%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL013+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 : n002.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 02:34:43 PM UTC 2026
% Result : Theorem 5.79s 6.37s
% Output : Proof 5.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 107
% Number of leaves : 15
% Syntax : Number of formulae : 282 ( 277 unt; 0 def)
% Number of atoms : 287 ( 286 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 3 |; 2 &)
% ( 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 : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 388 ( 44 sgn 77 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,conjecture,
! [X0] :
( composition(zero,X0) = zero
& composition(X0,zero) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0] :
( composition(zero,X0) = zero
& composition(X0,zero) = zero ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0] :
( composition(zero,X0) != zero
| composition(X0,zero) != zero ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( composition(zero,sk0) != zero
| composition(sk0,zero) != zero ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f13_nnf]) ).
cnf(c13,plain,
( composition(zero,sk0) != zero
| composition(sk0,zero) != zero ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t14,plain,
ifeq(composition(sk0,zero),zero,ifeq(composition(zero,sk0),zero,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t62,plain,
ifeq(composition(sk0,zero),zero,ifeq(composition(zero,sk0),zero,false,true),true) = true,
inference(orient,[status(thm)],[t14]) ).
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(t29,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(orient,[status(thm)],[t11]) ).
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]) ).
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(t5,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t21,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t4006,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t12,t21]) ).
cnf(t32,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t4006]) ).
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(t23,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
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(t46,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(t19,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t48,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t46,t19]) ).
cnf(t131,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t48]) ).
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(t132,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t131,t18]) ).
cnf(t4011,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t132,t19]) ).
cnf(t146,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t4011]) ).
cnf(t147,plain,
one = converse(one),
inference(cp,[status(thm)],[t146,t18]) ).
cnf(t153,plain,
converse(one) = one,
inference(orient,[status(thm)],[t147]) ).
cnf(t4012,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t146,t153]) ).
cnf(t163,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t4012]) ).
cnf(t164,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t163]) ).
cnf(t167,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t32,t164]) ).
cnf(t4014,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t167,t153]) ).
cnf(t4015,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t4014,t164]) ).
cnf(t191,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t4015]) ).
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(t53,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t6]) ).
cnf(t201,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t53,t191]) ).
cnf(t208,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t201]) ).
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(t15,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t22,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t15]) ).
cnf(t4027,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t22,t21]) ).
cnf(t4028,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t4027,t53]) ).
cnf(t4029,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t4028,t21]) ).
cnf(t287,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t4029]) ).
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(t60,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t288,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t287,t60]) ).
cnf(t4036,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t288,t53]) ).
cnf(t323,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t4036]) ).
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(t26,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t54,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t53,t26]) ).
cnf(t4007,plain,
zero = complement(top),
inference(step,[status(thm)],[t54,t60]) ).
cnf(t63,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t4007]) ).
cnf(t195,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t191,t63]) ).
cnf(t4016,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t195,t63]) ).
cnf(t4017,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t4016,t63]) ).
cnf(t202,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t4017]) ).
cnf(t203,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t23,t202]) ).
cnf(t218,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t203]) ).
cnf(t325,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t218,t323]) ).
cnf(t4037,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t325,t323]) ).
cnf(t327,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t4037]) ).
cnf(t4038,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t323,t327]) ).
cnf(t334,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t4038]) ).
cnf(t349,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t334]) ).
cnf(t4044,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t208,t349]) ).
cnf(t351,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t4044]) ).
cnf(t358,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t351]) ).
cnf(t360,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t191,t358]) ).
cnf(t4051,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t360,t358]) ).
cnf(t4052,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t4051,t358]) ).
cnf(t369,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t4052]) ).
cnf(t371,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t23,t369]) ).
cnf(t443,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t371]) ).
cnf(t445,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1),
inference(cp,[status(thm)],[t443,t287]) ).
cnf(t4056,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t445,t287]) ).
cnf(t4057,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t4056,t21]) ).
cnf(t449,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t4057]) ).
cnf(t55,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t53,t21]) ).
cnf(t4009,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t55,t53]) ).
cnf(t72,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t4009]) ).
cnf(t451,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t449,t72]) ).
cnf(t456,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t451]) ).
cnf(t459,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t23,t456]) ).
cnf(t1114,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t459]) ).
cnf(t359,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(cp,[status(thm)],[t358,t53]) ).
cnf(t606,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t359]) ).
cnf(t609,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(cp,[status(thm)],[t606,t358]) ).
cnf(t636,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(orient,[status(thm)],[t609]) ).
cnf(t646,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t358,t636]) ).
cnf(t683,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t646]) ).
cnf(t4079,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(step,[status(thm)],[t287,t683]) ).
cnf(t709,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[t4079]) ).
cnf(t1906,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(orient,[status(thm)],[t709]) ).
cnf(t1946,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(cp,[status(thm)],[t1114,t1906]) ).
cnf(t1956,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t1946]) ).
cnf(t1960,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(cp,[status(thm)],[t1956,t72]) ).
cnf(t1990,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t1960]) ).
cnf(t1999,plain,
join(complement(X1),X2) = join(complement(X1),meet(X1,X2)),
inference(cp,[status(thm)],[t1990,t358]) ).
cnf(t2770,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t1999]) ).
cnf(t447,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(cp,[status(thm)],[t443,t21]) ).
cnf(t462,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t447]) ).
cnf(t28,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(cp,[status(thm)],[t23,t26]) ).
cnf(t251,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(orient,[status(thm)],[t28]) ).
cnf(t213,plain,
top = join(complement(X1),meet(X1,X1)),
inference(cp,[status(thm)],[t26,t208]) ).
cnf(t229,plain,
join(complement(X1),meet(X1,X1)) = top,
inference(orient,[status(thm)],[t213]) ).
cnf(t255,plain,
join(top,meet(X1,X1)) = join(X1,top),
inference(cp,[status(thm)],[t251,t229]) ).
cnf(t257,plain,
join(top,complement(X1)) = join(X1,complement(X1)),
inference(cp,[status(thm)],[t251,t191]) ).
cnf(t4022,plain,
join(top,complement(X1)) = top,
inference(step,[status(thm)],[t257,t26]) ).
cnf(t268,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t4022]) ).
cnf(t269,plain,
top = join(top,meet(X1,X2)),
inference(cp,[status(thm)],[t268,t53]) ).
cnf(t276,plain,
join(top,meet(X1,X2)) = top,
inference(orient,[status(thm)],[t269]) ).
cnf(t4024,plain,
top = join(X1,top),
inference(step,[status(thm)],[t255,t276]) ).
cnf(t281,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t4024]) ).
cnf(t282,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t281,t21]) ).
cnf(t307,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t282]) ).
cnf(t4030,plain,
join(X1,join(complement(X1),X2)) = top,
inference(step,[status(thm)],[t251,t307]) ).
cnf(t308,plain,
join(X1,join(complement(X1),X2)) = top,
inference(orient,[status(thm)],[t4030]) ).
cnf(t464,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),top),
inference(cp,[status(thm)],[t462,t308]) ).
cnf(t4065,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),top),
inference(step,[status(thm)],[t464,t23]) ).
cnf(t4066,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,top)),
inference(step,[status(thm)],[t4065,t23]) ).
cnf(t4067,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),top),
inference(step,[status(thm)],[t4066,t281]) ).
cnf(t4068,plain,
join(complement(X1),join(X2,X1)) = top,
inference(step,[status(thm)],[t4067,t281]) ).
cnf(t520,plain,
join(complement(X1),join(X2,X1)) = top,
inference(orient,[status(thm)],[t4068]) ).
cnf(t527,plain,
top = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t520,t456]) ).
cnf(t4074,plain,
top = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t527,t21]) ).
cnf(t555,plain,
join(X1,complement(meet(X2,X1))) = top,
inference(orient,[status(thm)],[t4074]) ).
cnf(t560,plain,
meet(X1,meet(X2,complement(X1))) = complement(top),
inference(cp,[status(thm)],[t53,t555]) ).
cnf(t4076,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t560,t63]) ).
cnf(t569,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t4076]) ).
cnf(t570,plain,
zero = meet(complement(X1),meet(X2,X1)),
inference(cp,[status(thm)],[t569,t358]) ).
cnf(t580,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t570]) ).
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(t36,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t8]) ).
cnf(t38,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t36,t19]) ).
cnf(t100,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t38]) ).
cnf(t101,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(cp,[status(thm)],[t100,t26]) ).
cnf(t234,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(orient,[status(thm)],[t101]) ).
cnf(t310,plain,
top = converse(top),
inference(cp,[status(thm)],[t307,t234]) ).
cnf(t313,plain,
converse(top) = top,
inference(orient,[status(thm)],[t310]) ).
cnf(t4034,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(step,[status(thm)],[t234,t313]) ).
cnf(t316,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(orient,[status(thm)],[t4034]) ).
cnf(t686,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = complement(top),
inference(cp,[status(thm)],[t683,t316]) ).
cnf(t4105,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(step,[status(thm)],[t686,t63]) ).
cnf(t1901,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(orient,[status(thm)],[t4105]) ).
cnf(t1993,plain,
join(X1,complement(converse(complement(converse(complement(complement(X1))))))) = join(X1,zero),
inference(cp,[status(thm)],[t1990,t1901]) ).
cnf(t4108,plain,
join(X1,complement(converse(complement(converse(X1))))) = join(X1,zero),
inference(step,[status(thm)],[t1993,t358]) ).
cnf(t331,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t327,t21]) ).
cnf(t345,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t331]) ).
cnf(t4109,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t4108,t345]) ).
cnf(t2050,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t4109]) ).
cnf(t2082,plain,
join(X1,converse(complement(converse(complement(converse(converse(X1))))))) = converse(converse(X1)),
inference(cp,[status(thm)],[t100,t2050]) ).
cnf(t4116,plain,
join(X1,converse(complement(converse(complement(X1))))) = converse(converse(X1)),
inference(step,[status(thm)],[t2082,t19]) ).
cnf(t4117,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(step,[status(thm)],[t4116,t19]) ).
cnf(t2404,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(orient,[status(thm)],[t4117]) ).
cnf(t2426,plain,
meet(X1,complement(converse(complement(converse(complement(complement(X1))))))) = complement(complement(X1)),
inference(cp,[status(thm)],[t683,t2404]) ).
cnf(t4118,plain,
meet(X1,complement(converse(complement(converse(X1))))) = complement(complement(X1)),
inference(step,[status(thm)],[t2426,t358]) ).
cnf(t4119,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t4118,t358]) ).
cnf(t2433,plain,
meet(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t4119]) ).
cnf(t2455,plain,
zero = meet(complement(complement(converse(complement(converse(X1))))),X1),
inference(cp,[status(thm)],[t580,t2433]) ).
cnf(t4120,plain,
zero = meet(X1,complement(complement(converse(complement(converse(X1)))))),
inference(step,[status(thm)],[t2455,t72]) ).
cnf(t4121,plain,
zero = meet(X1,converse(complement(converse(X1)))),
inference(step,[status(thm)],[t4120,t358]) ).
cnf(t2470,plain,
meet(X1,converse(complement(converse(X1)))) = zero,
inference(orient,[status(thm)],[t4121]) ).
cnf(t2483,plain,
zero = meet(converse(X1),converse(complement(X1))),
inference(cp,[status(thm)],[t2470,t19]) ).
cnf(t2488,plain,
meet(converse(X1),converse(complement(X1))) = zero,
inference(orient,[status(thm)],[t2483]) ).
cnf(t2789,plain,
join(complement(converse(X1)),converse(complement(X1))) = join(complement(converse(X1)),zero),
inference(cp,[status(thm)],[t2770,t2488]) ).
cnf(t4134,plain,
join(converse(complement(X1)),complement(converse(X1))) = join(complement(converse(X1)),zero),
inference(step,[status(thm)],[t2789,t21]) ).
cnf(t4135,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(step,[status(thm)],[t4134,t345]) ).
cnf(t3176,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(orient,[status(thm)],[t4135]) ).
cnf(t3181,plain,
complement(converse(complement(X1))) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t3176,t358]) ).
cnf(t2060,plain,
converse(X1) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t2050,t19]) ).
cnf(t2981,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(orient,[status(thm)],[t2060]) ).
cnf(t4136,plain,
complement(converse(complement(X1))) = converse(X1),
inference(step,[status(thm)],[t3181,t2981]) ).
cnf(t3216,plain,
complement(converse(complement(X1))) = converse(X1),
inference(orient,[status(thm)],[t4136]) ).
cnf(t3221,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(cp,[status(thm)],[t3216,t358]) ).
cnf(t3256,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(orient,[status(thm)],[t3221]) ).
cnf(t319,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(cp,[status(thm)],[t46,t313]) ).
cnf(t411,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(orient,[status(thm)],[t319]) ).
cnf(t3263,plain,
converse(complement(composition(top,X1))) = complement(composition(converse(X1),top)),
inference(cp,[status(thm)],[t3256,t411]) ).
cnf(t3536,plain,
complement(composition(converse(X1),top)) = converse(complement(composition(top,X1))),
inference(orient,[status(thm)],[t3263]) ).
cnf(t3586,plain,
complement(top) = join(complement(top),composition(converse(converse(X1)),converse(complement(composition(top,X1))))),
inference(cp,[status(thm)],[t32,t3536]) ).
cnf(t4149,plain,
zero = join(complement(top),composition(converse(converse(X1)),converse(complement(composition(top,X1))))),
inference(step,[status(thm)],[t3586,t63]) ).
cnf(t4150,plain,
zero = join(zero,composition(converse(converse(X1)),converse(complement(composition(top,X1))))),
inference(step,[status(thm)],[t4149,t63]) ).
cnf(t4151,plain,
zero = composition(converse(converse(X1)),converse(complement(composition(top,X1)))),
inference(step,[status(thm)],[t4150,t327]) ).
cnf(t4152,plain,
zero = converse(composition(complement(composition(top,X1)),converse(X1))),
inference(step,[status(thm)],[t4151,t46]) ).
cnf(t47,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(cp,[status(thm)],[t46,t19]) ).
cnf(t119,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(orient,[status(thm)],[t47]) ).
cnf(t4153,plain,
zero = composition(X1,converse(complement(composition(top,X1)))),
inference(step,[status(thm)],[t4152,t119]) ).
cnf(t3852,plain,
composition(X1,converse(complement(composition(top,X1)))) = zero,
inference(orient,[status(thm)],[t4153]) ).
cnf(t3550,plain,
converse(complement(composition(top,top))) = complement(composition(top,top)),
inference(cp,[status(thm)],[t3536,t313]) ).
cnf(t3589,plain,
converse(complement(composition(top,top))) = complement(composition(top,top)),
inference(orient,[status(thm)],[t3550]) ).
cnf(t3856,plain,
zero = composition(top,complement(composition(top,top))),
inference(cp,[status(thm)],[t3852,t3589]) ).
cnf(t3874,plain,
composition(top,complement(composition(top,top))) = zero,
inference(orient,[status(thm)],[t3856]) ).
cnf(t3877,plain,
composition(join(top,X1),complement(composition(top,top))) = join(zero,composition(X1,complement(composition(top,top)))),
inference(cp,[status(thm)],[t29,t3874]) ).
cnf(t4158,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(X1,complement(composition(top,top)))),
inference(step,[status(thm)],[t3877,t307]) ).
cnf(t4159,plain,
zero = join(zero,composition(X1,complement(composition(top,top)))),
inference(step,[status(thm)],[t4158,t3874]) ).
cnf(t4160,plain,
zero = composition(X1,complement(composition(top,top))),
inference(step,[status(thm)],[t4159,t327]) ).
cnf(t3894,plain,
composition(X1,complement(composition(top,top))) = zero,
inference(orient,[status(thm)],[t4160]) ).
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(t41,plain,
composition(composition(X1,X2),X3) = composition(X1,composition(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t3896,plain,
zero = composition(X1,composition(X2,complement(composition(top,top)))),
inference(cp,[status(thm)],[t3894,t41]) ).
cnf(t4161,plain,
zero = composition(X1,zero),
inference(step,[status(thm)],[t3896,t3894]) ).
cnf(t3901,plain,
composition(X1,zero) = zero,
inference(orient,[status(thm)],[t4161]) ).
cnf(t4181,plain,
ifeq(zero,zero,ifeq(composition(zero,sk0),zero,false,true),true) = true,
inference(step,[status(thm)],[t62,t3901]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t20,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t4182,plain,
ifeq(composition(zero,sk0),zero,false,true) = true,
inference(step,[status(thm)],[t4181,t20]) ).
cnf(t3916,plain,
ifeq(composition(zero,sk0),zero,false,true) = true,
inference(rw,[status(thm)],[t4182]) ).
cnf(t3911,plain,
composition(converse(zero),X1) = converse(zero),
inference(cp,[status(thm)],[t131,t3901]) ).
cnf(t330,plain,
converse(complement(converse(zero))) = top,
inference(cp,[status(thm)],[t327,t316]) ).
cnf(t375,plain,
converse(complement(converse(zero))) = top,
inference(orient,[status(thm)],[t330]) ).
cnf(t376,plain,
complement(converse(zero)) = converse(top),
inference(cp,[status(thm)],[t19,t375]) ).
cnf(t4054,plain,
complement(converse(zero)) = top,
inference(step,[status(thm)],[t376,t313]) ).
cnf(t387,plain,
complement(converse(zero)) = top,
inference(orient,[status(thm)],[t4054]) ).
cnf(t388,plain,
converse(zero) = complement(top),
inference(cp,[status(thm)],[t358,t387]) ).
cnf(t4055,plain,
converse(zero) = zero,
inference(step,[status(thm)],[t388,t63]) ).
cnf(t393,plain,
converse(zero) = zero,
inference(orient,[status(thm)],[t4055]) ).
cnf(t4185,plain,
composition(zero,X1) = converse(zero),
inference(step,[status(thm)],[t3911,t393]) ).
cnf(t4186,plain,
composition(zero,X1) = zero,
inference(step,[status(thm)],[t4185,t393]) ).
cnf(t3919,plain,
composition(zero,X1) = zero,
inference(orient,[status(thm)],[t4186]) ).
cnf(t4194,plain,
ifeq(zero,zero,false,true) = true,
inference(step,[status(thm)],[t3916,t3919]) ).
cnf(t4195,plain,
false = true,
inference(step,[status(thm)],[t4194,t20]) ).
cnf(t4005,plain,
false = true,
inference(orient,[status(thm)],[t4195]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t4005]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL013+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/5.57 % Computer : n002.cluster.edu
% 0.08/5.57 % Model : x86_64 x86_64
% 0.08/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.57 % Memory : 8046.5625MB
% 0.08/5.57 % OS : Linux 6.8.0-71-generic
% 0.08/5.57 % CPULimit : 300
% 0.08/5.57 % WCLimit : 300
% 0.08/5.57 % DateTime : Thu Sep 24 07:14:40 UTC 2026
% 0.08/5.57 % CPUTime :
% 0.08/5.57 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.79/6.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.79/6.37 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------