%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL023+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 02:34:50 PM UTC 2026
% Result : Theorem 12.46s 7.15s
% Output : Proof 12.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 12
% Syntax : Number of formulae : 133 ( 133 unt; 0 def)
% Number of atoms : 133 ( 132 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 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 : 201 ( 3 sgn 66 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/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(t10,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t23,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(orient,[status(thm)],[t10]) ).
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(t4,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t42,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t4]) ).
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(t9,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t45,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
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(t11,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t16009,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t11,t42]) ).
cnf(t53,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t16009]) ).
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(t6,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)],[t6]) ).
fof(f7,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f7_nnf,plain,
! [X0] : converse(converse(X0)) = X0,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X0] : converse(converse(X0)) = X0,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
converse(converse(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t1,plain,
converse(converse(X1)) = X1,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t20,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t28,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t26,t20]) ).
cnf(t148,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(t16,plain,
composition(X1,one) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t149,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t148,t16]) ).
cnf(t16014,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t149,t20]) ).
cnf(t161,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t16014]) ).
cnf(t162,plain,
one = converse(one),
inference(cp,[status(thm)],[t161,t16]) ).
cnf(t171,plain,
converse(one) = one,
inference(orient,[status(thm)],[t162]) ).
cnf(t16015,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t161,t171]) ).
cnf(t181,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t16015]) ).
cnf(t182,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t181]) ).
cnf(t185,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t53,t182]) ).
cnf(t16017,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t185,t171]) ).
cnf(t16018,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t16017,t182]) ).
cnf(t211,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t16018]) ).
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(t5,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t82,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t5]) ).
cnf(t212,plain,
complement(join(complement(X1),complement(X2))) = join(meet(X1,X2),complement(join(complement(X1),complement(X2)))),
inference(cp,[status(thm)],[t211,t82]) ).
cnf(t16038,plain,
meet(X1,X2) = join(meet(X1,X2),complement(join(complement(X1),complement(X2)))),
inference(step,[status(thm)],[t212,t82]) ).
cnf(t16039,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X1,X2)),
inference(step,[status(thm)],[t16038,t82]) ).
cnf(t435,plain,
join(meet(X1,X2),meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t16039]) ).
cnf(t84,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t82,t42]) ).
cnf(t16012,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t84,t82]) ).
cnf(t103,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t16012]) ).
cnf(t436,plain,
meet(X1,X2) = join(meet(X2,X1),meet(X1,X2)),
inference(cp,[status(thm)],[t435,t103]) ).
cnf(t456,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X2,X1),
inference(orient,[status(thm)],[t436]) ).
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(t12,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t17,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t12]) ).
cnf(t44,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t17]) ).
cnf(t16554,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t44,t42]) ).
cnf(t16555,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t16554,t82]) ).
cnf(t16556,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t16555,t42]) ).
cnf(t15096,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t16556]) ).
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(t89,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t15097,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t15096,t89]) ).
cnf(t16664,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t15097,t82]) ).
cnf(t15771,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t16664]) ).
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(t50,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t83,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t82,t50]) ).
cnf(t16010,plain,
zero = complement(top),
inference(step,[status(thm)],[t83,t89]) ).
cnf(t94,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t16010]) ).
cnf(t215,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t211,t94]) ).
cnf(t16019,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t215,t94]) ).
cnf(t16020,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t16019,t94]) ).
cnf(t222,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t16020]) ).
cnf(t223,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t45,t222]) ).
cnf(t241,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t223]) ).
cnf(t15776,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t241,t15771]) ).
cnf(t16666,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t15776,t15771]) ).
cnf(t15791,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t16666]) ).
cnf(t16671,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t15771,t15791]) ).
cnf(t15817,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t16671]) ).
cnf(t15843,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t15817]) ).
cnf(t15844,plain,
meet(X1,X1) = join(X1,meet(X1,X1)),
inference(cp,[status(thm)],[t456,t15843]) ).
cnf(t16706,plain,
X1 = join(X1,meet(X1,X1)),
inference(step,[status(thm)],[t15844,t15843]) ).
cnf(t16707,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t16706,t15843]) ).
cnf(t15910,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t16707]) ).
cnf(t15914,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t45,t15910]) ).
cnf(t15957,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t15914]) ).
cnf(t15973,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1),
inference(cp,[status(thm)],[t15957,t15096]) ).
cnf(t16711,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t15973,t15096]) ).
cnf(t16712,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t16711,t42]) ).
cnf(t15982,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t16712]) ).
fof(f16,conjecture,
! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) != composition(X0,meet(X1,X2)),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
join(composition(meet(sk0,converse(sk1)),meet(sk1,sk2)),composition(sk0,meet(sk1,sk2))) != composition(sk0,meet(sk1,sk2)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f16_nnf]) ).
cnf(c16,plain,
join(composition(meet(sk0,converse(sk1)),meet(sk1,sk2)),composition(sk0,meet(sk1,sk2))) != composition(sk0,meet(sk1,sk2)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
join(composition(meet(sk0,converse(sk1)),meet(sk1,sk2)),composition(sk0,meet(sk1,sk2))) != composition(sk0,meet(sk1,sk2)),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(g0_0,plain,
composition(join(meet(sk0,converse(sk1)),sk0),meet(sk1,sk2)) != composition(sk0,meet(sk1,sk2)),
inference(rw,[status(thm)],[goal_0,t23]) ).
cnf(g0_1,plain,
composition(join(sk0,meet(sk0,converse(sk1))),meet(sk1,sk2)) != composition(sk0,meet(sk1,sk2)),
inference(rw,[status(thm)],[g0_0,t42]) ).
cnf(g0_2,plain,
composition(sk0,meet(sk1,sk2)) != composition(sk0,meet(sk1,sk2)),
inference(rw,[status(thm)],[g0_1,t15982]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL023+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.37 % Computer : n018.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 07:21:09 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.46/7.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.46/7.15 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------