%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL011+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 02:34:42 PM UTC 2026
% Result : Theorem 7.37s 1.65s
% Output : Proof 7.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 96
% Number of leaves : 15
% Syntax : Number of formulae : 302 ( 298 unt; 0 def)
% Number of atoms : 306 ( 305 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 412 ( 55 sgn 90 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f3_nnf,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t6,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t83,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/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f0_nnf,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t43,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t85,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t83,t43]) ).
cnf(t19510,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t85,t83]) ).
cnf(t107,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t19510]) ).
fof(f1,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
fof(f1_nnf,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t10,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t46,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
fof(f13,axiom,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dedekind_law) ).
fof(f13_nnf,plain,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t16,plain,
join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t33,plain,
join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
inference(orient,[status(thm)],[t16]) ).
cnf(t48,plain,
join(meet(composition(X1,X2),X3),join(composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),Y3)) = join(composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),Y3),
inference(cp,[status(thm)],[t46,t33]) ).
cnf(t19242,plain,
join(meet(composition(X1,X2),X3),join(composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),Y3)) = join(composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),Y3),
inference(orient,[status(thm)],[t48]) ).
fof(f16,conjecture,
! [X0,X1,X2] :
( meet(X0,composition(converse(X1),X2)) = zero
=> meet(composition(X1,X0),X2) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( meet(X0,composition(converse(X1),X2)) = zero
=> meet(composition(X1,X0),X2) = zero ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0,X1,X2] :
( meet(composition(X1,X0),X2) != zero
& meet(X0,composition(converse(X1),X2)) = zero ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( meet(composition(sk1,sk0),sk2) != zero
& meet(sk0,composition(converse(sk1),sk2)) = zero ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f16_nnf]) ).
cnf(c16,plain,
meet(sk0,composition(converse(sk1),sk2)) = zero,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t5,plain,
meet(sk0,composition(converse(sk1),sk2)) = zero,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t95,plain,
meet(sk0,composition(converse(sk1),sk2)) = zero,
inference(orient,[status(thm)],[t5]) ).
cnf(t19371,plain,
join(composition(meet(sk1,composition(sk2,converse(sk0))),meet(sk0,composition(converse(sk1),sk2))),X1) = join(meet(composition(sk1,sk0),sk2),join(composition(meet(sk1,composition(sk2,converse(sk0))),zero),X1)),
inference(cp,[status(thm)],[t19242,t95]) ).
cnf(t20266,plain,
join(composition(meet(sk1,composition(sk2,converse(sk0))),zero),X1) = join(meet(composition(sk1,sk0),sk2),join(composition(meet(sk1,composition(sk2,converse(sk0))),zero),X1)),
inference(step,[status(thm)],[t19371,t95]) ).
fof(f6,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
fof(f6_nnf,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t11,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t24,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(orient,[status(thm)],[t11]) ).
fof(f8,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/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(t60,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t8]) ).
cnf(t64,plain,
join(converse(X1),join(converse(X2),X3)) = join(converse(join(X1,X2)),X3),
inference(cp,[status(thm)],[t46,t60]) ).
cnf(t1765,plain,
join(converse(X1),join(converse(X2),X3)) = join(converse(join(X1,X2)),X3),
inference(orient,[status(thm)],[t64]) ).
fof(f11,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
fof(f11_nnf,plain,
! [X0] : top = join(X0,complement(X0)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X0] : top = join(X0,complement(X0)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
top = join(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t2,plain,
join(X1,complement(X1)) = top,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t51,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t53,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(cp,[status(thm)],[t46,t51]) ).
cnf(t314,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(orient,[status(thm)],[t53]) ).
cnf(t323,plain,
join(top,X1) = join(X2,join(X1,complement(X2))),
inference(cp,[status(thm)],[t314,t43]) ).
fof(f10,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f10_nnf,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t12,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t19507,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t12,t43]) ).
cnf(t54,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t19507]) ).
fof(f9,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f9_nnf,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t7,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t27,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/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f7_nnf,plain,
! [X0] : converse(converse(X0)) = X0,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X0] : converse(converse(X0)) = X0,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
converse(converse(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t1,plain,
converse(converse(X1)) = X1,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t21,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t29,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t27,t21]) ).
cnf(t152,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t29]) ).
fof(f5,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
fof(f5_nnf,plain,
! [X0] : composition(X0,one) = X0,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X0] : composition(X0,one) = X0,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
composition(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t0,plain,
composition(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t17,plain,
composition(X1,one) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t153,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t152,t17]) ).
cnf(t19512,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t153,t21]) ).
cnf(t165,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t19512]) ).
cnf(t166,plain,
one = converse(one),
inference(cp,[status(thm)],[t165,t17]) ).
cnf(t175,plain,
converse(one) = one,
inference(orient,[status(thm)],[t166]) ).
cnf(t19513,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t165,t175]) ).
cnf(t185,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t19513]) ).
cnf(t186,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t185]) ).
cnf(t189,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t54,t186]) ).
cnf(t19515,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t189,t175]) ).
cnf(t19516,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t19515,t186]) ).
cnf(t215,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t19516]) ).
cnf(t225,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t83,t215]) ).
cnf(t232,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t225]) ).
cnf(t240,plain,
top = join(complement(X1),meet(X1,X1)),
inference(cp,[status(thm)],[t51,t232]) ).
cnf(t256,plain,
join(complement(X1),meet(X1,X1)) = top,
inference(orient,[status(thm)],[t240]) ).
cnf(t318,plain,
join(top,meet(X1,X1)) = join(X1,top),
inference(cp,[status(thm)],[t314,t256]) ).
cnf(t320,plain,
join(top,complement(X1)) = join(X1,complement(X1)),
inference(cp,[status(thm)],[t314,t215]) ).
cnf(t19523,plain,
join(top,complement(X1)) = top,
inference(step,[status(thm)],[t320,t51]) ).
cnf(t331,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t19523]) ).
cnf(t332,plain,
top = join(top,meet(X1,X2)),
inference(cp,[status(thm)],[t331,t83]) ).
cnf(t348,plain,
join(top,meet(X1,X2)) = top,
inference(orient,[status(thm)],[t332]) ).
cnf(t19525,plain,
top = join(X1,top),
inference(step,[status(thm)],[t318,t348]) ).
cnf(t354,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t19525]) ).
cnf(t355,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t354,t43]) ).
cnf(t360,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t355]) ).
cnf(t19534,plain,
top = join(X2,join(X1,complement(X2))),
inference(step,[status(thm)],[t323,t360]) ).
cnf(t404,plain,
join(X1,join(X2,complement(X1))) = top,
inference(orient,[status(thm)],[t19534]) ).
cnf(t1769,plain,
join(converse(join(X1,X2)),complement(converse(X1))) = top,
inference(cp,[status(thm)],[t1765,t404]) ).
cnf(t19614,plain,
join(complement(converse(X1)),converse(join(X1,X2))) = top,
inference(step,[status(thm)],[t1769,t43]) ).
cnf(t1820,plain,
join(complement(converse(X1)),converse(join(X1,X2))) = top,
inference(orient,[status(thm)],[t19614]) ).
cnf(t1853,plain,
top = join(complement(converse(converse(X1))),converse(converse(join(X1,X2)))),
inference(cp,[status(thm)],[t1820,t60]) ).
cnf(t19615,plain,
top = join(complement(X1),converse(converse(join(X1,X2)))),
inference(step,[status(thm)],[t1853,t21]) ).
cnf(t19616,plain,
top = join(complement(X1),join(X1,X2)),
inference(step,[status(thm)],[t19615,t21]) ).
cnf(t1866,plain,
join(complement(X1),join(X1,X2)) = top,
inference(orient,[status(thm)],[t19616]) ).
cnf(t1896,plain,
top = join(complement(X1),join(X2,X1)),
inference(cp,[status(thm)],[t1866,t43]) ).
cnf(t1899,plain,
join(complement(X1),join(X2,X1)) = top,
inference(orient,[status(thm)],[t1896]) ).
cnf(t56,plain,
complement(one) = join(complement(one),composition(converse(X1),complement(X1))),
inference(cp,[status(thm)],[t54,t17]) ).
cnf(t1150,plain,
join(complement(one),composition(converse(X1),complement(X1))) = complement(one),
inference(orient,[status(thm)],[t56]) ).
cnf(t1160,plain,
complement(one) = join(complement(one),composition(X1,complement(converse(X1)))),
inference(cp,[status(thm)],[t1150,t21]) ).
cnf(t1178,plain,
join(complement(one),composition(X1,complement(converse(X1)))) = complement(one),
inference(orient,[status(thm)],[t1160]) ).
cnf(t1910,plain,
top = join(complement(composition(X1,complement(converse(X1)))),complement(one)),
inference(cp,[status(thm)],[t1899,t1178]) ).
cnf(t19627,plain,
top = join(complement(one),complement(composition(X1,complement(converse(X1))))),
inference(step,[status(thm)],[t1910,t43]) ).
cnf(t2249,plain,
join(complement(one),complement(composition(X1,complement(converse(X1))))) = top,
inference(orient,[status(thm)],[t19627]) ).
cnf(t2264,plain,
meet(one,composition(X1,complement(converse(X1)))) = complement(top),
inference(cp,[status(thm)],[t83,t2249]) ).
cnf(t84,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t83,t51]) ).
fof(f12,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
fof(f12_nnf,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t3,plain,
meet(X1,complement(X1)) = zero,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t90,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t19508,plain,
zero = complement(top),
inference(step,[status(thm)],[t84,t90]) ).
cnf(t98,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t19508]) ).
cnf(t19628,plain,
meet(one,composition(X1,complement(converse(X1)))) = zero,
inference(step,[status(thm)],[t2264,t98]) ).
cnf(t2270,plain,
meet(one,composition(X1,complement(converse(X1)))) = zero,
inference(orient,[status(thm)],[t19628]) ).
cnf(t2291,plain,
composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),meet(one,composition(converse(X1),complement(converse(converse(X1)))))) = join(meet(composition(X1,one),complement(converse(converse(X1)))),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(cp,[status(thm)],[t33,t2270]) ).
cnf(t19629,plain,
composition(meet(X1,composition(complement(X1),converse(one))),meet(one,composition(converse(X1),complement(converse(converse(X1)))))) = join(meet(composition(X1,one),complement(converse(converse(X1)))),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t2291,t21]) ).
cnf(t19630,plain,
composition(meet(X1,composition(complement(X1),one)),meet(one,composition(converse(X1),complement(converse(converse(X1)))))) = join(meet(composition(X1,one),complement(converse(converse(X1)))),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t19629,t175]) ).
cnf(t19631,plain,
composition(meet(X1,complement(X1)),meet(one,composition(converse(X1),complement(converse(converse(X1)))))) = join(meet(composition(X1,one),complement(converse(converse(X1)))),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t19630,t17]) ).
cnf(t19632,plain,
composition(zero,meet(one,composition(converse(X1),complement(converse(converse(X1)))))) = join(meet(composition(X1,one),complement(converse(converse(X1)))),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t19631,t90]) ).
cnf(t19633,plain,
composition(zero,zero) = join(meet(composition(X1,one),complement(converse(converse(X1)))),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t19632,t2270]) ).
cnf(t19634,plain,
composition(zero,zero) = join(meet(X1,complement(converse(converse(X1)))),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t19633,t17]) ).
cnf(t19635,plain,
composition(zero,zero) = join(meet(X1,complement(X1)),composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t19634,t21]) ).
cnf(t19636,plain,
composition(zero,zero) = join(zero,composition(meet(X1,composition(complement(converse(converse(X1))),converse(one))),zero)),
inference(step,[status(thm)],[t19635,t90]) ).
cnf(t19637,plain,
composition(zero,zero) = join(zero,composition(meet(X1,composition(complement(X1),converse(one))),zero)),
inference(step,[status(thm)],[t19636,t21]) ).
cnf(t19638,plain,
composition(zero,zero) = join(zero,composition(meet(X1,composition(complement(X1),one)),zero)),
inference(step,[status(thm)],[t19637,t175]) ).
cnf(t19639,plain,
composition(zero,zero) = join(zero,composition(meet(X1,complement(X1)),zero)),
inference(step,[status(thm)],[t19638,t17]) ).
cnf(t19640,plain,
composition(zero,zero) = join(zero,composition(zero,zero)),
inference(step,[status(thm)],[t19639,t90]) ).
cnf(t2292,plain,
join(zero,composition(zero,zero)) = composition(zero,zero),
inference(orient,[status(thm)],[t19640]) ).
cnf(t2295,plain,
join(zero,join(composition(zero,zero),X1)) = join(composition(zero,zero),X1),
inference(cp,[status(thm)],[t46,t2292]) ).
cnf(t2397,plain,
join(zero,join(composition(zero,zero),X1)) = join(composition(zero,zero),X1),
inference(orient,[status(thm)],[t2295]) ).
cnf(t2405,plain,
join(composition(zero,zero),composition(X1,zero)) = join(zero,composition(join(zero,X1),zero)),
inference(cp,[status(thm)],[t2397,t24]) ).
cnf(t19649,plain,
composition(join(zero,X1),zero) = join(zero,composition(join(zero,X1),zero)),
inference(step,[status(thm)],[t2405,t24]) ).
cnf(t2468,plain,
join(zero,composition(join(zero,X1),zero)) = composition(join(zero,X1),zero),
inference(orient,[status(thm)],[t19649]) ).
cnf(t2487,plain,
composition(join(zero,X1),zero) = join(zero,composition(join(X1,zero),zero)),
inference(cp,[status(thm)],[t2468,t43]) ).
cnf(t2578,plain,
join(zero,composition(join(X1,zero),zero)) = composition(join(zero,X1),zero),
inference(orient,[status(thm)],[t2487]) ).
cnf(t62,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t60,t21]) ).
cnf(t261,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t62]) ).
cnf(t263,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(cp,[status(thm)],[t261,t51]) ).
cnf(t297,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(orient,[status(thm)],[t263]) ).
cnf(t363,plain,
top = converse(top),
inference(cp,[status(thm)],[t360,t297]) ).
cnf(t366,plain,
converse(top) = top,
inference(orient,[status(thm)],[t363]) ).
cnf(t371,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(cp,[status(thm)],[t27,t366]) ).
cnf(t378,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(orient,[status(thm)],[t371]) ).
cnf(t380,plain,
converse(join(composition(X1,top),X2)) = join(composition(top,converse(X1)),converse(X2)),
inference(cp,[status(thm)],[t60,t378]) ).
cnf(t4096,plain,
join(composition(top,converse(X1)),converse(X2)) = converse(join(composition(X1,top),X2)),
inference(orient,[status(thm)],[t380]) ).
cnf(t4109,plain,
converse(join(composition(top,top),X1)) = join(composition(top,top),converse(X1)),
inference(cp,[status(thm)],[t4096,t366]) ).
cnf(t4143,plain,
converse(join(composition(top,top),X1)) = join(composition(top,top),converse(X1)),
inference(orient,[status(thm)],[t4109]) ).
cnf(t4147,plain,
join(composition(top,top),converse(composition(X1,top))) = converse(composition(join(top,X1),top)),
inference(cp,[status(thm)],[t4143,t24]) ).
cnf(t19711,plain,
join(composition(top,top),composition(top,converse(X1))) = converse(composition(join(top,X1),top)),
inference(step,[status(thm)],[t4147,t378]) ).
cnf(t19712,plain,
join(composition(top,top),composition(top,converse(X1))) = composition(top,converse(join(top,X1))),
inference(step,[status(thm)],[t19711,t378]) ).
cnf(t19713,plain,
join(composition(top,top),composition(top,converse(X1))) = composition(top,converse(top)),
inference(step,[status(thm)],[t19712,t360]) ).
cnf(t19714,plain,
join(composition(top,top),composition(top,converse(X1))) = composition(top,top),
inference(step,[status(thm)],[t19713,t366]) ).
cnf(t4261,plain,
join(composition(top,top),composition(top,converse(X1))) = composition(top,top),
inference(orient,[status(thm)],[t19714]) ).
cnf(t4277,plain,
composition(top,top) = join(composition(top,top),composition(top,one)),
inference(cp,[status(thm)],[t4261,t175]) ).
cnf(t19715,plain,
composition(top,top) = join(composition(top,top),top),
inference(step,[status(thm)],[t4277,t17]) ).
cnf(t19716,plain,
composition(top,top) = top,
inference(step,[status(thm)],[t19715,t354]) ).
cnf(t4290,plain,
composition(top,top) = top,
inference(orient,[status(thm)],[t19716]) ).
cnf(t4295,plain,
complement(top) = join(complement(top),composition(converse(top),complement(top))),
inference(cp,[status(thm)],[t54,t4290]) ).
cnf(t19724,plain,
zero = join(complement(top),composition(converse(top),complement(top))),
inference(step,[status(thm)],[t4295,t98]) ).
cnf(t19725,plain,
zero = join(zero,composition(converse(top),complement(top))),
inference(step,[status(thm)],[t19724,t98]) ).
cnf(t19726,plain,
zero = join(zero,composition(top,complement(top))),
inference(step,[status(thm)],[t19725,t366]) ).
cnf(t19727,plain,
zero = join(zero,composition(top,zero)),
inference(step,[status(thm)],[t19726,t98]) ).
cnf(t52,plain,
top = join(X1,join(X2,complement(join(X1,X2)))),
inference(cp,[status(thm)],[t51,t46]) ).
cnf(t475,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(orient,[status(thm)],[t52]) ).
cnf(t492,plain,
top = join(X1,join(X2,complement(join(X2,X1)))),
inference(cp,[status(thm)],[t475,t43]) ).
cnf(t576,plain,
join(X1,join(X2,complement(join(X2,X1)))) = top,
inference(orient,[status(thm)],[t492]) ).
cnf(t588,plain,
top = join(complement(X1),join(X1,complement(top))),
inference(cp,[status(thm)],[t576,t51]) ).
cnf(t19545,plain,
top = join(complement(X1),join(X1,zero)),
inference(step,[status(thm)],[t588,t98]) ).
cnf(t608,plain,
join(complement(X1),join(X1,zero)) = top,
inference(orient,[status(thm)],[t19545]) ).
cnf(t615,plain,
top = join(complement(X1),join(zero,X1)),
inference(cp,[status(thm)],[t608,t43]) ).
cnf(t617,plain,
join(complement(X1),join(zero,X1)) = top,
inference(orient,[status(thm)],[t615]) ).
cnf(t103,plain,
complement(top) = join(zero,composition(converse(X1),complement(composition(X1,top)))),
inference(cp,[status(thm)],[t54,t98]) ).
cnf(t19573,plain,
zero = join(zero,composition(converse(X1),complement(composition(X1,top)))),
inference(step,[status(thm)],[t103,t98]) ).
cnf(t1353,plain,
join(zero,composition(converse(X1),complement(composition(X1,top)))) = zero,
inference(orient,[status(thm)],[t19573]) ).
cnf(t1358,plain,
zero = join(zero,composition(top,complement(composition(top,top)))),
inference(cp,[status(thm)],[t1353,t366]) ).
cnf(t1375,plain,
join(zero,composition(top,complement(composition(top,top)))) = zero,
inference(orient,[status(thm)],[t1358]) ).
cnf(t1377,plain,
top = join(complement(composition(top,complement(composition(top,top)))),zero),
inference(cp,[status(thm)],[t617,t1375]) ).
cnf(t19594,plain,
top = join(zero,complement(composition(top,complement(composition(top,top))))),
inference(step,[status(thm)],[t1377,t43]) ).
cnf(t1619,plain,
join(zero,complement(composition(top,complement(composition(top,top))))) = top,
inference(orient,[status(thm)],[t19594]) ).
cnf(t2471,plain,
composition(join(zero,complement(composition(top,complement(composition(top,top))))),zero) = join(zero,composition(top,zero)),
inference(cp,[status(thm)],[t2468,t1619]) ).
cnf(t19650,plain,
composition(top,zero) = join(zero,composition(top,zero)),
inference(step,[status(thm)],[t2471,t1619]) ).
cnf(t2527,plain,
join(zero,composition(top,zero)) = composition(top,zero),
inference(orient,[status(thm)],[t19650]) ).
cnf(t19728,plain,
zero = composition(top,zero),
inference(step,[status(thm)],[t19727,t2527]) ).
cnf(t4301,plain,
composition(top,zero) = zero,
inference(orient,[status(thm)],[t19728]) ).
cnf(t4303,plain,
composition(join(top,X1),zero) = join(zero,composition(X1,zero)),
inference(cp,[status(thm)],[t24,t4301]) ).
cnf(t19734,plain,
composition(top,zero) = join(zero,composition(X1,zero)),
inference(step,[status(thm)],[t4303,t360]) ).
cnf(t19735,plain,
zero = join(zero,composition(X1,zero)),
inference(step,[status(thm)],[t19734,t4301]) ).
cnf(t4337,plain,
join(zero,composition(X1,zero)) = zero,
inference(orient,[status(thm)],[t19735]) ).
cnf(t19738,plain,
zero = composition(join(zero,X1),zero),
inference(step,[status(thm)],[t2578,t4337]) ).
cnf(t4355,plain,
zero = composition(join(zero,X1),zero),
inference(rw,[status(thm)],[t19738]) ).
cnf(t4387,plain,
composition(join(zero,X1),zero) = zero,
inference(orient,[status(thm)],[t4355]) ).
cnf(t4390,plain,
zero = composition(join(X1,zero),zero),
inference(cp,[status(thm)],[t4387,t43]) ).
cnf(t4507,plain,
composition(join(X1,zero),zero) = zero,
inference(orient,[status(thm)],[t4390]) ).
cnf(t4509,plain,
composition(join(join(X1,zero),X2),zero) = join(zero,composition(X2,zero)),
inference(cp,[status(thm)],[t24,t4507]) ).
cnf(t19764,plain,
composition(join(X1,join(zero,X2)),zero) = join(zero,composition(X2,zero)),
inference(step,[status(thm)],[t4509,t46]) ).
cnf(t19765,plain,
composition(join(X1,join(zero,X2)),zero) = zero,
inference(step,[status(thm)],[t19764,t4337]) ).
cnf(t4690,plain,
composition(join(X1,join(zero,X2)),zero) = zero,
inference(orient,[status(thm)],[t19765]) ).
cnf(t176,plain,
converse(join(one,X1)) = join(one,converse(X1)),
inference(cp,[status(thm)],[t60,t175]) ).
cnf(t192,plain,
converse(join(one,X1)) = join(one,converse(X1)),
inference(orient,[status(thm)],[t176]) ).
cnf(t198,plain,
composition(converse(X1),join(one,X2)) = converse(composition(join(one,converse(X2)),X1)),
inference(cp,[status(thm)],[t152,t192]) ).
cnf(t3866,plain,
converse(composition(join(one,converse(X1)),X2)) = composition(converse(X2),join(one,X1)),
inference(orient,[status(thm)],[t198]) ).
fof(f4,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
fof(f4_nnf,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t9,plain,
composition(composition(X1,X2),X3) = composition(X1,composition(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t22,plain,
composition(composition(X1,X2),X3) = composition(X1,composition(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t26,plain,
composition(join(X1,composition(X2,X3)),Y3) = join(composition(X1,Y3),composition(X2,composition(X3,Y3))),
inference(cp,[status(thm)],[t24,t22]) ).
cnf(t838,plain,
join(composition(X1,X2),composition(X3,composition(Y3,X2))) = composition(join(X1,composition(X3,Y3)),X2),
inference(orient,[status(thm)],[t26]) ).
cnf(t4293,plain,
composition(join(X1,composition(X2,top)),top) = join(composition(X1,top),composition(X2,top)),
inference(cp,[status(thm)],[t838,t4290]) ).
cnf(t19850,plain,
composition(join(X1,composition(X2,top)),top) = composition(join(X1,X2),top),
inference(step,[status(thm)],[t4293,t24]) ).
cnf(t6206,plain,
composition(join(X1,composition(X2,top)),top) = composition(join(X1,X2),top),
inference(orient,[status(thm)],[t19850]) ).
cnf(t6218,plain,
composition(join(X1,one),top) = composition(join(X1,top),top),
inference(cp,[status(thm)],[t6206,t186]) ).
cnf(t19851,plain,
composition(join(X1,one),top) = composition(top,top),
inference(step,[status(thm)],[t6218,t354]) ).
cnf(t19852,plain,
composition(join(X1,one),top) = top,
inference(step,[status(thm)],[t19851,t4290]) ).
cnf(t6241,plain,
composition(join(X1,one),top) = top,
inference(orient,[status(thm)],[t19852]) ).
cnf(t6243,plain,
top = composition(join(one,X1),top),
inference(cp,[status(thm)],[t6241,t43]) ).
cnf(t6264,plain,
composition(join(one,X1),top) = top,
inference(orient,[status(thm)],[t6243]) ).
cnf(t6279,plain,
composition(converse(top),join(one,X1)) = converse(top),
inference(cp,[status(thm)],[t3866,t6264]) ).
cnf(t19855,plain,
composition(top,join(one,X1)) = converse(top),
inference(step,[status(thm)],[t6279,t366]) ).
cnf(t19856,plain,
composition(top,join(one,X1)) = top,
inference(step,[status(thm)],[t19855,t366]) ).
cnf(t6298,plain,
composition(top,join(one,X1)) = top,
inference(orient,[status(thm)],[t19856]) ).
cnf(t6299,plain,
top = composition(top,join(X1,one)),
inference(cp,[status(thm)],[t6298,t43]) ).
cnf(t6313,plain,
composition(top,join(X1,one)) = top,
inference(orient,[status(thm)],[t6299]) ).
cnf(t6320,plain,
complement(join(X1,one)) = join(complement(join(X1,one)),composition(converse(top),complement(top))),
inference(cp,[status(thm)],[t54,t6313]) ).
cnf(t19878,plain,
complement(join(X1,one)) = join(complement(join(X1,one)),composition(top,complement(top))),
inference(step,[status(thm)],[t6320,t366]) ).
cnf(t19879,plain,
complement(join(X1,one)) = join(composition(top,complement(top)),complement(join(X1,one))),
inference(step,[status(thm)],[t19878,t43]) ).
cnf(t19880,plain,
complement(join(X1,one)) = join(composition(top,zero),complement(join(X1,one))),
inference(step,[status(thm)],[t19879,t98]) ).
cnf(t19881,plain,
complement(join(X1,one)) = join(zero,complement(join(X1,one))),
inference(step,[status(thm)],[t19880,t4301]) ).
cnf(t7095,plain,
join(zero,complement(join(X1,one))) = complement(join(X1,one)),
inference(orient,[status(thm)],[t19881]) ).
cnf(t7104,plain,
zero = composition(join(X1,complement(join(X2,one))),zero),
inference(cp,[status(thm)],[t4690,t7095]) ).
cnf(t7364,plain,
composition(join(X1,complement(join(X2,one))),zero) = zero,
inference(orient,[status(thm)],[t7104]) ).
fof(f2,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(f2_nnf,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t13,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t18,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t45,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t18]) ).
cnf(t20052,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t45,t43]) ).
cnf(t20053,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t20052,t83]) ).
cnf(t20054,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t20053,t43]) ).
cnf(t15067,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t20054]) ).
cnf(t15282,plain,
zero = composition(X1,zero),
inference(cp,[status(thm)],[t7364,t15067]) ).
cnf(t15287,plain,
composition(X1,zero) = zero,
inference(orient,[status(thm)],[t15282]) ).
cnf(t20267,plain,
join(zero,X1) = join(meet(composition(sk1,sk0),sk2),join(composition(meet(sk1,composition(sk2,converse(sk0))),zero),X1)),
inference(step,[status(thm)],[t20266,t15287]) ).
cnf(t219,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t215,t98]) ).
cnf(t19517,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t219,t98]) ).
cnf(t19518,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t19517,t98]) ).
cnf(t226,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t19518]) ).
cnf(t227,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t46,t226]) ).
cnf(t245,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t227]) ).
cnf(t15068,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t15067,t90]) ).
cnf(t20162,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t15068,t83]) ).
cnf(t15742,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t20162]) ).
cnf(t15747,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t245,t15742]) ).
cnf(t20164,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t15747,t15742]) ).
cnf(t15762,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t20164]) ).
cnf(t20268,plain,
X1 = join(meet(composition(sk1,sk0),sk2),join(composition(meet(sk1,composition(sk2,converse(sk0))),zero),X1)),
inference(step,[status(thm)],[t20267,t15762]) ).
cnf(t20269,plain,
X1 = join(meet(sk2,composition(sk1,sk0)),join(composition(meet(sk1,composition(sk2,converse(sk0))),zero),X1)),
inference(step,[status(thm)],[t20268,t107]) ).
cnf(t20270,plain,
X1 = join(meet(sk2,composition(sk1,sk0)),join(zero,X1)),
inference(step,[status(thm)],[t20269,t15287]) ).
cnf(t20271,plain,
X1 = join(meet(sk2,composition(sk1,sk0)),X1),
inference(step,[status(thm)],[t20270,t15762]) ).
cnf(t19422,plain,
join(meet(sk2,composition(sk1,sk0)),X1) = X1,
inference(orient,[status(thm)],[t20271]) ).
cnf(t15768,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t15762,t43]) ).
cnf(t15800,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t15768]) ).
cnf(t19438,plain,
zero = meet(sk2,composition(sk1,sk0)),
inference(cp,[status(thm)],[t19422,t15800]) ).
cnf(t19500,plain,
meet(sk2,composition(sk1,sk0)) = zero,
inference(orient,[status(thm)],[t19438]) ).
cnf(c17,plain,
meet(composition(sk1,sk0),sk2) != zero,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
meet(composition(sk1,sk0),sk2) != zero,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(g0_0,plain,
meet(sk2,composition(sk1,sk0)) != zero,
inference(rw,[status(thm)],[goal_0,t107]) ).
cnf(g0_1,plain,
zero != zero,
inference(rw,[status(thm)],[g0_0,t19500]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL011+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n003.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
% 0.09/0.35 % DateTime : Thu Sep 24 07:13:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.37/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.37/1.65 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------