%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL008+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 02:34:40 PM UTC 2026
% Result : Theorem 43.51s 5.83s
% Output : Proof 43.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 14
% Syntax : Number of formulae : 171 ( 166 unt; 0 def)
% Number of atoms : 176 ( 175 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 37 ( 32 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 247 ( 2 sgn 72 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f0_nnf,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(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]) ).
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]) ).
cnf(t24,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(cp,[status(thm)],[t23,t21]) ).
cnf(t780,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(orient,[status(thm)],[t24]) ).
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]) ).
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]) ).
cnf(t139,plain,
converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)),
inference(cp,[status(thm)],[t36,t131]) ).
cnf(t53833,plain,
converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)),
inference(orient,[status(thm)],[t139]) ).
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]) ).
cnf(t51,plain,
composition(join(X1,converse(X2)),converse(X3)) = join(composition(X1,converse(X3)),converse(composition(X3,X2))),
inference(cp,[status(thm)],[t29,t46]) ).
cnf(t31762,plain,
join(composition(X1,converse(X2)),converse(composition(X2,X3))) = composition(join(X1,converse(X3)),converse(X2)),
inference(orient,[status(thm)],[t51]) ).
cnf(t53841,plain,
join(composition(converse(converse(X1)),X2),converse(converse(composition(X1,X3)))) = converse(composition(join(converse(X2),converse(X3)),converse(X1))),
inference(cp,[status(thm)],[t53833,t31762]) ).
cnf(t55050,plain,
join(composition(X1,X2),converse(converse(composition(X1,X3)))) = converse(composition(join(converse(X2),converse(X3)),converse(X1))),
inference(step,[status(thm)],[t53841,t19]) ).
cnf(t55051,plain,
join(composition(X1,X2),composition(X1,X3)) = converse(composition(join(converse(X2),converse(X3)),converse(X1))),
inference(step,[status(thm)],[t55050,t19]) ).
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(t105,plain,
converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))),
inference(cp,[status(thm)],[t46,t100]) ).
cnf(t51370,plain,
converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))),
inference(orient,[status(thm)],[t105]) ).
cnf(t55052,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(converse(converse(X1)),join(X2,converse(converse(X3)))),
inference(step,[status(thm)],[t55051,t51370]) ).
cnf(t55053,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,converse(converse(X3)))),
inference(step,[status(thm)],[t55052,t19]) ).
cnf(t55054,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(step,[status(thm)],[t55053,t19]) ).
cnf(t54133,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(orient,[status(thm)],[t55054]) ).
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]) ).
cnf(t54358,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)],[t54358]) ).
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(t54370,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t132,t19]) ).
cnf(t146,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t54370]) ).
cnf(t147,plain,
one = converse(one),
inference(cp,[status(thm)],[t146,t18]) ).
cnf(t153,plain,
converse(one) = one,
inference(orient,[status(thm)],[t147]) ).
cnf(t54371,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t146,t153]) ).
cnf(t163,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t54371]) ).
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(t54373,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t167,t153]) ).
cnf(t54374,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t54373,t164]) ).
cnf(t191,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t54374]) ).
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(t54386,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t22,t21]) ).
cnf(t54387,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t54386,t53]) ).
cnf(t54388,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t54387,t21]) ).
cnf(t287,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t54388]) ).
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(t61,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,t61]) ).
cnf(t54395,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)],[t54395]) ).
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(t54366,plain,
zero = complement(top),
inference(step,[status(thm)],[t54,t61]) ).
cnf(t63,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t54366]) ).
cnf(t195,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t191,t63]) ).
cnf(t54375,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t195,t63]) ).
cnf(t54376,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t54375,t63]) ).
cnf(t202,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t54376]) ).
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(t54396,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t325,t323]) ).
cnf(t327,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t54396]) ).
cnf(t54397,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t323,t327]) ).
cnf(t334,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t54397]) ).
cnf(t349,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t334]) ).
cnf(t54403,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t208,t349]) ).
cnf(t351,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t54403]) ).
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(t54410,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t360,t358]) ).
cnf(t54411,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t54410,t358]) ).
cnf(t369,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t54411]) ).
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(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t20,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( join(join(composition(X0,X1),composition(X0,X2)),composition(X0,join(X1,X2))) = composition(X0,join(X1,X2))
& join(join(composition(X0,join(X1,X2)),composition(X0,X1)),composition(X0,X2)) = join(composition(X0,X1),composition(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( join(join(composition(X0,X1),composition(X0,X2)),composition(X0,join(X1,X2))) = composition(X0,join(X1,X2))
& join(join(composition(X0,join(X1,X2)),composition(X0,X1)),composition(X0,X2)) = join(composition(X0,X1),composition(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0,X1,X2] :
( join(join(composition(X0,X1),composition(X0,X2)),composition(X0,join(X1,X2))) != composition(X0,join(X1,X2))
| join(join(composition(X0,join(X1,X2)),composition(X0,X1)),composition(X0,X2)) != join(composition(X0,X1),composition(X0,X2)) ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( join(join(composition(sk0,sk1),composition(sk0,sk2)),composition(sk0,join(sk1,sk2))) != composition(sk0,join(sk1,sk2))
| join(join(composition(sk0,join(sk1,sk2)),composition(sk0,sk1)),composition(sk0,sk2)) != join(composition(sk0,sk1),composition(sk0,sk2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f13_nnf]) ).
cnf(c13,plain,
( join(join(composition(sk0,sk1),composition(sk0,sk2)),composition(sk0,join(sk1,sk2))) != composition(sk0,join(sk1,sk2))
| join(join(composition(sk0,join(sk1,sk2)),composition(sk0,sk1)),composition(sk0,sk2)) != join(composition(sk0,sk1),composition(sk0,sk2)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(g0_0,plain,
true != ifeq(join(composition(sk0,join(sk2,sk1)),join(composition(sk0,sk2),composition(sk0,sk1))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(join(composition(sk0,sk1),join(composition(sk0,sk2),composition(sk0,join(sk2,sk1)))),composition(sk0,join(sk2,sk1)),false,true),true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(join(composition(sk0,join(sk2,sk1)),join(composition(sk0,sk2),composition(sk0,sk1))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(join(composition(sk0,sk1),join(composition(sk0,join(sk2,sk1)),composition(sk0,sk2))),composition(sk0,join(sk2,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_0,t21]) ).
cnf(g0_2,plain,
true != ifeq(join(composition(sk0,join(sk2,sk1)),join(composition(sk0,sk2),composition(sk0,sk1))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),composition(sk0,join(sk2,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_1,t780]) ).
cnf(g0_3,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),composition(sk0,join(sk2,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_2,t780]) ).
cnf(g0_4,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(join(composition(sk0,sk2),composition(sk0,join(sk1,join(sk2,sk1)))),composition(sk0,join(sk2,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_3,t54133]) ).
cnf(g0_5,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(join(composition(sk0,sk2),composition(sk0,join(sk1,join(sk2,sk1)))),composition(sk0,join(sk1,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_4,t21]) ).
cnf(g0_6,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(join(composition(sk0,sk2),composition(sk0,join(join(sk2,sk1),sk1))),composition(sk0,join(sk1,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_5,t21]) ).
cnf(g0_7,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(join(composition(sk0,sk2),composition(sk0,join(join(sk1,sk2),sk1))),composition(sk0,join(sk1,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_6,t21]) ).
cnf(g0_8,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(join(composition(sk0,sk2),composition(sk0,join(join(sk1,sk2),sk1))),composition(sk0,join(sk2,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_7,t21]) ).
cnf(g0_9,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(join(composition(sk0,join(join(sk1,sk2),sk1)),composition(sk0,sk2)),composition(sk0,join(sk2,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_8,t21]) ).
cnf(g0_10,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(join(composition(sk0,join(join(sk2,sk1),sk1)),composition(sk0,sk2)),composition(sk0,join(sk2,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_9,t21]) ).
cnf(g0_11,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(join(composition(sk0,join(sk2,join(sk1,sk1))),composition(sk0,sk2)),composition(sk0,join(sk2,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_10,t23]) ).
cnf(g0_12,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(join(composition(sk0,join(sk2,sk1)),composition(sk0,sk2)),composition(sk0,join(sk2,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_11,t369]) ).
cnf(g0_13,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(join(composition(sk0,sk2),composition(sk0,join(sk2,sk1))),composition(sk0,join(sk2,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_12,t21]) ).
cnf(g0_14,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(composition(sk0,join(sk2,join(sk2,sk1))),composition(sk0,join(sk2,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_13,t54133]) ).
cnf(g0_15,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),join(composition(sk0,sk2),composition(sk0,sk1)),ifeq(composition(sk0,join(sk2,sk1)),composition(sk0,join(sk2,sk1)),false,true),true),
inference(rw,[status(thm)],[g0_14,t443]) ).
cnf(g0_16,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),join(composition(sk0,sk2),composition(sk0,sk1)),false,true),
inference(rw,[status(thm)],[g0_15,t20]) ).
cnf(g0_17,plain,
true != ifeq(join(composition(sk0,sk2),join(composition(sk0,sk1),composition(sk0,join(sk2,sk1)))),composition(sk0,join(sk2,sk1)),false,true),
inference(rw,[status(thm)],[g0_16,t54133]) ).
cnf(g0_18,plain,
true != ifeq(join(composition(sk0,sk2),composition(sk0,join(sk1,join(sk2,sk1)))),composition(sk0,join(sk2,sk1)),false,true),
inference(rw,[status(thm)],[g0_17,t54133]) ).
cnf(g0_19,plain,
true != ifeq(join(composition(sk0,sk2),composition(sk0,join(sk2,join(sk1,sk1)))),composition(sk0,join(sk2,sk1)),false,true),
inference(rw,[status(thm)],[g0_18,t780]) ).
cnf(g0_20,plain,
true != ifeq(join(composition(sk0,sk2),composition(sk0,join(sk2,sk1))),composition(sk0,join(sk2,sk1)),false,true),
inference(rw,[status(thm)],[g0_19,t369]) ).
cnf(g0_21,plain,
true != ifeq(composition(sk0,join(sk2,join(sk2,sk1))),composition(sk0,join(sk2,sk1)),false,true),
inference(rw,[status(thm)],[g0_20,t54133]) ).
cnf(g0_22,plain,
true != ifeq(composition(sk0,join(sk2,sk1)),composition(sk0,join(sk2,sk1)),false,true),
inference(rw,[status(thm)],[g0_21,t443]) ).
cnf(g0_23,plain,
true != false,
inference(rw,[status(thm)],[g0_22,t20]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : REL008+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Thu Sep 24 07:09:35 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 43.51/5.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.51/5.83 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------