%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL050-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 02:36:13 PM UTC 2026
% Result : Unsatisfiable 22.95s 3.34s
% Output : Proof 22.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 101
% Number of leaves : 20
% Syntax : Number of formulae : 411 ( 407 unt; 0 def)
% Number of atoms : 415 ( 414 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 11 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-4 aty)
% Number of variables : 282 ( 16 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f13,negated_conjecture,
( join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f13_nnf,plain,
( join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
( join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t13,plain,
ifeq(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),composition(complement(composition(sk1,top)),top),ifeq(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),complement(composition(sk1,top)),false,true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t14,axiom,
sF0 = composition(sk1,top),
introduced(definition) ).
cnf(t23,plain,
composition(sk1,top) = sF0,
inference(orient,[status(thm)],[t14]) ).
cnf(t8967,plain,
ifeq(join(complement(sF0),composition(complement(composition(sk1,top)),top)),composition(complement(composition(sk1,top)),top),ifeq(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),complement(composition(sk1,top)),false,true),true) = true,
inference(step,[status(thm)],[t13,t23]) ).
cnf(t15,axiom,
sF1 = complement(composition(sk1,top)),
introduced(definition) ).
cnf(t8939,plain,
sF1 = complement(sF0),
inference(step,[status(thm)],[t15,t23]) ).
cnf(t25,plain,
complement(sF0) = sF1,
inference(orient,[status(thm)],[t8939]) ).
cnf(t8968,plain,
ifeq(join(sF1,composition(complement(composition(sk1,top)),top)),composition(complement(composition(sk1,top)),top),ifeq(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),complement(composition(sk1,top)),false,true),true) = true,
inference(step,[status(thm)],[t8967,t25]) ).
cnf(t8969,plain,
ifeq(join(sF1,composition(complement(sF0),top)),composition(complement(composition(sk1,top)),top),ifeq(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),complement(composition(sk1,top)),false,true),true) = true,
inference(step,[status(thm)],[t8968,t23]) ).
cnf(t8970,plain,
ifeq(join(sF1,composition(sF1,top)),composition(complement(composition(sk1,top)),top),ifeq(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),complement(composition(sk1,top)),false,true),true) = true,
inference(step,[status(thm)],[t8969,t25]) ).
cnf(t8971,plain,
ifeq(join(sF1,composition(sF1,top)),composition(complement(sF0),top),ifeq(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),complement(composition(sk1,top)),false,true),true) = true,
inference(step,[status(thm)],[t8970,t23]) ).
cnf(t8972,plain,
ifeq(join(sF1,composition(sF1,top)),composition(sF1,top),ifeq(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),complement(composition(sk1,top)),false,true),true) = true,
inference(step,[status(thm)],[t8971,t25]) ).
cnf(f0,axiom,
join(A,B) = join(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f0_nnf,plain,
! [A,B] : join(A,B) = join(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : join(A,B) = join(B,A),
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(t39,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t8973,plain,
ifeq(join(sF1,composition(sF1,top)),composition(sF1,top),ifeq(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),complement(composition(sk1,top)),false,true),true) = true,
inference(step,[status(thm)],[t8972,t39]) ).
cnf(t8974,plain,
ifeq(join(sF1,composition(sF1,top)),composition(sF1,top),ifeq(join(complement(sF0),composition(complement(composition(sk1,top)),top)),complement(composition(sk1,top)),false,true),true) = true,
inference(step,[status(thm)],[t8973,t23]) ).
cnf(t8975,plain,
ifeq(join(sF1,composition(sF1,top)),composition(sF1,top),ifeq(join(sF1,composition(complement(composition(sk1,top)),top)),complement(composition(sk1,top)),false,true),true) = true,
inference(step,[status(thm)],[t8974,t25]) ).
cnf(t8976,plain,
ifeq(join(sF1,composition(sF1,top)),composition(sF1,top),ifeq(join(sF1,composition(complement(sF0),top)),complement(composition(sk1,top)),false,true),true) = true,
inference(step,[status(thm)],[t8975,t23]) ).
cnf(t8977,plain,
ifeq(join(sF1,composition(sF1,top)),composition(sF1,top),ifeq(join(sF1,composition(sF1,top)),complement(composition(sk1,top)),false,true),true) = true,
inference(step,[status(thm)],[t8976,t25]) ).
cnf(t8978,plain,
ifeq(join(sF1,composition(sF1,top)),composition(sF1,top),ifeq(join(sF1,composition(sF1,top)),complement(sF0),false,true),true) = true,
inference(step,[status(thm)],[t8977,t23]) ).
cnf(t8979,plain,
ifeq(join(sF1,composition(sF1,top)),composition(sF1,top),ifeq(join(sF1,composition(sF1,top)),sF1,false,true),true) = true,
inference(step,[status(thm)],[t8978,t25]) ).
cnf(t229,plain,
ifeq(join(sF1,composition(sF1,top)),composition(sF1,top),ifeq(join(sF1,composition(sF1,top)),sF1,false,true),true) = true,
inference(orient,[status(thm)],[t8979]) ).
cnf(t16,axiom,
sF2 = composition(complement(composition(sk1,top)),top),
introduced(definition) ).
cnf(t8989,plain,
sF2 = composition(complement(sF0),top),
inference(step,[status(thm)],[t16,t23]) ).
cnf(t8990,plain,
sF2 = composition(sF1,top),
inference(step,[status(thm)],[t8989,t25]) ).
cnf(t273,plain,
composition(sF1,top) = sF2,
inference(orient,[status(thm)],[t8990]) ).
cnf(t8991,plain,
ifeq(join(sF1,sF2),composition(sF1,top),ifeq(join(sF1,composition(sF1,top)),sF1,false,true),true) = true,
inference(step,[status(thm)],[t229,t273]) ).
cnf(t8992,plain,
ifeq(join(sF1,sF2),sF2,ifeq(join(sF1,composition(sF1,top)),sF1,false,true),true) = true,
inference(step,[status(thm)],[t8991,t273]) ).
cnf(t8993,plain,
ifeq(join(sF1,sF2),sF2,ifeq(join(sF1,sF2),sF1,false,true),true) = true,
inference(step,[status(thm)],[t8992,t273]) ).
cnf(t274,plain,
ifeq(join(sF1,sF2),sF2,ifeq(join(sF1,sF2),sF1,false,true),true) = true,
inference(rw,[status(thm)],[t8993]) ).
cnf(f2,axiom,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
fof(f2_nnf,plain,
! [A,B] : A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
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(t8953,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t12,t39]) ).
cnf(t188,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(orient,[status(thm)],[t8953]) ).
cnf(f10,axiom,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f10_nnf,plain,
! [A,B] : join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A,B] : join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t11,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t8949,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t11,t39]) ).
cnf(t155,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t8949]) ).
cnf(f9,axiom,
converse(composition(A,B)) = composition(converse(B),converse(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f9_nnf,plain,
! [A,B] : converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] : converse(composition(A,B)) = composition(converse(B),converse(A)),
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(t29,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(orient,[status(thm)],[t6]) ).
cnf(f7,axiom,
converse(converse(A)) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f7_nnf,plain,
! [A] : converse(converse(A)) = A,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A] : converse(converse(A)) = A,
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(t22,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t31,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t29,t22]) ).
cnf(t55,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t31]) ).
cnf(f5,axiom,
composition(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f5_nnf,plain,
! [A] : composition(A,one) = A,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : composition(A,one) = A,
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(t21,plain,
composition(X1,one) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t56,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t55,t21]) ).
cnf(t8940,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t56,t22]) ).
cnf(t59,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t8940]) ).
cnf(t60,plain,
one = converse(one),
inference(cp,[status(thm)],[t59,t21]) ).
cnf(t61,plain,
converse(one) = one,
inference(orient,[status(thm)],[t60]) ).
cnf(t165,plain,
complement(X1) = join(complement(X1),composition(one,complement(composition(one,X1)))),
inference(cp,[status(thm)],[t155,t61]) ).
cnf(t8941,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t59,t61]) ).
cnf(t62,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t8941]) ).
cnf(t66,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t62]) ).
cnf(t8954,plain,
complement(X1) = join(complement(X1),complement(composition(one,X1))),
inference(step,[status(thm)],[t165,t66]) ).
cnf(t8955,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t8954,t66]) ).
cnf(t202,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t8955]) ).
cnf(t206,plain,
X1 = join(complement(complement(X1)),complement(join(complement(X1),complement(complement(X1))))),
inference(cp,[status(thm)],[t188,t202]) ).
cnf(f11,axiom,
top = join(A,complement(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
fof(f11_nnf,plain,
! [A] : top = join(A,complement(A)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] : top = join(A,complement(A)),
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(t24,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t8964,plain,
X1 = join(complement(complement(X1)),complement(top)),
inference(step,[status(thm)],[t206,t24]) ).
cnf(t8965,plain,
X1 = join(complement(top),complement(complement(X1))),
inference(step,[status(thm)],[t8964,t39]) ).
cnf(f12,axiom,
zero = meet(A,complement(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(f12_nnf,plain,
! [A] : zero = meet(A,complement(A)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A] : zero = meet(A,complement(A)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(u0,axiom,
zero = meet(X0,complement(X0)),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f3,axiom,
meet(A,B) = complement(join(complement(A),complement(B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f3_nnf,plain,
! [A,B] : meet(A,B) = complement(join(complement(A),complement(B))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] : meet(A,B) = complement(join(complement(A),complement(B))),
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(d0,axiom,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t5,plain,
complement(join(complement(X1),complement(complement(X1)))) = zero,
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(t8942,plain,
complement(top) = zero,
inference(step,[status(thm)],[t5,t24]) ).
cnf(t75,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t8942]) ).
cnf(t8966,plain,
X1 = join(zero,complement(complement(X1))),
inference(step,[status(thm)],[t8965,t75]) ).
cnf(t221,plain,
join(zero,complement(complement(X1))) = X1,
inference(orient,[status(thm)],[t8966]) ).
cnf(f1,axiom,
join(A,join(B,C)) = join(join(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f1_nnf,plain,
! [A,B,C] : join(A,join(B,C)) = join(join(A,B),C),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] : join(A,join(B,C)) = join(join(A,B),C),
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(t43,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t204,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t202,t75]) ).
cnf(t8958,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t204,t75]) ).
cnf(t8959,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t8958,t75]) ).
cnf(t211,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t8959]) ).
cnf(t212,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t43,t211]) ).
cnf(t236,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t212]) ).
cnf(t239,plain,
join(zero,complement(complement(X1))) = join(zero,X1),
inference(cp,[status(thm)],[t236,t221]) ).
cnf(t8980,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t239,t221]) ).
cnf(t240,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t8980]) ).
cnf(t8986,plain,
complement(complement(X1)) = X1,
inference(step,[status(thm)],[t221,t240]) ).
cnf(t246,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[t8986]) ).
cnf(t268,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t246]) ).
cnf(f6,axiom,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f6_nnf,plain,
! [A,B,C] : composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] : composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t10,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t111,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(orient,[status(thm)],[t10]) ).
cnf(t119,plain,
composition(join(one,X1),X2) = join(X2,composition(X1,X2)),
inference(cp,[status(thm)],[t111,t66]) ).
cnf(t3435,plain,
composition(join(one,X1),X2) = join(X2,composition(X1,X2)),
inference(orient,[status(thm)],[t119]) ).
cnf(t272,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t202,t268]) ).
cnf(t9002,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t272,t268]) ).
cnf(t9003,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t9002,t268]) ).
cnf(t291,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t9003]) ).
cnf(t297,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t43,t291]) ).
cnf(t422,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t297]) ).
cnf(t425,plain,
join(X1,complement(X1)) = join(X1,top),
inference(cp,[status(thm)],[t422,t24]) ).
cnf(t9065,plain,
top = join(X1,top),
inference(step,[status(thm)],[t425,t24]) ).
cnf(t436,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t9065]) ).
cnf(t3443,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(cp,[status(thm)],[t3435,t436]) ).
cnf(t3517,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(orient,[status(thm)],[t3443]) ).
cnf(f8,axiom,
converse(join(A,B)) = join(converse(A),converse(B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f8_nnf,plain,
! [A,B] : converse(join(A,B)) = join(converse(A),converse(B)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B] : converse(join(A,B)) = join(converse(A),converse(B)),
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(t32,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t7]) ).
cnf(t33,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t32,t22]) ).
cnf(t89,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t33]) ).
cnf(t445,plain,
join(X1,converse(top)) = converse(top),
inference(cp,[status(thm)],[t89,t436]) ).
cnf(t480,plain,
join(X1,converse(top)) = converse(top),
inference(orient,[status(thm)],[t445]) ).
cnf(t26,plain,
top = join(sF0,sF1),
inference(cp,[status(thm)],[t24,t25]) ).
cnf(t27,plain,
join(sF0,sF1) = top,
inference(orient,[status(thm)],[t26]) ).
cnf(t46,plain,
join(sF0,join(sF1,X1)) = join(top,X1),
inference(cp,[status(thm)],[t43,t27]) ).
cnf(t104,plain,
join(sF0,join(sF1,X1)) = join(top,X1),
inference(orient,[status(thm)],[t46]) ).
cnf(t107,plain,
join(top,X1) = join(sF0,join(X1,sF1)),
inference(cp,[status(thm)],[t104,t39]) ).
cnf(t137,plain,
join(sF0,join(X1,sF1)) = join(top,X1),
inference(orient,[status(thm)],[t107]) ).
cnf(t138,plain,
join(top,X1) = join(join(X1,sF1),sF0),
inference(cp,[status(thm)],[t137,t39]) ).
cnf(t8950,plain,
join(top,X1) = join(X1,join(sF1,sF0)),
inference(step,[status(thm)],[t138,t43]) ).
cnf(t8951,plain,
join(top,X1) = join(X1,join(sF0,sF1)),
inference(step,[status(thm)],[t8950,t39]) ).
cnf(t8952,plain,
join(top,X1) = join(X1,top),
inference(step,[status(thm)],[t8951,t27]) ).
cnf(t181,plain,
join(top,X1) = join(X1,top),
inference(orient,[status(thm)],[t8952]) ).
cnf(t9066,plain,
join(top,X1) = top,
inference(step,[status(thm)],[t181,t436]) ).
cnf(t437,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t9066]) ).
cnf(t483,plain,
converse(top) = top,
inference(cp,[status(thm)],[t480,t437]) ).
cnf(t489,plain,
converse(top) = top,
inference(orient,[status(thm)],[t483]) ).
cnf(t493,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(cp,[status(thm)],[t29,t489]) ).
cnf(t522,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(orient,[status(thm)],[t493]) ).
cnf(t112,plain,
composition(join(sk1,X1),top) = join(sF0,composition(X1,top)),
inference(cp,[status(thm)],[t111,t23]) ).
cnf(t141,plain,
composition(join(sk1,X1),top) = join(sF0,composition(X1,top)),
inference(orient,[status(thm)],[t112]) ).
cnf(t158,plain,
complement(top) = join(complement(top),composition(converse(sk1),complement(sF0))),
inference(cp,[status(thm)],[t155,t23]) ).
cnf(t9104,plain,
zero = join(complement(top),composition(converse(sk1),complement(sF0))),
inference(step,[status(thm)],[t158,t75]) ).
cnf(t9105,plain,
zero = join(zero,composition(converse(sk1),complement(sF0))),
inference(step,[status(thm)],[t9104,t75]) ).
cnf(t9106,plain,
zero = composition(converse(sk1),complement(sF0)),
inference(step,[status(thm)],[t9105,t240]) ).
cnf(t9107,plain,
zero = composition(converse(sk1),sF1),
inference(step,[status(thm)],[t9106,t25]) ).
cnf(t1323,plain,
composition(converse(sk1),sF1) = zero,
inference(orient,[status(thm)],[t9107]) ).
cnf(t1325,plain,
composition(converse(sF1),sk1) = converse(zero),
inference(cp,[status(thm)],[t55,t1323]) ).
cnf(t34,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(cp,[status(thm)],[t32,t22]) ).
cnf(t97,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(orient,[status(thm)],[t34]) ).
cnf(t252,plain,
join(converse(zero),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t97,t240]) ).
cnf(t9024,plain,
join(converse(zero),X1) = X1,
inference(step,[status(thm)],[t252,t22]) ).
cnf(t319,plain,
join(converse(zero),X1) = X1,
inference(orient,[status(thm)],[t9024]) ).
cnf(t250,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t240,t39]) ).
cnf(t279,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t250]) ).
cnf(t321,plain,
zero = converse(zero),
inference(cp,[status(thm)],[t319,t279]) ).
cnf(t324,plain,
converse(zero) = zero,
inference(orient,[status(thm)],[t321]) ).
cnf(t9108,plain,
composition(converse(sF1),sk1) = zero,
inference(step,[status(thm)],[t1325,t324]) ).
cnf(t1332,plain,
composition(converse(sF1),sk1) = zero,
inference(orient,[status(thm)],[t9108]) ).
cnf(t1336,plain,
complement(sk1) = join(complement(sk1),composition(converse(converse(sF1)),complement(zero))),
inference(cp,[status(thm)],[t155,t1332]) ).
cnf(t9109,plain,
complement(sk1) = join(complement(sk1),composition(sF1,complement(zero))),
inference(step,[status(thm)],[t1336,t22]) ).
cnf(t249,plain,
complement(zero) = top,
inference(cp,[status(thm)],[t240,t24]) ).
cnf(t262,plain,
complement(zero) = top,
inference(orient,[status(thm)],[t249]) ).
cnf(t9110,plain,
complement(sk1) = join(complement(sk1),composition(sF1,top)),
inference(step,[status(thm)],[t9109,t262]) ).
cnf(t9111,plain,
complement(sk1) = join(complement(sk1),sF2),
inference(step,[status(thm)],[t9110,t273]) ).
cnf(t9112,plain,
complement(sk1) = join(sF2,complement(sk1)),
inference(step,[status(thm)],[t9111,t39]) ).
cnf(t1338,plain,
join(sF2,complement(sk1)) = complement(sk1),
inference(orient,[status(thm)],[t9112]) ).
cnf(t1340,plain,
join(sF2,join(complement(sk1),X1)) = join(complement(sk1),X1),
inference(cp,[status(thm)],[t43,t1338]) ).
cnf(t2434,plain,
join(sF2,join(complement(sk1),X1)) = join(complement(sk1),X1),
inference(orient,[status(thm)],[t1340]) ).
cnf(t45,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(cp,[status(thm)],[t43,t24]) ).
cnf(t9077,plain,
join(X1,join(complement(X1),X2)) = top,
inference(step,[status(thm)],[t45,t437]) ).
cnf(t576,plain,
join(X1,join(complement(X1),X2)) = top,
inference(orient,[status(thm)],[t9077]) ).
cnf(t579,plain,
top = join(X1,join(X2,complement(X1))),
inference(cp,[status(thm)],[t576,t39]) ).
cnf(t1660,plain,
join(X1,join(X2,complement(X1))) = top,
inference(orient,[status(thm)],[t579]) ).
cnf(t2442,plain,
join(complement(sk1),complement(sF2)) = top,
inference(cp,[status(thm)],[t2434,t1660]) ).
cnf(t9210,plain,
join(complement(sF2),complement(sk1)) = top,
inference(step,[status(thm)],[t2442,t39]) ).
cnf(t2447,plain,
join(complement(sF2),complement(sk1)) = top,
inference(orient,[status(thm)],[t9210]) ).
cnf(t2450,plain,
sF2 = join(complement(top),complement(join(complement(sF2),complement(complement(sk1))))),
inference(cp,[status(thm)],[t188,t2447]) ).
cnf(t9211,plain,
sF2 = join(zero,complement(join(complement(sF2),complement(complement(sk1))))),
inference(step,[status(thm)],[t2450,t75]) ).
cnf(t9212,plain,
sF2 = complement(join(complement(sF2),complement(complement(sk1)))),
inference(step,[status(thm)],[t9211,t240]) ).
cnf(t9213,plain,
sF2 = complement(join(complement(sF2),sk1)),
inference(step,[status(thm)],[t9212,t268]) ).
cnf(t9214,plain,
sF2 = complement(join(sk1,complement(sF2))),
inference(step,[status(thm)],[t9213,t39]) ).
cnf(t2455,plain,
complement(join(sk1,complement(sF2))) = sF2,
inference(orient,[status(thm)],[t9214]) ).
cnf(t2460,plain,
join(sk1,complement(sF2)) = complement(sF2),
inference(cp,[status(thm)],[t268,t2455]) ).
cnf(t2462,plain,
join(sk1,complement(sF2)) = complement(sF2),
inference(orient,[status(thm)],[t2460]) ).
cnf(t2466,plain,
join(sF0,composition(complement(sF2),top)) = composition(complement(sF2),top),
inference(cp,[status(thm)],[t141,t2462]) ).
cnf(t278,plain,
complement(top) = join(complement(top),composition(converse(sF1),complement(sF2))),
inference(cp,[status(thm)],[t155,t273]) ).
cnf(t9058,plain,
zero = join(complement(top),composition(converse(sF1),complement(sF2))),
inference(step,[status(thm)],[t278,t75]) ).
cnf(t9059,plain,
zero = join(zero,composition(converse(sF1),complement(sF2))),
inference(step,[status(thm)],[t9058,t75]) ).
cnf(t9060,plain,
zero = composition(converse(sF1),complement(sF2)),
inference(step,[status(thm)],[t9059,t240]) ).
cnf(t394,plain,
composition(converse(sF1),complement(sF2)) = zero,
inference(orient,[status(thm)],[t9060]) ).
cnf(t396,plain,
composition(converse(complement(sF2)),sF1) = converse(zero),
inference(cp,[status(thm)],[t55,t394]) ).
cnf(t9083,plain,
composition(converse(complement(sF2)),sF1) = zero,
inference(step,[status(thm)],[t396,t324]) ).
cnf(t726,plain,
composition(converse(complement(sF2)),sF1) = zero,
inference(orient,[status(thm)],[t9083]) ).
cnf(t730,plain,
complement(sF1) = join(complement(sF1),composition(converse(converse(complement(sF2))),complement(zero))),
inference(cp,[status(thm)],[t155,t726]) ).
cnf(t222,plain,
sF0 = join(zero,complement(sF1)),
inference(cp,[status(thm)],[t221,t25]) ).
cnf(t226,plain,
join(zero,complement(sF1)) = sF0,
inference(orient,[status(thm)],[t222]) ).
cnf(t8987,plain,
complement(sF1) = sF0,
inference(step,[status(thm)],[t226,t240]) ).
cnf(t247,plain,
complement(sF1) = sF0,
inference(rw,[status(thm)],[t8987]) ).
cnf(t255,plain,
complement(sF1) = sF0,
inference(orient,[status(thm)],[t247]) ).
cnf(t9137,plain,
sF0 = join(complement(sF1),composition(converse(converse(complement(sF2))),complement(zero))),
inference(step,[status(thm)],[t730,t255]) ).
cnf(t9138,plain,
sF0 = join(sF0,composition(converse(converse(complement(sF2))),complement(zero))),
inference(step,[status(thm)],[t9137,t255]) ).
cnf(t9139,plain,
sF0 = join(sF0,composition(complement(sF2),complement(zero))),
inference(step,[status(thm)],[t9138,t22]) ).
cnf(t9140,plain,
sF0 = join(sF0,composition(complement(sF2),top)),
inference(step,[status(thm)],[t9139,t262]) ).
cnf(t1714,plain,
join(sF0,composition(complement(sF2),top)) = sF0,
inference(orient,[status(thm)],[t9140]) ).
cnf(t9215,plain,
sF0 = composition(complement(sF2),top),
inference(step,[status(thm)],[t2466,t1714]) ).
cnf(t2471,plain,
composition(complement(sF2),top) = sF0,
inference(orient,[status(thm)],[t9215]) ).
cnf(t2476,plain,
composition(top,converse(complement(sF2))) = converse(sF0),
inference(cp,[status(thm)],[t522,t2471]) ).
cnf(t2479,plain,
composition(top,converse(complement(sF2))) = converse(sF0),
inference(orient,[status(thm)],[t2476]) ).
cnf(t3527,plain,
composition(top,converse(complement(sF2))) = join(converse(complement(sF2)),converse(sF0)),
inference(cp,[status(thm)],[t3517,t2479]) ).
cnf(t9375,plain,
converse(sF0) = join(converse(complement(sF2)),converse(sF0)),
inference(step,[status(thm)],[t3527,t2479]) ).
cnf(t9376,plain,
converse(sF0) = converse(join(complement(sF2),sF0)),
inference(step,[status(thm)],[t9375,t32]) ).
cnf(t42,plain,
join(converse(X1),converse(X2)) = converse(join(X2,X1)),
inference(cp,[status(thm)],[t39,t32]) ).
cnf(t9072,plain,
converse(join(X1,X2)) = converse(join(X2,X1)),
inference(step,[status(thm)],[t42,t32]) ).
cnf(t451,plain,
converse(join(X1,X2)) = converse(join(X2,X1)),
inference(orient,[status(thm)],[t9072]) ).
cnf(t9377,plain,
converse(sF0) = converse(join(sF0,complement(sF2))),
inference(step,[status(thm)],[t9376,t451]) ).
cnf(f4,axiom,
composition(A,composition(B,C)) = composition(composition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity_5) ).
fof(f4_nnf,plain,
! [A,B,C] : composition(A,composition(B,C)) = composition(composition(A,B),C),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] : composition(A,composition(B,C)) = composition(composition(A,B),C),
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(t8,plain,
composition(composition(X1,X2),X3) = composition(X1,composition(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t35,plain,
composition(composition(X1,X2),X3) = composition(X1,composition(X2,X3)),
inference(orient,[status(thm)],[t8]) ).
cnf(t527,plain,
composition(top,converse(sF1)) = converse(sF2),
inference(cp,[status(thm)],[t522,t273]) ).
cnf(t554,plain,
composition(top,converse(sF1)) = converse(sF2),
inference(orient,[status(thm)],[t527]) ).
cnf(t555,plain,
composition(top,composition(converse(sF1),X1)) = composition(converse(sF2),X1),
inference(cp,[status(thm)],[t35,t554]) ).
cnf(t1587,plain,
composition(top,composition(converse(sF1),X1)) = composition(converse(sF2),X1),
inference(orient,[status(thm)],[t555]) ).
cnf(t523,plain,
composition(top,converse(sk1)) = converse(sF0),
inference(cp,[status(thm)],[t522,t23]) ).
cnf(t547,plain,
composition(top,converse(sk1)) = converse(sF0),
inference(orient,[status(thm)],[t523]) ).
cnf(t548,plain,
composition(top,composition(converse(sk1),X1)) = composition(converse(sF0),X1),
inference(cp,[status(thm)],[t35,t547]) ).
cnf(t1563,plain,
composition(top,composition(converse(sk1),X1)) = composition(converse(sF0),X1),
inference(orient,[status(thm)],[t548]) ).
cnf(t1565,plain,
composition(converse(sF0),sF1) = composition(top,zero),
inference(cp,[status(thm)],[t1563,t1323]) ).
cnf(t1569,plain,
composition(converse(sF0),sF1) = composition(top,zero),
inference(orient,[status(thm)],[t1565]) ).
cnf(t1571,plain,
composition(converse(sF1),sF0) = converse(composition(top,zero)),
inference(cp,[status(thm)],[t55,t1569]) ).
cnf(t327,plain,
converse(composition(X1,zero)) = composition(zero,converse(X1)),
inference(cp,[status(thm)],[t29,t324]) ).
cnf(t331,plain,
converse(composition(X1,zero)) = composition(zero,converse(X1)),
inference(orient,[status(thm)],[t327]) ).
cnf(t9117,plain,
composition(converse(sF1),sF0) = composition(zero,converse(top)),
inference(step,[status(thm)],[t1571,t331]) ).
cnf(t9118,plain,
composition(converse(sF1),sF0) = composition(zero,top),
inference(step,[status(thm)],[t9117,t489]) ).
cnf(t1579,plain,
composition(converse(sF1),sF0) = composition(zero,top),
inference(orient,[status(thm)],[t9118]) ).
cnf(t1591,plain,
composition(converse(sF2),sF0) = composition(top,composition(zero,top)),
inference(cp,[status(thm)],[t1587,t1579]) ).
cnf(t1622,plain,
composition(top,composition(zero,top)) = composition(converse(sF2),sF0),
inference(orient,[status(thm)],[t1591]) ).
cnf(t494,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(cp,[status(thm)],[t29,t489]) ).
cnf(t540,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(orient,[status(thm)],[t494]) ).
cnf(t1629,plain,
composition(converse(composition(zero,top)),top) = converse(composition(converse(sF2),sF0)),
inference(cp,[status(thm)],[t540,t1622]) ).
cnf(t328,plain,
converse(composition(zero,X1)) = composition(converse(X1),zero),
inference(cp,[status(thm)],[t29,t324]) ).
cnf(t341,plain,
converse(composition(zero,X1)) = composition(converse(X1),zero),
inference(orient,[status(thm)],[t328]) ).
cnf(t9121,plain,
composition(composition(converse(top),zero),top) = converse(composition(converse(sF2),sF0)),
inference(step,[status(thm)],[t1629,t341]) ).
cnf(t9122,plain,
composition(converse(top),composition(zero,top)) = converse(composition(converse(sF2),sF0)),
inference(step,[status(thm)],[t9121,t35]) ).
cnf(t9123,plain,
composition(top,composition(zero,top)) = converse(composition(converse(sF2),sF0)),
inference(step,[status(thm)],[t9122,t489]) ).
cnf(t9124,plain,
composition(converse(sF2),sF0) = converse(composition(converse(sF2),sF0)),
inference(step,[status(thm)],[t9123,t1622]) ).
cnf(t9125,plain,
composition(converse(sF2),sF0) = composition(converse(sF0),sF2),
inference(step,[status(thm)],[t9124,t55]) ).
cnf(t1630,plain,
composition(converse(sF2),sF0) = composition(converse(sF0),sF2),
inference(orient,[status(thm)],[t9125]) ).
cnf(t9126,plain,
composition(top,composition(zero,top)) = composition(converse(sF0),sF2),
inference(step,[status(thm)],[t1622,t1630]) ).
cnf(t1631,plain,
composition(top,composition(zero,top)) = composition(converse(sF0),sF2),
inference(orient,[status(thm)],[t9126]) ).
cnf(t1326,plain,
composition(join(converse(sk1),X1),sF1) = join(zero,composition(X1,sF1)),
inference(cp,[status(thm)],[t111,t1323]) ).
cnf(t9152,plain,
composition(join(converse(sk1),X1),sF1) = composition(X1,sF1),
inference(step,[status(thm)],[t1326,t240]) ).
cnf(t1984,plain,
composition(join(converse(sk1),X1),sF1) = composition(X1,sF1),
inference(orient,[status(thm)],[t9152]) ).
cnf(t1988,plain,
composition(zero,sF1) = composition(converse(sk1),sF1),
inference(cp,[status(thm)],[t1984,t279]) ).
cnf(t9153,plain,
composition(zero,sF1) = zero,
inference(step,[status(thm)],[t1988,t1323]) ).
cnf(t2002,plain,
composition(zero,sF1) = zero,
inference(orient,[status(thm)],[t9153]) ).
cnf(t2004,plain,
composition(converse(sF1),zero) = converse(zero),
inference(cp,[status(thm)],[t341,t2002]) ).
cnf(t9154,plain,
composition(converse(sF1),zero) = zero,
inference(step,[status(thm)],[t2004,t324]) ).
cnf(t2006,plain,
composition(converse(sF1),zero) = zero,
inference(orient,[status(thm)],[t9154]) ).
cnf(t2012,plain,
composition(converse(sF2),zero) = composition(top,zero),
inference(cp,[status(thm)],[t1587,t2006]) ).
cnf(t2013,plain,
composition(converse(sF2),zero) = composition(top,zero),
inference(orient,[status(thm)],[t2012]) ).
cnf(t2015,plain,
composition(converse(zero),sF2) = converse(composition(top,zero)),
inference(cp,[status(thm)],[t55,t2013]) ).
cnf(t9155,plain,
composition(zero,sF2) = converse(composition(top,zero)),
inference(step,[status(thm)],[t2015,t324]) ).
cnf(t9156,plain,
composition(zero,sF2) = composition(zero,converse(top)),
inference(step,[status(thm)],[t9155,t331]) ).
cnf(t9157,plain,
composition(zero,sF2) = composition(zero,top),
inference(step,[status(thm)],[t9156,t489]) ).
cnf(t2023,plain,
composition(zero,top) = composition(zero,sF2),
inference(orient,[status(thm)],[t9157]) ).
cnf(t9165,plain,
composition(top,composition(zero,sF2)) = composition(converse(sF0),sF2),
inference(step,[status(thm)],[t1631,t2023]) ).
cnf(t2031,plain,
composition(top,composition(zero,sF2)) = composition(converse(sF0),sF2),
inference(rw,[status(thm)],[t9165]) ).
cnf(t2131,plain,
composition(top,composition(zero,sF2)) = composition(converse(sF0),sF2),
inference(orient,[status(thm)],[t2031]) ).
cnf(t1334,plain,
composition(join(converse(sF1),X1),sk1) = join(zero,composition(X1,sk1)),
inference(cp,[status(thm)],[t111,t1332]) ).
cnf(t9176,plain,
composition(join(converse(sF1),X1),sk1) = composition(X1,sk1),
inference(step,[status(thm)],[t1334,t240]) ).
cnf(t2206,plain,
composition(join(converse(sF1),X1),sk1) = composition(X1,sk1),
inference(orient,[status(thm)],[t9176]) ).
cnf(t2210,plain,
composition(zero,sk1) = composition(converse(sF1),sk1),
inference(cp,[status(thm)],[t2206,t279]) ).
cnf(t9177,plain,
composition(zero,sk1) = zero,
inference(step,[status(thm)],[t2210,t1332]) ).
cnf(t2273,plain,
composition(zero,sk1) = zero,
inference(orient,[status(thm)],[t9177]) ).
cnf(t2276,plain,
composition(converse(sk1),zero) = converse(zero),
inference(cp,[status(thm)],[t341,t2273]) ).
cnf(t9180,plain,
composition(converse(sk1),zero) = zero,
inference(step,[status(thm)],[t2276,t324]) ).
cnf(t2290,plain,
composition(converse(sk1),zero) = zero,
inference(orient,[status(thm)],[t9180]) ).
cnf(t2296,plain,
composition(converse(sF0),zero) = composition(top,zero),
inference(cp,[status(thm)],[t1563,t2290]) ).
cnf(t2304,plain,
composition(converse(sF0),zero) = composition(top,zero),
inference(orient,[status(thm)],[t2296]) ).
cnf(t2306,plain,
composition(converse(zero),sF0) = converse(composition(top,zero)),
inference(cp,[status(thm)],[t55,t2304]) ).
cnf(t9182,plain,
composition(zero,sF0) = converse(composition(top,zero)),
inference(step,[status(thm)],[t2306,t324]) ).
cnf(t9183,plain,
composition(zero,sF0) = composition(zero,converse(top)),
inference(step,[status(thm)],[t9182,t331]) ).
cnf(t9184,plain,
composition(zero,sF0) = composition(zero,top),
inference(step,[status(thm)],[t9183,t489]) ).
cnf(t9185,plain,
composition(zero,sF0) = composition(zero,sF2),
inference(step,[status(thm)],[t9184,t2023]) ).
cnf(t2314,plain,
composition(zero,sF2) = composition(zero,sF0),
inference(orient,[status(thm)],[t9185]) ).
cnf(t9197,plain,
composition(top,composition(zero,sF0)) = composition(converse(sF0),sF2),
inference(step,[status(thm)],[t2131,t2314]) ).
cnf(t2326,plain,
composition(top,composition(zero,sF0)) = composition(converse(sF0),sF2),
inference(rw,[status(thm)],[t9197]) ).
cnf(t2391,plain,
composition(top,composition(zero,sF0)) = composition(converse(sF0),sF2),
inference(orient,[status(thm)],[t2326]) ).
cnf(t3837,plain,
composition(top,zero) = composition(converse(sF0),sF2),
inference(rw,[status(thm)],[t2391]) ).
cnf(t3520,plain,
composition(top,top) = top,
inference(cp,[status(thm)],[t3517,t437]) ).
cnf(t3658,plain,
composition(top,top) = top,
inference(orient,[status(thm)],[t3520]) ).
cnf(t3668,plain,
complement(top) = join(complement(top),composition(converse(top),complement(top))),
inference(cp,[status(thm)],[t155,t3658]) ).
cnf(t9286,plain,
zero = join(complement(top),composition(converse(top),complement(top))),
inference(step,[status(thm)],[t3668,t75]) ).
cnf(t9287,plain,
zero = composition(join(one,converse(top)),complement(top)),
inference(step,[status(thm)],[t9286,t3435]) ).
cnf(t9288,plain,
zero = composition(join(one,top),complement(top)),
inference(step,[status(thm)],[t9287,t489]) ).
cnf(t118,plain,
composition(join(X1,X2),X3) = join(composition(X2,X3),composition(X1,X3)),
inference(cp,[status(thm)],[t111,t39]) ).
cnf(t9255,plain,
composition(join(X1,X2),X3) = composition(join(X2,X1),X3),
inference(step,[status(thm)],[t118,t111]) ).
cnf(t3354,plain,
composition(join(X1,X2),X3) = composition(join(X2,X1),X3),
inference(orient,[status(thm)],[t9255]) ).
cnf(t9289,plain,
zero = composition(join(top,one),complement(top)),
inference(step,[status(thm)],[t9288,t3354]) ).
cnf(t9290,plain,
zero = composition(top,complement(top)),
inference(step,[status(thm)],[t9289,t437]) ).
cnf(t9291,plain,
zero = composition(top,zero),
inference(step,[status(thm)],[t9290,t75]) ).
cnf(t3725,plain,
composition(top,zero) = zero,
inference(orient,[status(thm)],[t9291]) ).
cnf(t3747,plain,
composition(join(X1,top),zero) = join(composition(X1,zero),zero),
inference(cp,[status(thm)],[t111,t3725]) ).
cnf(t9307,plain,
composition(top,zero) = join(composition(X1,zero),zero),
inference(step,[status(thm)],[t3747,t436]) ).
cnf(t9308,plain,
zero = join(composition(X1,zero),zero),
inference(step,[status(thm)],[t9307,t3725]) ).
cnf(t9309,plain,
zero = composition(X1,zero),
inference(step,[status(thm)],[t9308,t279]) ).
cnf(t3784,plain,
composition(X1,zero) = zero,
inference(orient,[status(thm)],[t9309]) ).
cnf(t9355,plain,
zero = composition(converse(sF0),sF2),
inference(step,[status(thm)],[t3837,t3784]) ).
cnf(t4137,plain,
composition(converse(sF0),sF2) = zero,
inference(orient,[status(thm)],[t9355]) ).
cnf(t4144,plain,
complement(sF2) = join(complement(sF2),composition(converse(converse(sF0)),complement(zero))),
inference(cp,[status(thm)],[t155,t4137]) ).
cnf(t9371,plain,
complement(sF2) = join(complement(sF2),composition(sF0,complement(zero))),
inference(step,[status(thm)],[t4144,t22]) ).
cnf(t9372,plain,
complement(sF2) = join(complement(sF2),composition(sF0,top)),
inference(step,[status(thm)],[t9371,t262]) ).
cnf(t37,plain,
composition(sk1,composition(top,X1)) = composition(sF0,X1),
inference(cp,[status(thm)],[t35,t23]) ).
cnf(t103,plain,
composition(sk1,composition(top,X1)) = composition(sF0,X1),
inference(orient,[status(thm)],[t37]) ).
cnf(t3666,plain,
composition(sF0,top) = composition(sk1,top),
inference(cp,[status(thm)],[t103,t3658]) ).
cnf(t9284,plain,
composition(sF0,top) = sF0,
inference(step,[status(thm)],[t3666,t23]) ).
cnf(t3708,plain,
composition(sF0,top) = sF0,
inference(orient,[status(thm)],[t9284]) ).
cnf(t9373,plain,
complement(sF2) = join(complement(sF2),sF0),
inference(step,[status(thm)],[t9372,t3708]) ).
cnf(t9374,plain,
complement(sF2) = join(sF0,complement(sF2)),
inference(step,[status(thm)],[t9373,t39]) ).
cnf(t4250,plain,
join(sF0,complement(sF2)) = complement(sF2),
inference(orient,[status(thm)],[t9374]) ).
cnf(t9378,plain,
converse(sF0) = converse(complement(sF2)),
inference(step,[status(thm)],[t9377,t4250]) ).
cnf(t4258,plain,
converse(complement(sF2)) = converse(sF0),
inference(orient,[status(thm)],[t9378]) ).
cnf(t4264,plain,
complement(sF2) = converse(converse(sF0)),
inference(cp,[status(thm)],[t22,t4258]) ).
cnf(t9380,plain,
complement(sF2) = sF0,
inference(step,[status(thm)],[t4264,t22]) ).
cnf(t4293,plain,
complement(sF2) = sF0,
inference(orient,[status(thm)],[t9380]) ).
cnf(t4307,plain,
sF2 = complement(sF0),
inference(cp,[status(thm)],[t268,t4293]) ).
cnf(t9383,plain,
sF2 = sF1,
inference(step,[status(thm)],[t4307,t25]) ).
cnf(t4309,plain,
sF2 = sF1,
inference(orient,[status(thm)],[t9383]) ).
cnf(t9682,plain,
ifeq(join(sF1,sF1),sF2,ifeq(join(sF1,sF2),sF1,false,true),true) = true,
inference(step,[status(thm)],[t274,t4309]) ).
cnf(t9683,plain,
ifeq(sF1,sF2,ifeq(join(sF1,sF2),sF1,false,true),true) = true,
inference(step,[status(thm)],[t9682,t291]) ).
cnf(t9684,plain,
ifeq(sF1,sF1,ifeq(join(sF1,sF2),sF1,false,true),true) = true,
inference(step,[status(thm)],[t9683,t4309]) ).
cnf(t3,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t9685,plain,
ifeq(join(sF1,sF2),sF1,false,true) = true,
inference(step,[status(thm)],[t9684,t28]) ).
cnf(t9686,plain,
ifeq(join(sF1,sF1),sF1,false,true) = true,
inference(step,[status(thm)],[t9685,t4309]) ).
cnf(t9687,plain,
ifeq(sF1,sF1,false,true) = true,
inference(step,[status(thm)],[t9686,t291]) ).
cnf(t9688,plain,
false = true,
inference(step,[status(thm)],[t9687,t28]) ).
cnf(t19,axiom,
sF5 = ifeq(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),complement(composition(sk1,top)),false,true),
introduced(definition) ).
cnf(t9025,plain,
sF5 = ifeq(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),complement(composition(sk1,top)),false,true),
inference(step,[status(thm)],[t19,t39]) ).
cnf(t9026,plain,
sF5 = ifeq(join(complement(sF0),composition(complement(composition(sk1,top)),top)),complement(composition(sk1,top)),false,true),
inference(step,[status(thm)],[t9025,t23]) ).
cnf(t9027,plain,
sF5 = ifeq(join(sF1,composition(complement(composition(sk1,top)),top)),complement(composition(sk1,top)),false,true),
inference(step,[status(thm)],[t9026,t25]) ).
cnf(t9028,plain,
sF5 = ifeq(join(sF1,composition(complement(sF0),top)),complement(composition(sk1,top)),false,true),
inference(step,[status(thm)],[t9027,t23]) ).
cnf(t9029,plain,
sF5 = ifeq(join(sF1,composition(sF1,top)),complement(composition(sk1,top)),false,true),
inference(step,[status(thm)],[t9028,t25]) ).
cnf(t9030,plain,
sF5 = ifeq(join(sF1,sF2),complement(composition(sk1,top)),false,true),
inference(step,[status(thm)],[t9029,t273]) ).
cnf(t17,axiom,
sF3 = join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),
introduced(definition) ).
cnf(t9008,plain,
sF3 = join(complement(sF0),composition(complement(composition(sk1,top)),top)),
inference(step,[status(thm)],[t17,t23]) ).
cnf(t9009,plain,
sF3 = join(sF1,composition(complement(composition(sk1,top)),top)),
inference(step,[status(thm)],[t9008,t25]) ).
cnf(t9010,plain,
sF3 = join(sF1,composition(complement(sF0),top)),
inference(step,[status(thm)],[t9009,t23]) ).
cnf(t9011,plain,
sF3 = join(sF1,composition(sF1,top)),
inference(step,[status(thm)],[t9010,t25]) ).
cnf(t9012,plain,
sF3 = join(sF1,sF2),
inference(step,[status(thm)],[t9011,t273]) ).
cnf(t301,plain,
join(sF1,sF2) = sF3,
inference(orient,[status(thm)],[t9012]) ).
cnf(t9031,plain,
sF5 = ifeq(sF3,complement(composition(sk1,top)),false,true),
inference(step,[status(thm)],[t9030,t301]) ).
cnf(t9032,plain,
sF5 = ifeq(sF3,complement(sF0),false,true),
inference(step,[status(thm)],[t9031,t23]) ).
cnf(t9033,plain,
sF5 = ifeq(sF3,sF1,false,true),
inference(step,[status(thm)],[t9032,t25]) ).
cnf(t330,plain,
ifeq(sF3,sF1,false,true) = sF5,
inference(orient,[status(thm)],[t9033]) ).
cnf(t3522,plain,
composition(top,converse(sF1)) = join(converse(sF1),converse(sF2)),
inference(cp,[status(thm)],[t3517,t554]) ).
cnf(t9260,plain,
converse(sF2) = join(converse(sF1),converse(sF2)),
inference(step,[status(thm)],[t3522,t554]) ).
cnf(t9261,plain,
converse(sF2) = converse(join(sF1,sF2)),
inference(step,[status(thm)],[t9260,t32]) ).
cnf(t9262,plain,
converse(sF2) = converse(sF3),
inference(step,[status(thm)],[t9261,t301]) ).
cnf(t3591,plain,
converse(sF3) = converse(sF2),
inference(orient,[status(thm)],[t9262]) ).
cnf(t3592,plain,
sF3 = converse(converse(sF2)),
inference(cp,[status(thm)],[t22,t3591]) ).
cnf(t9263,plain,
sF3 = sF2,
inference(step,[status(thm)],[t3592,t22]) ).
cnf(t3620,plain,
sF3 = sF2,
inference(orient,[status(thm)],[t9263]) ).
cnf(t9268,plain,
ifeq(sF2,sF1,false,true) = sF5,
inference(step,[status(thm)],[t330,t3620]) ).
cnf(t3626,plain,
ifeq(sF2,sF1,false,true) = sF5,
inference(rw,[status(thm)],[t9268]) ).
cnf(t9422,plain,
ifeq(sF1,sF1,false,true) = sF5,
inference(step,[status(thm)],[t3626,t4309]) ).
cnf(t9423,plain,
false = sF5,
inference(step,[status(thm)],[t9422,t28]) ).
cnf(t4481,plain,
false = sF5,
inference(orient,[status(thm)],[t9423]) ).
cnf(t9689,plain,
sF5 = true,
inference(step,[status(thm)],[t9688,t4481]) ).
cnf(t8938,plain,
true = sF5,
inference(orient,[status(thm)],[t9689]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(g0_0,plain,
sF5 != false,
inference(rw,[status(thm)],[goal_0,t8938]) ).
cnf(g0_1,plain,
sF5 != sF5,
inference(rw,[status(thm)],[g0_0,t4481]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL050-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n011.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 07:38:43 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 22.95/3.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.95/3.34 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------