%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL031+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 02:35:53 PM UTC 2026
% Result : Theorem 204.61s 30.69s
% Output : Proof 204.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 109
% Number of leaves : 14
% Syntax : Number of formulae : 314 ( 310 unt; 0 def)
% Number of atoms : 322 ( 321 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 7 ~; 0 |; 6 &)
% ( 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 447 ( 49 sgn 79 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(t20,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/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(t11,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t22,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
fof(f13,conjecture,
! [X0,X1] :
( ( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X0),X0),one) = one )
=> join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) = one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0,X1] :
( ( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X0),X0),one) = one )
=> join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) = one ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0,X1] :
( join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) != one
& join(composition(converse(X1),X1),one) = one
& join(composition(converse(X0),X0),one) = one ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( join(composition(converse(composition(sk0,sk1)),composition(sk0,sk1)),one) != one
& join(composition(converse(sk1),sk1),one) = one
& join(composition(converse(sk0),sk0),one) = one ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f13_nnf]) ).
cnf(c14,plain,
join(composition(converse(sk1),sk1),one) = one,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t6,plain,
join(composition(converse(sk1),sk1),one) = one,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t814721,plain,
join(one,composition(converse(sk1),sk1)) = one,
inference(step,[status(thm)],[t6,t20]) ).
cnf(t37,plain,
join(one,composition(converse(sk1),sk1)) = one,
inference(orient,[status(thm)],[t814721]) ).
cnf(t38,plain,
join(one,join(composition(converse(sk1),sk1),X1)) = join(one,X1),
inference(cp,[status(thm)],[t22,t37]) ).
cnf(t9981,plain,
join(one,join(composition(converse(sk1),sk1),X1)) = join(one,X1),
inference(orient,[status(thm)],[t38]) ).
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(t12,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t28,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(orient,[status(thm)],[t12]) ).
cnf(t9983,plain,
join(one,composition(X1,sk1)) = join(one,composition(join(converse(sk1),X1),sk1)),
inference(cp,[status(thm)],[t9981,t28]) ).
cnf(t116280,plain,
join(one,composition(join(converse(sk1),X1),sk1)) = join(one,composition(X1,sk1)),
inference(orient,[status(thm)],[t9983]) ).
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(t19,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
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(t8,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t49,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(orient,[status(thm)],[t8]) ).
cnf(t53,plain,
composition(join(converse(X1),X2),converse(X3)) = join(converse(composition(X3,X1)),composition(X2,converse(X3))),
inference(cp,[status(thm)],[t28,t49]) ).
cnf(t25067,plain,
join(converse(composition(X1,X2)),composition(X3,converse(X1))) = composition(join(converse(X2),X3),converse(X1)),
inference(orient,[status(thm)],[t53]) ).
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(t18,plain,
composition(X1,one) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t25072,plain,
composition(join(converse(one),X1),converse(X2)) = join(converse(X2),composition(X1,converse(X2))),
inference(cp,[status(thm)],[t25067,t18]) ).
cnf(t51,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t49,t19]) ).
cnf(t133,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t51]) ).
cnf(t134,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t133,t18]) ).
cnf(t814726,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t134,t19]) ).
cnf(t148,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t814726]) ).
cnf(t149,plain,
one = converse(one),
inference(cp,[status(thm)],[t148,t18]) ).
cnf(t155,plain,
converse(one) = one,
inference(orient,[status(thm)],[t149]) ).
cnf(t815295,plain,
composition(join(one,X1),converse(X2)) = join(converse(X2),composition(X1,converse(X2))),
inference(step,[status(thm)],[t25072,t155]) ).
cnf(t39891,plain,
join(converse(X1),composition(X2,converse(X1))) = composition(join(one,X2),converse(X1)),
inference(orient,[status(thm)],[t815295]) ).
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(t13,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t814719,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t13,t20]) ).
cnf(t31,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t814719]) ).
cnf(t814727,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t148,t155]) ).
cnf(t165,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t814727]) ).
cnf(t166,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t165]) ).
cnf(t169,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t31,t166]) ).
cnf(t814729,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t169,t155]) ).
cnf(t814730,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t814729,t166]) ).
cnf(t193,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t814730]) ).
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(t7,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t56,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t7]) ).
cnf(t203,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t56,t193]) ).
cnf(t210,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t203]) ).
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(t14,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t15,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t14]) ).
cnf(t21,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t15]) ).
cnf(t814742,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t21,t20]) ).
cnf(t814743,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t814742,t56]) ).
cnf(t814744,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t814743,t20]) ).
cnf(t289,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t814744]) ).
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(t63,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t290,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t289,t63]) ).
cnf(t814751,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t290,t56]) ).
cnf(t325,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t814751]) ).
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(t25,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t57,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t56,t25]) ).
cnf(t814722,plain,
zero = complement(top),
inference(step,[status(thm)],[t57,t63]) ).
cnf(t65,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t814722]) ).
cnf(t197,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t193,t65]) ).
cnf(t814731,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t197,t65]) ).
cnf(t814732,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t814731,t65]) ).
cnf(t204,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t814732]) ).
cnf(t205,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t22,t204]) ).
cnf(t220,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t205]) ).
cnf(t327,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t220,t325]) ).
cnf(t814752,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t327,t325]) ).
cnf(t329,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t814752]) ).
cnf(t814753,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t325,t329]) ).
cnf(t336,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t814753]) ).
cnf(t351,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t336]) ).
cnf(t814759,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t210,t351]) ).
cnf(t353,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t814759]) ).
cnf(t360,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t353]) ).
cnf(t362,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t193,t360]) ).
cnf(t814766,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t362,t360]) ).
cnf(t814767,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t814766,t360]) ).
cnf(t371,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t814767]) ).
cnf(t373,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t22,t371]) ).
cnf(t445,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t373]) ).
cnf(t447,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1),
inference(cp,[status(thm)],[t445,t289]) ).
cnf(t814771,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t447,t289]) ).
cnf(t814772,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t814771,t20]) ).
cnf(t451,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t814772]) ).
cnf(t58,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t56,t20]) ).
cnf(t814724,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t58,t56]) ).
cnf(t74,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t814724]) ).
cnf(t453,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t451,t74]) ).
cnf(t458,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t453]) ).
cnf(t461,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t22,t458]) ).
cnf(t1160,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t461]) ).
cnf(t361,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(cp,[status(thm)],[t360,t56]) ).
cnf(t616,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t361]) ).
cnf(t619,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(cp,[status(thm)],[t616,t360]) ).
cnf(t646,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(orient,[status(thm)],[t619]) ).
cnf(t656,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t360,t646]) ).
cnf(t693,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t656]) ).
cnf(t814794,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(step,[status(thm)],[t289,t693]) ).
cnf(t719,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[t814794]) ).
cnf(t2089,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(orient,[status(thm)],[t719]) ).
cnf(t2130,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(cp,[status(thm)],[t1160,t2089]) ).
cnf(t2142,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t2130]) ).
cnf(t2146,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(cp,[status(thm)],[t2142,t74]) ).
cnf(t2177,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t2146]) ).
cnf(t2186,plain,
join(complement(X1),X2) = join(complement(X1),meet(X1,X2)),
inference(cp,[status(thm)],[t2177,t360]) ).
cnf(t2874,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t2186]) ).
cnf(t449,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(cp,[status(thm)],[t445,t20]) ).
cnf(t464,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t449]) ).
cnf(t27,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(cp,[status(thm)],[t22,t25]) ).
cnf(t253,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(orient,[status(thm)],[t27]) ).
cnf(t215,plain,
top = join(complement(X1),meet(X1,X1)),
inference(cp,[status(thm)],[t25,t210]) ).
cnf(t231,plain,
join(complement(X1),meet(X1,X1)) = top,
inference(orient,[status(thm)],[t215]) ).
cnf(t257,plain,
join(top,meet(X1,X1)) = join(X1,top),
inference(cp,[status(thm)],[t253,t231]) ).
cnf(t259,plain,
join(top,complement(X1)) = join(X1,complement(X1)),
inference(cp,[status(thm)],[t253,t193]) ).
cnf(t814737,plain,
join(top,complement(X1)) = top,
inference(step,[status(thm)],[t259,t25]) ).
cnf(t270,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t814737]) ).
cnf(t271,plain,
top = join(top,meet(X1,X2)),
inference(cp,[status(thm)],[t270,t56]) ).
cnf(t278,plain,
join(top,meet(X1,X2)) = top,
inference(orient,[status(thm)],[t271]) ).
cnf(t814739,plain,
top = join(X1,top),
inference(step,[status(thm)],[t257,t278]) ).
cnf(t283,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t814739]) ).
cnf(t284,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t283,t20]) ).
cnf(t309,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t284]) ).
cnf(t814745,plain,
join(X1,join(complement(X1),X2)) = top,
inference(step,[status(thm)],[t253,t309]) ).
cnf(t310,plain,
join(X1,join(complement(X1),X2)) = top,
inference(orient,[status(thm)],[t814745]) ).
cnf(t466,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),top),
inference(cp,[status(thm)],[t464,t310]) ).
cnf(t814780,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),top),
inference(step,[status(thm)],[t466,t22]) ).
cnf(t814781,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,top)),
inference(step,[status(thm)],[t814780,t22]) ).
cnf(t814782,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),top),
inference(step,[status(thm)],[t814781,t283]) ).
cnf(t814783,plain,
join(complement(X1),join(X2,X1)) = top,
inference(step,[status(thm)],[t814782,t283]) ).
cnf(t526,plain,
join(complement(X1),join(X2,X1)) = top,
inference(orient,[status(thm)],[t814783]) ).
cnf(t533,plain,
top = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t526,t458]) ).
cnf(t814789,plain,
top = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t533,t20]) ).
cnf(t563,plain,
join(X1,complement(meet(X2,X1))) = top,
inference(orient,[status(thm)],[t814789]) ).
cnf(t569,plain,
meet(X1,meet(X2,complement(X1))) = complement(top),
inference(cp,[status(thm)],[t56,t563]) ).
cnf(t814791,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t569,t65]) ).
cnf(t577,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t814791]) ).
cnf(t578,plain,
zero = meet(complement(X1),meet(X2,X1)),
inference(cp,[status(thm)],[t577,t360]) ).
cnf(t588,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t578]) ).
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(t9,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t39,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t9]) ).
cnf(t41,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t39,t19]) ).
cnf(t102,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t41]) ).
cnf(t103,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(cp,[status(thm)],[t102,t25]) ).
cnf(t236,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(orient,[status(thm)],[t103]) ).
cnf(t312,plain,
top = converse(top),
inference(cp,[status(thm)],[t309,t236]) ).
cnf(t315,plain,
converse(top) = top,
inference(orient,[status(thm)],[t312]) ).
cnf(t814749,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(step,[status(thm)],[t236,t315]) ).
cnf(t318,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(orient,[status(thm)],[t814749]) ).
cnf(t696,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = complement(top),
inference(cp,[status(thm)],[t693,t318]) ).
cnf(t814827,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(step,[status(thm)],[t696,t65]) ).
cnf(t2084,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(orient,[status(thm)],[t814827]) ).
cnf(t2180,plain,
join(X1,complement(converse(complement(converse(complement(complement(X1))))))) = join(X1,zero),
inference(cp,[status(thm)],[t2177,t2084]) ).
cnf(t814830,plain,
join(X1,complement(converse(complement(converse(X1))))) = join(X1,zero),
inference(step,[status(thm)],[t2180,t360]) ).
cnf(t333,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t329,t20]) ).
cnf(t347,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t333]) ).
cnf(t814831,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t814830,t347]) ).
cnf(t2238,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t814831]) ).
cnf(t2270,plain,
join(X1,converse(complement(converse(complement(converse(converse(X1))))))) = converse(converse(X1)),
inference(cp,[status(thm)],[t102,t2238]) ).
cnf(t814837,plain,
join(X1,converse(complement(converse(complement(X1))))) = converse(converse(X1)),
inference(step,[status(thm)],[t2270,t19]) ).
cnf(t814838,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(step,[status(thm)],[t814837,t19]) ).
cnf(t2496,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(orient,[status(thm)],[t814838]) ).
cnf(t2517,plain,
meet(X1,complement(converse(complement(converse(complement(complement(X1))))))) = complement(complement(X1)),
inference(cp,[status(thm)],[t693,t2496]) ).
cnf(t814839,plain,
meet(X1,complement(converse(complement(converse(X1))))) = complement(complement(X1)),
inference(step,[status(thm)],[t2517,t360]) ).
cnf(t814840,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t814839,t360]) ).
cnf(t2525,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t814840]) ).
cnf(t2547,plain,
zero = meet(complement(complement(converse(complement(converse(X1))))),X1),
inference(cp,[status(thm)],[t588,t2525]) ).
cnf(t814841,plain,
zero = meet(X1,complement(complement(converse(complement(converse(X1)))))),
inference(step,[status(thm)],[t2547,t74]) ).
cnf(t814842,plain,
zero = meet(X1,converse(complement(converse(X1)))),
inference(step,[status(thm)],[t814841,t360]) ).
cnf(t2562,plain,
meet(X1,converse(complement(converse(X1)))) = zero,
inference(orient,[status(thm)],[t814842]) ).
cnf(t2575,plain,
zero = meet(converse(X1),converse(complement(X1))),
inference(cp,[status(thm)],[t2562,t19]) ).
cnf(t2580,plain,
meet(converse(X1),converse(complement(X1))) = zero,
inference(orient,[status(thm)],[t2575]) ).
cnf(t2893,plain,
join(complement(converse(X1)),converse(complement(X1))) = join(complement(converse(X1)),zero),
inference(cp,[status(thm)],[t2874,t2580]) ).
cnf(t814855,plain,
join(converse(complement(X1)),complement(converse(X1))) = join(complement(converse(X1)),zero),
inference(step,[status(thm)],[t2893,t20]) ).
cnf(t814856,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(step,[status(thm)],[t814855,t347]) ).
cnf(t3284,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(orient,[status(thm)],[t814856]) ).
cnf(t3289,plain,
complement(converse(complement(X1))) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t3284,t360]) ).
cnf(t2248,plain,
converse(X1) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t2238,t19]) ).
cnf(t3089,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(orient,[status(thm)],[t2248]) ).
cnf(t814857,plain,
complement(converse(complement(X1))) = converse(X1),
inference(step,[status(thm)],[t3289,t3089]) ).
cnf(t3324,plain,
complement(converse(complement(X1))) = converse(X1),
inference(orient,[status(thm)],[t814857]) ).
cnf(t3329,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(cp,[status(thm)],[t3324,t360]) ).
cnf(t3364,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(orient,[status(thm)],[t3329]) ).
cnf(t618,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(cp,[status(thm)],[t616,t360]) ).
cnf(t625,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t618]) ).
cnf(t636,plain,
meet(complement(X1),X2) = complement(join(X1,complement(X2))),
inference(cp,[status(thm)],[t360,t625]) ).
cnf(t667,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(orient,[status(thm)],[t636]) ).
cnf(t2244,plain,
one = join(one,complement(converse(complement(one)))),
inference(cp,[status(thm)],[t2238,t155]) ).
cnf(t2278,plain,
join(one,complement(converse(complement(one)))) = one,
inference(orient,[status(thm)],[t2244]) ).
cnf(t2292,plain,
meet(complement(one),converse(complement(one))) = complement(one),
inference(cp,[status(thm)],[t667,t2278]) ).
cnf(t2302,plain,
meet(complement(one),converse(complement(one))) = complement(one),
inference(orient,[status(thm)],[t2292]) ).
cnf(t2311,plain,
converse(complement(one)) = join(converse(complement(one)),complement(one)),
inference(cp,[status(thm)],[t458,t2302]) ).
cnf(t814835,plain,
converse(complement(one)) = join(complement(one),converse(complement(one))),
inference(step,[status(thm)],[t2311,t20]) ).
cnf(t462,plain,
join(X1,converse(meet(X2,converse(X1)))) = converse(converse(X1)),
inference(cp,[status(thm)],[t102,t458]) ).
cnf(t814796,plain,
join(X1,converse(meet(X2,converse(X1)))) = X1,
inference(step,[status(thm)],[t462,t19]) ).
cnf(t752,plain,
join(X1,converse(meet(X2,converse(X1)))) = X1,
inference(orient,[status(thm)],[t814796]) ).
cnf(t2319,plain,
complement(one) = join(complement(one),converse(complement(one))),
inference(cp,[status(thm)],[t752,t2302]) ).
cnf(t2321,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(orient,[status(thm)],[t2319]) ).
cnf(t814836,plain,
converse(complement(one)) = complement(one),
inference(step,[status(thm)],[t814835,t2321]) ).
cnf(t2362,plain,
converse(complement(one)) = complement(one),
inference(orient,[status(thm)],[t814836]) ).
cnf(t2366,plain,
converse(join(X1,complement(one))) = join(converse(X1),complement(one)),
inference(cp,[status(thm)],[t39,t2362]) ).
cnf(t2473,plain,
converse(join(X1,complement(one))) = join(converse(X1),complement(one)),
inference(orient,[status(thm)],[t2366]) ).
cnf(t3365,plain,
converse(complement(join(X1,complement(one)))) = complement(join(converse(X1),complement(one))),
inference(cp,[status(thm)],[t3364,t2473]) ).
cnf(t814860,plain,
converse(meet(complement(X1),one)) = complement(join(converse(X1),complement(one))),
inference(step,[status(thm)],[t3365,t667]) ).
cnf(t814861,plain,
converse(meet(one,complement(X1))) = complement(join(converse(X1),complement(one))),
inference(step,[status(thm)],[t814860,t74]) ).
cnf(t814862,plain,
converse(meet(one,complement(X1))) = meet(complement(converse(X1)),one),
inference(step,[status(thm)],[t814861,t667]) ).
cnf(t814863,plain,
converse(meet(one,complement(X1))) = meet(one,complement(converse(X1))),
inference(step,[status(thm)],[t814862,t74]) ).
cnf(t814864,plain,
converse(meet(one,complement(X1))) = meet(one,converse(complement(X1))),
inference(step,[status(thm)],[t814863,t3364]) ).
cnf(t3408,plain,
converse(meet(one,complement(X1))) = meet(one,converse(complement(X1))),
inference(orient,[status(thm)],[t814864]) ).
cnf(t3419,plain,
meet(one,converse(complement(complement(X1)))) = converse(meet(one,X1)),
inference(cp,[status(thm)],[t3408,t360]) ).
cnf(t814865,plain,
meet(one,converse(X1)) = converse(meet(one,X1)),
inference(step,[status(thm)],[t3419,t360]) ).
cnf(t3438,plain,
converse(meet(one,X1)) = meet(one,converse(X1)),
inference(orient,[status(thm)],[t814865]) ).
cnf(t3450,plain,
converse(composition(X1,meet(one,X2))) = composition(meet(one,converse(X2)),converse(X1)),
inference(cp,[status(thm)],[t49,t3438]) ).
cnf(t34796,plain,
composition(meet(one,converse(X1)),converse(X2)) = converse(composition(X2,meet(one,X1))),
inference(orient,[status(thm)],[t3450]) ).
cnf(t39941,plain,
composition(join(one,meet(one,converse(X1))),converse(X2)) = join(converse(X2),converse(composition(X2,meet(one,X1)))),
inference(cp,[status(thm)],[t39891,t34796]) ).
cnf(t815296,plain,
composition(one,converse(X2)) = join(converse(X2),converse(composition(X2,meet(one,X1)))),
inference(step,[status(thm)],[t39941,t451]) ).
cnf(t815297,plain,
converse(X2) = join(converse(X2),converse(composition(X2,meet(one,X1)))),
inference(step,[status(thm)],[t815296,t166]) ).
cnf(t815298,plain,
converse(X2) = converse(join(X2,composition(X2,meet(one,X1)))),
inference(step,[status(thm)],[t815297,t39]) ).
cnf(t40073,plain,
converse(join(X1,composition(X1,meet(one,X2)))) = converse(X1),
inference(orient,[status(thm)],[t815298]) ).
cnf(t40092,plain,
join(X1,composition(X1,meet(one,X2))) = converse(converse(X1)),
inference(cp,[status(thm)],[t19,t40073]) ).
cnf(t815302,plain,
join(X1,composition(X1,meet(one,X2))) = X1,
inference(step,[status(thm)],[t40092,t19]) ).
cnf(t40280,plain,
join(X1,composition(X1,meet(one,X2))) = X1,
inference(orient,[status(thm)],[t815302]) ).
cnf(t366,plain,
top = join(complement(X1),join(X1,X2)),
inference(cp,[status(thm)],[t310,t360]) ).
cnf(t474,plain,
join(complement(X1),join(X1,X2)) = top,
inference(orient,[status(thm)],[t366]) ).
cnf(t489,plain,
X1 = join(meet(X1,join(X1,X2)),complement(top)),
inference(cp,[status(thm)],[t289,t474]) ).
cnf(t814773,plain,
X1 = join(complement(top),meet(X1,join(X1,X2))),
inference(step,[status(thm)],[t489,t20]) ).
cnf(t814774,plain,
X1 = join(zero,meet(X1,join(X1,X2))),
inference(step,[status(thm)],[t814773,t65]) ).
cnf(t814775,plain,
X1 = meet(X1,join(X1,X2)),
inference(step,[status(thm)],[t814774,t329]) ).
cnf(t490,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t814775]) ).
cnf(t495,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t490,t20]) ).
cnf(t496,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t495]) ).
cnf(c13,plain,
join(composition(converse(sk0),sk0),one) = one,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t5,plain,
join(composition(converse(sk0),sk0),one) = one,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t814720,plain,
join(one,composition(converse(sk0),sk0)) = one,
inference(step,[status(thm)],[t5,t20]) ).
cnf(t35,plain,
join(one,composition(converse(sk0),sk0)) = one,
inference(orient,[status(thm)],[t814720]) ).
cnf(t503,plain,
composition(converse(sk0),sk0) = meet(composition(converse(sk0),sk0),one),
inference(cp,[status(thm)],[t496,t35]) ).
cnf(t814811,plain,
composition(converse(sk0),sk0) = meet(one,composition(converse(sk0),sk0)),
inference(step,[status(thm)],[t503,t74]) ).
cnf(t980,plain,
meet(one,composition(converse(sk0),sk0)) = composition(converse(sk0),sk0),
inference(orient,[status(thm)],[t814811]) ).
cnf(t40284,plain,
X1 = join(X1,composition(X1,composition(converse(sk0),sk0))),
inference(cp,[status(thm)],[t40280,t980]) ).
cnf(t40841,plain,
join(X1,composition(X1,composition(converse(sk0),sk0))) = X1,
inference(orient,[status(thm)],[t40284]) ).
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(t10,plain,
composition(composition(X1,X2),X3) = composition(X1,composition(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t44,plain,
composition(composition(X1,X2),X3) = composition(X1,composition(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t52,plain,
composition(converse(X1),composition(converse(X2),X3)) = composition(converse(composition(X2,X1)),X3),
inference(cp,[status(thm)],[t44,t49]) ).
cnf(t17900,plain,
composition(converse(X1),composition(converse(X2),X3)) = composition(converse(composition(X2,X1)),X3),
inference(orient,[status(thm)],[t52]) ).
cnf(t40845,plain,
converse(X1) = join(converse(X1),composition(converse(composition(sk0,X1)),sk0)),
inference(cp,[status(thm)],[t40841,t17900]) ).
cnf(t86942,plain,
join(converse(X1),composition(converse(composition(sk0,X1)),sk0)) = converse(X1),
inference(orient,[status(thm)],[t40845]) ).
cnf(t116293,plain,
join(one,composition(composition(converse(composition(sk0,sk1)),sk0),sk1)) = join(one,composition(converse(sk1),sk1)),
inference(cp,[status(thm)],[t116280,t86942]) ).
cnf(t818856,plain,
join(one,composition(converse(composition(sk0,sk1)),composition(sk0,sk1))) = join(one,composition(converse(sk1),sk1)),
inference(step,[status(thm)],[t116293,t44]) ).
cnf(t818857,plain,
join(one,composition(converse(composition(sk0,sk1)),composition(sk0,sk1))) = one,
inference(step,[status(thm)],[t818856,t37]) ).
cnf(t814509,plain,
join(one,composition(converse(composition(sk0,sk1)),composition(sk0,sk1))) = one,
inference(orient,[status(thm)],[t818857]) ).
cnf(c15,plain,
join(composition(converse(composition(sk0,sk1)),composition(sk0,sk1)),one) != one,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
join(composition(converse(composition(sk0,sk1)),composition(sk0,sk1)),one) != one,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(g0_0,plain,
join(one,composition(converse(composition(sk0,sk1)),composition(sk0,sk1))) != one,
inference(rw,[status(thm)],[goal_0,t20]) ).
cnf(g0_1,plain,
one != one,
inference(rw,[status(thm)],[g0_0,t814509]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL031+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 07:29:08 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 204.61/30.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 204.61/30.69 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------