leaves : 13
% Syntax : Number of formulae : 262 ( 257 unt; 0 def)
% Number of atoms : 267 ( 266 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 : 355 ( 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(t73,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(t48,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t6]) ).
cnf(t76,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t48,t73]) ).
cnf(t8331,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t76,t48]) ).
cnf(t107,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t8331]) ).
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(t77,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(t8327,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t12,t73]) ).
cnf(t90,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t8327]) ).
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(t26,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(t19,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t28,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t26,t19]) ).
cnf(t153,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t28]) ).
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(t18,plain,
composition(X1,one) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t154,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t153,t18]) ).
cnf(t8333,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t154,t19]) ).
cnf(t166,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t8333]) ).
cnf(t167,plain,
one = converse(one),
inference(cp,[status(thm)],[t166,t18]) ).
cnf(t176,plain,
converse(one) = one,
inference(orient,[status(thm)],[t167]) ).
cnf(t8334,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t166,t176]) ).
cnf(t186,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t8334]) ).
cnf(t187,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t186]) ).
cnf(t190,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t90,t187]) ).
cnf(t8336,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t190,t176]) ).
cnf(t8337,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t8336,t187]) ).
cnf(t216,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t8337]) ).
cnf(t217,plain,
complement(join(complement(X1),complement(X2))) = join(meet(X1,X2),complement(join(complement(X1),complement(X2)))),
inference(cp,[status(thm)],[t216,t48]) ).
cnf(t8357,plain,
meet(X1,X2) = join(meet(X1,X2),complement(join(complement(X1),complement(X2)))),
inference(step,[status(thm)],[t217,t48]) ).
cnf(t8358,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X1,X2)),
inference(step,[status(thm)],[t8357,t48]) ).
cnf(t452,plain,
join(meet(X1,X2),meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t8358]) ).
cnf(t453,plain,
meet(X1,X2) = join(meet(X2,X1),meet(X1,X2)),
inference(cp,[status(thm)],[t452,t107]) ).
cnf(t473,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X2,X1),
inference(orient,[status(thm)],[t453]) ).
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(t20,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t8326,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t20,t48]) ).
cnf(t51,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t8326]) ).
cnf(t1332,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t51]) ).
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(t52,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t1333,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t1332,t52]) ).
cnf(t8396,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t1333,t48]) ).
cnf(t1402,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t8396]) ).
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(t85,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t89,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t48,t85]) ).
cnf(t8329,plain,
zero = complement(top),
inference(step,[status(thm)],[t89,t52]) ).
cnf(t98,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t8329]) ).
cnf(t220,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t216,t98]) ).
cnf(t8338,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t220,t98]) ).
cnf(t8339,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t8338,t98]) ).
cnf(t227,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t8339]) ).
cnf(t228,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t77,t227]) ).
cnf(t246,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t228]) ).
cnf(t1406,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t246,t1402]) ).
cnf(t8398,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t1406,t1402]) ).
cnf(t1419,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t8398]) ).
cnf(t8399,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t1402,t1419]) ).
cnf(t1439,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t8399]) ).
cnf(t1483,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t1439]) ).
cnf(t1484,plain,
meet(X1,X1) = join(X1,meet(X1,X1)),
inference(cp,[status(thm)],[t473,t1483]) ).
cnf(t8445,plain,
X1 = join(X1,meet(X1,X1)),
inference(step,[status(thm)],[t1484,t1483]) ).
cnf(t8446,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t8445,t1483]) ).
cnf(t1510,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t8446]) ).
cnf(t1512,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t77,t1510]) ).
cnf(t1639,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t1512]) ).
cnf(t1641,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1),
inference(cp,[status(thm)],[t1639,t1332]) ).
cnf(t8450,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t1641,t1332]) ).
cnf(t8451,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t8450,t73]) ).
cnf(t1645,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t8451]) ).
cnf(t1647,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t1645,t107]) ).
cnf(t1653,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t1647]) ).
cnf(t1656,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t77,t1653]) ).
cnf(t2622,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t1656]) ).
cnf(t226,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t48,t216]) ).
cnf(t233,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t226]) ).
cnf(t243,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),meet(X2,X2))),
inference(cp,[status(thm)],[t48,t233]) ).
cnf(t1113,plain,
complement(join(complement(X1),meet(X2,X2))) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t243]) ).
cnf(t8435,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t1113,t1483]) ).
cnf(t1497,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(rw,[status(thm)],[t8435]) ).
cnf(t1944,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t1497]) ).
cnf(t8474,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(step,[status(thm)],[t1332,t1944]) ).
cnf(t1983,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[t8474]) ).
cnf(t4267,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(orient,[status(thm)],[t1983]) ).
cnf(t4315,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(cp,[status(thm)],[t2622,t4267]) ).
cnf(t4425,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t4315]) ).
cnf(t4430,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(cp,[status(thm)],[t4425,t107]) ).
cnf(t4688,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t4430]) ).
cnf(t8432,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t233,t1483]) ).
cnf(t1494,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t8432]) ).
cnf(t1519,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t1494]) ).
cnf(t4698,plain,
join(complement(X1),X2) = join(complement(X1),meet(X1,X2)),
inference(cp,[status(thm)],[t4688,t1519]) ).
cnf(t5376,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t4698]) ).
cnf(t88,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(cp,[status(thm)],[t77,t85]) ).
cnf(t315,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(orient,[status(thm)],[t88]) ).
cnf(t324,plain,
join(top,X1) = join(X2,join(X1,complement(X2))),
inference(cp,[status(thm)],[t315,t73]) ).
cnf(t240,plain,
top = join(complement(X1),meet(X1,X1)),
inference(cp,[status(thm)],[t85,t233]) ).
cnf(t253,plain,
join(complement(X1),meet(X1,X1)) = top,
inference(orient,[status(thm)],[t240]) ).
cnf(t319,plain,
join(top,meet(X1,X1)) = join(X1,top),
inference(cp,[status(thm)],[t315,t253]) ).
cnf(t321,plain,
join(top,complement(X1)) = join(X1,complement(X1)),
inference(cp,[status(thm)],[t315,t216]) ).
cnf(t8344,plain,
join(top,complement(X1)) = top,
inference(step,[status(thm)],[t321,t85]) ).
cnf(t332,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t8344]) ).
cnf(t333,plain,
top = join(top,meet(X1,X2)),
inference(cp,[status(thm)],[t332,t48]) ).
cnf(t357,plain,
join(top,meet(X1,X2)) = top,
inference(orient,[status(thm)],[t333]) ).
cnf(t8346,plain,
top = join(X1,top),
inference(step,[status(thm)],[t319,t357]) ).
cnf(t362,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t8346]) ).
cnf(t363,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t362,t73]) ).
cnf(t368,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t363]) ).
cnf(t8355,plain,
top = join(X2,join(X1,complement(X2))),
inference(step,[status(thm)],[t324,t368]) ).
cnf(t416,plain,
join(X1,join(X2,complement(X1))) = top,
inference(orient,[status(thm)],[t8355]) ).
cnf(t1398,plain,
top = join(join(complement(X1),X2),X1),
inference(cp,[status(thm)],[t416,t1332]) ).
cnf(t8454,plain,
top = join(complement(X1),join(X2,X1)),
inference(step,[status(thm)],[t1398,t77]) ).
cnf(t1688,plain,
join(complement(X1),join(X2,X1)) = top,
inference(orient,[status(thm)],[t8454]) ).
cnf(t1694,plain,
top = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t1688,t1653]) ).
cnf(t8463,plain,
top = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t1694,t73]) ).
cnf(t1802,plain,
join(X1,complement(meet(X2,X1))) = top,
inference(orient,[status(thm)],[t8463]) ).
cnf(t1807,plain,
meet(X1,meet(X2,complement(X1))) = complement(top),
inference(cp,[status(thm)],[t48,t1802]) ).
cnf(t8465,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t1807,t98]) ).
cnf(t1819,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t8465]) ).
cnf(t1820,plain,
zero = meet(complement(X1),meet(X2,X1)),
inference(cp,[status(thm)],[t1819,t1519]) ).
cnf(t1904,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t1820]) ).
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(t45,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t8]) ).
cnf(t46,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t45,t19]) ).
cnf(t262,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t46]) ).
cnf(t264,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(cp,[status(thm)],[t262,t85]) ).
cnf(t298,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(orient,[status(thm)],[t264]) ).
cnf(t371,plain,
top = converse(top),
inference(cp,[status(thm)],[t368,t298]) ).
cnf(t374,plain,
converse(top) = top,
inference(orient,[status(thm)],[t371]) ).
cnf(t8353,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(step,[status(thm)],[t298,t374]) ).
cnf(t377,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(orient,[status(thm)],[t8353]) ).
cnf(t1958,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = complement(top),
inference(cp,[status(thm)],[t1944,t377]) ).
cnf(t8538,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(step,[status(thm)],[t1958,t98]) ).
cnf(t4255,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(orient,[status(thm)],[t8538]) ).
cnf(t4691,plain,
join(X1,complement(converse(complement(converse(complement(complement(X1))))))) = join(X1,zero),
inference(cp,[status(thm)],[t4688,t4255]) ).
cnf(t8555,plain,
join(X1,complement(converse(complement(converse(X1))))) = join(X1,zero),
inference(step,[status(thm)],[t4691,t1519]) ).
cnf(t1431,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t1419,t73]) ).
cnf(t1476,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t1431]) ).
cnf(t8556,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t8555,t1476]) ).
cnf(t4764,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t8556]) ).
cnf(t4806,plain,
join(X1,converse(complement(converse(complement(converse(converse(X1))))))) = converse(converse(X1)),
inference(cp,[status(thm)],[t262,t4764]) ).
cnf(t8557,plain,
join(X1,converse(complement(converse(complement(X1))))) = converse(converse(X1)),
inference(step,[status(thm)],[t4806,t19]) ).
cnf(t8558,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(step,[status(thm)],[t8557,t19]) ).
cnf(t4810,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(orient,[status(thm)],[t8558]) ).
cnf(t4838,plain,
meet(X1,complement(converse(complement(converse(complement(complement(X1))))))) = complement(complement(X1)),
inference(cp,[status(thm)],[t1944,t4810]) ).
cnf(t8559,plain,
meet(X1,complement(converse(complement(converse(X1))))) = complement(complement(X1)),
inference(step,[status(thm)],[t4838,t1519]) ).
cnf(t8560,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t8559,t1519]) ).
cnf(t4846,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t8560]) ).
cnf(t4873,plain,
zero = meet(complement(complement(converse(complement(converse(X1))))),X1),
inference(cp,[status(thm)],[t1904,t4846]) ).
cnf(t8564,plain,
zero = meet(X1,complement(complement(converse(complement(converse(X1)))))),
inference(step,[status(thm)],[t4873,t107]) ).
cnf(t8565,plain,
zero = meet(X1,converse(complement(converse(X1)))),
inference(step,[status(thm)],[t8564,t1519]) ).
cnf(t4977,plain,
meet(X1,converse(complement(converse(X1)))) = zero,
inference(orient,[status(thm)],[t8565]) ).
cnf(t4993,plain,
zero = meet(converse(X1),converse(complement(X1))),
inference(cp,[status(thm)],[t4977,t19]) ).
cnf(t5004,plain,
meet(converse(X1),converse(complement(X1))) = zero,
inference(orient,[status(thm)],[t4993]) ).
cnf(t5396,plain,
join(complement(converse(X1)),converse(complement(X1))) = join(complement(converse(X1)),zero),
inference(cp,[status(thm)],[t5376,t5004]) ).
cnf(t8578,plain,
join(converse(complement(X1)),complement(converse(X1))) = join(complement(converse(X1)),zero),
inference(step,[status(thm)],[t5396,t73]) ).
cnf(t8579,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(step,[status(thm)],[t8578,t1476]) ).
cnf(t5889,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(orient,[status(thm)],[t8579]) ).
cnf(t5894,plain,
complement(converse(complement(X1))) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t5889,t1519]) ).
cnf(t4780,plain,
converse(X1) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t4764,t19]) ).
cnf(t5662,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(orient,[status(thm)],[t4780]) ).
cnf(t8580,plain,
complement(converse(complement(X1))) = converse(X1),
inference(step,[status(thm)],[t5894,t5662]) ).
cnf(t5934,plain,
complement(converse(complement(X1))) = converse(X1),
inference(orient,[status(thm)],[t8580]) ).
cnf(t5939,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(cp,[status(thm)],[t5934,t1519]) ).
cnf(t5980,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(orient,[status(thm)],[t5939]) ).
cnf(t5991,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(cp,[status(thm)],[t5980,t262]) ).
cnf(t7751,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(orient,[status(thm)],[t5991]) ).
cnf(t1967,plain,
join(complement(X1),X2) = complement(meet(X1,complement(X2))),
inference(cp,[status(thm)],[t1519,t1944]) ).
cnf(t2034,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(orient,[status(thm)],[t1967]) ).
cnf(t2039,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(cp,[status(thm)],[t2034,t1519]) ).
cnf(t2090,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t2039]) ).
cnf(t6002,plain,
complement(meet(converse(X1),X2)) = join(converse(complement(X1)),complement(X2)),
inference(cp,[status(thm)],[t2090,t5980]) ).
cnf(t8029,plain,
join(converse(complement(X1)),complement(X2)) = complement(meet(converse(X1),X2)),
inference(orient,[status(thm)],[t6002]) ).
cnf(t8079,plain,
complement(join(complement(X1),converse(complement(X2)))) = converse(complement(complement(meet(converse(X1),X2)))),
inference(cp,[status(thm)],[t7751,t8029]) ).
cnf(t8674,plain,
meet(X1,complement(converse(complement(X2)))) = converse(complement(complement(meet(converse(X1),X2)))),
inference(step,[status(thm)],[t8079,t1944]) ).
cnf(t8675,plain,
meet(X1,converse(X2)) = converse(complement(complement(meet(converse(X1),X2)))),
inference(step,[status(thm)],[t8674,t5934]) ).
cnf(t8676,plain,
meet(X1,converse(X2)) = converse(meet(converse(X1),X2)),
inference(step,[status(thm)],[t8675,t1519]) ).
cnf(t8083,plain,
converse(meet(converse(X1),X2)) = meet(X1,converse(X2)),
inference(orient,[status(thm)],[t8676]) ).
cnf(t8119,plain,
meet(converse(X1),converse(X2)) = converse(meet(X1,X2)),
inference(cp,[status(thm)],[t8083,t19]) ).
cnf(t8250,plain,
meet(converse(X1),converse(X2)) = converse(meet(X1,X2)),
inference(orient,[status(thm)],[t8119]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t23,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
fof(f16,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(f16_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)],[f16]) ).
fof(f16_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)],[f16_neg]) ).
fof(f16_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])],[f16_nnf]) ).
cnf(c16,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)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c16]) ).
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,t73]) ).
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,t107]) ).
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,t107]) ).
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,t8250]) ).
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,t8250]) ).
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,t107]) ).
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,t107]) ).
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,t107]) ).
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,t107]) ).
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,t107]) ).
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,t107]) ).
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,t107]) ).
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,t107]) ).
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,t107]) ).
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,t107]) ).
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,t107]) ).
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,t73]) ).
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,t107]) ).
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,t1510]) ).
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,t23]) ).
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,t8250]) ).
cnf(g0_22,plain,
true != ifeq(converse(meet(sk1,sk0)),converse(meet(sk1,sk0)),false,true),
inference(rw,[status(thm)],[g0_21,t1510]) ).
cnf(g0_23,plain,
true != false,
inference(rw,[status(thm)],[g0_22,t23]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL005+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/11.63 % Computer : n013.cluster.edu
% 0.11/11.63 % Model : x86_64 x86_64
% 0.11/11.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/11.63 % Memory : 8046.5625MB
% 0.11/11.63 % OS : Linux 6.8.0-71-generic
% 0.11/11.63 % CPULimit : 300
% 0.11/11.63 % WCLimit : 300
% 0.11/11.63 % DateTime : Thu Sep 24 07:06:27 UTC 2026
% 0.11/11.64 % CPUTime :
% 0.11/11.64 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 68.06/20.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 68.06/20.59 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------