%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL008+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 176.12s 23.63s
% Output : Proof 176.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 14
% Syntax : Number of formulae : 175 ( 170 unt; 0 def)
% Number of atoms : 180 ( 179 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 : 258 ( 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(t45,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(t48,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t49,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(cp,[status(thm)],[t48,t45]) ).
cnf(t16895,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(orient,[status(thm)],[t49]) ).
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(t62,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(t29,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(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(t152,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t31]) ).
cnf(t156,plain,
converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)),
inference(cp,[status(thm)],[t62,t152]) ).
cnf(t117883,plain,
converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)),
inference(orient,[status(thm)],[t156]) ).
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(t26,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(orient,[status(thm)],[t11]) ).
cnf(t33,plain,
composition(join(X1,converse(X2)),converse(X3)) = join(composition(X1,converse(X3)),converse(composition(X3,X2))),
inference(cp,[status(thm)],[t26,t29]) ).
cnf(t2459,plain,
join(composition(X1,converse(X2)),converse(composition(X2,X3))) = composition(join(X1,converse(X3)),converse(X2)),
inference(orient,[status(thm)],[t33]) ).
cnf(t117895,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)],[t117883,t2459]) ).
cnf(t120901,plain,
join(composition(X1,X2),converse(converse(composition(X1,X3)))) = converse(composition(join(converse(X2),converse(X3)),converse(X1))),
inference(step,[status(thm)],[t117895,t22]) ).
cnf(t120902,plain,
join(composition(X1,X2),composition(X1,X3)) = converse(composition(join(converse(X2),converse(X3)),converse(X1))),
inference(step,[status(thm)],[t120901,t22]) ).
cnf(t30,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(cp,[status(thm)],[t29,t22]) ).
cnf(t142,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(orient,[status(thm)],[t30]) ).
cnf(t120903,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,converse(join(converse(X2),converse(X3)))),
inference(step,[status(thm)],[t120902,t142]) ).
cnf(t64,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t62,t22]) ).
cnf(t261,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t64]) ).
cnf(t120904,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,converse(converse(X3)))),
inference(step,[status(thm)],[t120903,t261]) ).
cnf(t120905,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(step,[status(thm)],[t120904,t22]) ).
cnf(t118396,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(orient,[status(thm)],[t120905]) ).
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(t118915,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t12,t45]) ).
cnf(t56,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t118915]) ).
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(t153,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t152,t18]) ).
cnf(t118927,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t153,t22]) ).
cnf(t165,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t118927]) ).
cnf(t166,plain,
one = converse(one),
inference(cp,[status(thm)],[t165,t18]) ).
cnf(t175,plain,
converse(one) = one,
inference(orient,[status(thm)],[t166]) ).
cnf(t118928,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t165,t175]) ).
cnf(t185,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t118928]) ).
cnf(t186,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t185]) ).
cnf(t189,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t56,t186]) ).
cnf(t118930,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t189,t175]) ).
cnf(t118931,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t118930,t186]) ).
cnf(t215,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t118931]) ).
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(t85,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t6]) ).
cnf(t216,plain,
complement(join(complement(X1),complement(X2))) = join(meet(X1,X2),complement(join(complement(X1),complement(X2)))),
inference(cp,[status(thm)],[t215,t85]) ).
cnf(t118951,plain,
meet(X1,X2) = join(meet(X1,X2),complement(join(complement(X1),complement(X2)))),
inference(step,[status(thm)],[t216,t85]) ).
cnf(t118952,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X1,X2)),
inference(step,[status(thm)],[t118951,t85]) ).
cnf(t439,plain,
join(meet(X1,X2),meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t118952]) ).
cnf(t87,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t85,t45]) ).
cnf(t118925,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t87,t85]) ).
cnf(t107,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t118925]) ).
cnf(t440,plain,
meet(X1,X2) = join(meet(X2,X1),meet(X1,X2)),
inference(cp,[status(thm)],[t439,t107]) ).
cnf(t460,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X2,X1),
inference(orient,[status(thm)],[t440]) ).
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(t19,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t47,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t19]) ).
cnf(t119467,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t47,t45]) ).
cnf(t119468,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t119467,t85]) ).
cnf(t119469,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t119468,t45]) ).
cnf(t15024,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t119469]) ).
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(t92,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t15025,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t15024,t92]) ).
cnf(t119577,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t15025,t85]) ).
cnf(t15698,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t119577]) ).
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(t53,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t86,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t85,t53]) ).
cnf(t118923,plain,
zero = complement(top),
inference(step,[status(thm)],[t86,t92]) ).
cnf(t98,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t118923]) ).
cnf(t219,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t215,t98]) ).
cnf(t118932,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t219,t98]) ).
cnf(t118933,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t118932,t98]) ).
cnf(t226,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t118933]) ).
cnf(t227,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t48,t226]) ).
cnf(t245,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t227]) ).
cnf(t15703,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t245,t15698]) ).
cnf(t119579,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t15703,t15698]) ).
cnf(t15718,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t119579]) ).
cnf(t119584,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t15698,t15718]) ).
cnf(t15744,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t119584]) ).
cnf(t15770,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t15744]) ).
cnf(t15771,plain,
meet(X1,X1) = join(X1,meet(X1,X1)),
inference(cp,[status(thm)],[t460,t15770]) ).
cnf(t119619,plain,
X1 = join(X1,meet(X1,X1)),
inference(step,[status(thm)],[t15771,t15770]) ).
cnf(t119620,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t119619,t15770]) ).
cnf(t15837,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t119620]) ).
cnf(t15841,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t48,t15837]) ).
cnf(t15884,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t15841]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t23,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
fof(f16,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(f16_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)],[f16]) ).
fof(f16_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)],[f16_neg]) ).
fof(f16_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])],[f16_nnf]) ).
cnf(c16,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)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c16]) ).
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,t45]) ).
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,t16895]) ).
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,t16895]) ).
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,t118396]) ).
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,t45]) ).
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,t45]) ).
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,t45]) ).
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,t45]) ).
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,t45]) ).
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,t45]) ).
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,t48]) ).
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,t15837]) ).
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,t45]) ).
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,t118396]) ).
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,t15884]) ).
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,t23]) ).
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,t118396]) ).
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,t118396]) ).
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,t16895]) ).
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,t15837]) ).
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,t118396]) ).
cnf(g0_22,plain,
true != ifeq(composition(sk0,join(sk2,sk1)),composition(sk0,join(sk2,sk1)),false,true),
inference(rw,[status(thm)],[g0_21,t15884]) ).
cnf(g0_23,plain,
true != false,
inference(rw,[status(thm)],[g0_22,t23]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL008+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/1.00 % Computer : n006.cluster.edu
% 0.10/1.00 % Model : x86_64 x86_64
% 0.10/1.00 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/1.00 % Memory : 8046.5625MB
% 0.10/1.00 % OS : Linux 6.8.0-71-generic
% 0.10/1.00 % CPULimit : 300
% 0.10/1.00 % WCLimit : 300
% 0.10/1.00 % DateTime : Thu Sep 24 07:08:36 UTC 2026
% 0.10/1.00 % CPUTime :
% 0.10/1.00 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 176.12/23.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 176.12/23.63 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------