%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL004+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 02:34:36 PM UTC 2026
% Result : Theorem 4.26s 0.99s
% Output : Proof 4.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 81
% Number of leaves : 12
% Syntax : Number of formulae : 223 ( 223 unt; 0 def)
% Number of atoms : 223 ( 222 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 318 ( 30 sgn 59 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(t20,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]) ).
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(t18,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t3296,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t11,t18]) ).
cnf(t29,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t3296]) ).
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(t50,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(t17,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t52,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t50,t17]) ).
cnf(t127,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t52]) ).
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(t128,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t127,t16]) ).
cnf(t3301,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t128,t17]) ).
cnf(t142,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t3301]) ).
cnf(t143,plain,
one = converse(one),
inference(cp,[status(thm)],[t142,t16]) ).
cnf(t149,plain,
converse(one) = one,
inference(orient,[status(thm)],[t143]) ).
cnf(t3302,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t142,t149]) ).
cnf(t159,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t3302]) ).
cnf(t160,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t159]) ).
cnf(t163,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t29,t160]) ).
cnf(t3304,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t163,t149]) ).
cnf(t3305,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t3304,t160]) ).
cnf(t187,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t3305]) ).
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(t38,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t5]) ).
cnf(t197,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t38,t187]) ).
cnf(t204,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t197]) ).
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(t13,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t12]) ).
cnf(t19,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t13]) ).
cnf(t3323,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t19,t18]) ).
cnf(t3324,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t3323,t38]) ).
cnf(t3325,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t3324,t18]) ).
cnf(t299,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t3325]) ).
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(t57,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t300,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t299,t57]) ).
cnf(t3326,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t300,t38]) ).
cnf(t319,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t3326]) ).
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(t23,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t39,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t38,t23]) ).
cnf(t3297,plain,
zero = complement(top),
inference(step,[status(thm)],[t39,t57]) ).
cnf(t59,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t3297]) ).
cnf(t191,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t187,t59]) ).
cnf(t3306,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t191,t59]) ).
cnf(t3307,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t3306,t59]) ).
cnf(t198,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t3307]) ).
cnf(t199,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t20,t198]) ).
cnf(t214,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t199]) ).
cnf(t321,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t214,t319]) ).
cnf(t3327,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t321,t319]) ).
cnf(t323,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t3327]) ).
cnf(t3328,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t319,t323]) ).
cnf(t330,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t3328]) ).
cnf(t345,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t330]) ).
cnf(t3334,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t204,t345]) ).
cnf(t347,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t3334]) ).
cnf(t354,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t347]) ).
cnf(t356,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t187,t354]) ).
cnf(t3341,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t356,t354]) ).
cnf(t3342,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t3341,t354]) ).
cnf(t365,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t3342]) ).
cnf(t367,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t20,t365]) ).
cnf(t439,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t367]) ).
cnf(t441,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1),
inference(cp,[status(thm)],[t439,t299]) ).
cnf(t3346,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t441,t299]) ).
cnf(t3347,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t3346,t18]) ).
cnf(t445,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t3347]) ).
cnf(t40,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t38,t18]) ).
cnf(t3299,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t40,t38]) ).
cnf(t68,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t3299]) ).
cnf(t447,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t445,t68]) ).
cnf(t452,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t447]) ).
cnf(t455,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t20,t452]) ).
cnf(t1110,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t455]) ).
cnf(t355,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(cp,[status(thm)],[t354,t38]) ).
cnf(t602,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t355]) ).
cnf(t605,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(cp,[status(thm)],[t602,t354]) ).
cnf(t632,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(orient,[status(thm)],[t605]) ).
cnf(t642,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t354,t632]) ).
cnf(t679,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t642]) ).
cnf(t3369,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(step,[status(thm)],[t299,t679]) ).
cnf(t705,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[t3369]) ).
cnf(t1902,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(orient,[status(thm)],[t705]) ).
cnf(t1942,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(cp,[status(thm)],[t1110,t1902]) ).
cnf(t1952,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t1942]) ).
cnf(t1956,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(cp,[status(thm)],[t1952,t68]) ).
cnf(t1986,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t1956]) ).
cnf(t1995,plain,
join(complement(X1),X2) = join(complement(X1),meet(X1,X2)),
inference(cp,[status(thm)],[t1986,t354]) ).
cnf(t2766,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t1995]) ).
cnf(t443,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(cp,[status(thm)],[t439,t18]) ).
cnf(t458,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t443]) ).
cnf(t25,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(cp,[status(thm)],[t20,t23]) ).
cnf(t247,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(orient,[status(thm)],[t25]) ).
cnf(t209,plain,
top = join(complement(X1),meet(X1,X1)),
inference(cp,[status(thm)],[t23,t204]) ).
cnf(t225,plain,
join(complement(X1),meet(X1,X1)) = top,
inference(orient,[status(thm)],[t209]) ).
cnf(t251,plain,
join(top,meet(X1,X1)) = join(X1,top),
inference(cp,[status(thm)],[t247,t225]) ).
cnf(t253,plain,
join(top,complement(X1)) = join(X1,complement(X1)),
inference(cp,[status(thm)],[t247,t187]) ).
cnf(t3312,plain,
join(top,complement(X1)) = top,
inference(step,[status(thm)],[t253,t23]) ).
cnf(t264,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t3312]) ).
cnf(t265,plain,
top = join(top,meet(X1,X2)),
inference(cp,[status(thm)],[t264,t38]) ).
cnf(t272,plain,
join(top,meet(X1,X2)) = top,
inference(orient,[status(thm)],[t265]) ).
cnf(t3314,plain,
top = join(X1,top),
inference(step,[status(thm)],[t251,t272]) ).
cnf(t277,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t3314]) ).
cnf(t278,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t277,t18]) ).
cnf(t283,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t278]) ).
cnf(t3317,plain,
join(X1,join(complement(X1),X2)) = top,
inference(step,[status(thm)],[t247,t283]) ).
cnf(t284,plain,
join(X1,join(complement(X1),X2)) = top,
inference(orient,[status(thm)],[t3317]) ).
cnf(t460,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),top),
inference(cp,[status(thm)],[t458,t284]) ).
cnf(t3355,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),top),
inference(step,[status(thm)],[t460,t20]) ).
cnf(t3356,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,top)),
inference(step,[status(thm)],[t3355,t20]) ).
cnf(t3357,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),top),
inference(step,[status(thm)],[t3356,t277]) ).
cnf(t3358,plain,
join(complement(X1),join(X2,X1)) = top,
inference(step,[status(thm)],[t3357,t277]) ).
cnf(t516,plain,
join(complement(X1),join(X2,X1)) = top,
inference(orient,[status(thm)],[t3358]) ).
cnf(t523,plain,
top = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t516,t452]) ).
cnf(t3364,plain,
top = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t523,t18]) ).
cnf(t551,plain,
join(X1,complement(meet(X2,X1))) = top,
inference(orient,[status(thm)],[t3364]) ).
cnf(t556,plain,
meet(X1,meet(X2,complement(X1))) = complement(top),
inference(cp,[status(thm)],[t38,t551]) ).
cnf(t3366,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t556,t59]) ).
cnf(t565,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t3366]) ).
cnf(t566,plain,
zero = meet(complement(X1),meet(X2,X1)),
inference(cp,[status(thm)],[t565,t354]) ).
cnf(t576,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t566]) ).
fof(f8,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).
fof(f8_nnf,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t7,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t33,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t7]) ).
cnf(t35,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t33,t17]) ).
cnf(t96,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t35]) ).
cnf(t97,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(cp,[status(thm)],[t96,t23]) ).
cnf(t230,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(orient,[status(thm)],[t97]) ).
cnf(t286,plain,
top = converse(top),
inference(cp,[status(thm)],[t283,t230]) ).
cnf(t289,plain,
converse(top) = top,
inference(orient,[status(thm)],[t286]) ).
cnf(t3321,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(step,[status(thm)],[t230,t289]) ).
cnf(t292,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(orient,[status(thm)],[t3321]) ).
cnf(t682,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = complement(top),
inference(cp,[status(thm)],[t679,t292]) ).
cnf(t3395,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(step,[status(thm)],[t682,t59]) ).
cnf(t1897,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(orient,[status(thm)],[t3395]) ).
cnf(t1989,plain,
join(X1,complement(converse(complement(converse(complement(complement(X1))))))) = join(X1,zero),
inference(cp,[status(thm)],[t1986,t1897]) ).
cnf(t3398,plain,
join(X1,complement(converse(complement(converse(X1))))) = join(X1,zero),
inference(step,[status(thm)],[t1989,t354]) ).
cnf(t327,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t323,t18]) ).
cnf(t341,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t327]) ).
cnf(t3399,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t3398,t341]) ).
cnf(t2046,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t3399]) ).
cnf(t2078,plain,
join(X1,converse(complement(converse(complement(converse(converse(X1))))))) = converse(converse(X1)),
inference(cp,[status(thm)],[t96,t2046]) ).
cnf(t3406,plain,
join(X1,converse(complement(converse(complement(X1))))) = converse(converse(X1)),
inference(step,[status(thm)],[t2078,t17]) ).
cnf(t3407,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(step,[status(thm)],[t3406,t17]) ).
cnf(t2400,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(orient,[status(thm)],[t3407]) ).
cnf(t2422,plain,
meet(X1,complement(converse(complement(converse(complement(complement(X1))))))) = complement(complement(X1)),
inference(cp,[status(thm)],[t679,t2400]) ).
cnf(t3408,plain,
meet(X1,complement(converse(complement(converse(X1))))) = complement(complement(X1)),
inference(step,[status(thm)],[t2422,t354]) ).
cnf(t3409,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t3408,t354]) ).
cnf(t2429,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t3409]) ).
cnf(t2451,plain,
zero = meet(complement(complement(converse(complement(converse(X1))))),X1),
inference(cp,[status(thm)],[t576,t2429]) ).
cnf(t3410,plain,
zero = meet(X1,complement(complement(converse(complement(converse(X1)))))),
inference(step,[status(thm)],[t2451,t68]) ).
cnf(t3411,plain,
zero = meet(X1,converse(complement(converse(X1)))),
inference(step,[status(thm)],[t3410,t354]) ).
cnf(t2466,plain,
meet(X1,converse(complement(converse(X1)))) = zero,
inference(orient,[status(thm)],[t3411]) ).
cnf(t2479,plain,
zero = meet(converse(X1),converse(complement(X1))),
inference(cp,[status(thm)],[t2466,t17]) ).
cnf(t2484,plain,
meet(converse(X1),converse(complement(X1))) = zero,
inference(orient,[status(thm)],[t2479]) ).
cnf(t2785,plain,
join(complement(converse(X1)),converse(complement(X1))) = join(complement(converse(X1)),zero),
inference(cp,[status(thm)],[t2766,t2484]) ).
cnf(t3424,plain,
join(converse(complement(X1)),complement(converse(X1))) = join(complement(converse(X1)),zero),
inference(step,[status(thm)],[t2785,t18]) ).
cnf(t3425,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(step,[status(thm)],[t3424,t341]) ).
cnf(t3172,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(orient,[status(thm)],[t3425]) ).
cnf(t3177,plain,
complement(converse(complement(X1))) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t3172,t354]) ).
cnf(t2056,plain,
converse(X1) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t2046,t17]) ).
cnf(t2977,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(orient,[status(thm)],[t2056]) ).
cnf(t3426,plain,
complement(converse(complement(X1))) = converse(X1),
inference(step,[status(thm)],[t3177,t2977]) ).
cnf(t3212,plain,
complement(converse(complement(X1))) = converse(X1),
inference(orient,[status(thm)],[t3426]) ).
cnf(t3217,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(cp,[status(thm)],[t3212,t354]) ).
cnf(t3252,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(orient,[status(thm)],[t3217]) ).
fof(f13,conjecture,
! [X0] : converse(complement(X0)) = complement(converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0] : converse(complement(X0)) = complement(converse(X0)),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0] : converse(complement(X0)) != complement(converse(X0)),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
converse(complement(sk0)) != complement(converse(sk0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f13_nnf]) ).
cnf(c13,plain,
converse(complement(sk0)) != complement(converse(sk0)),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
converse(complement(sk0)) != complement(converse(sk0)),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(g0_0,plain,
converse(complement(sk0)) != converse(complement(sk0)),
inference(rw,[status(thm)],[goal_0,t3252]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL004+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n007.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 07:03:53 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.26/0.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.26/0.99 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------