%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL040-3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 : Tue Sep 29 12:34:04 PM UTC 2026
% Result : Unsatisfiable 20.50s 3.75s
% Output : Refutation 20.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 30
% Syntax : Number of formulae : 297 ( 297 unt; 14 def)
% Number of atoms : 297 ( 296 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 20 con; 0-2 aty)
% Number of variables : 284 ( 284 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f3,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_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity_5) ).
fof(f8,negated_conjecture,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,negated_conjecture,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
fof(f19,axiom,
! [X2,X0,X1] : join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law_1_15) ).
fof(f20,plain,
! [X2,X0,X1] : meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2) = join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)),
inference(reorient_equations,[],[f19]) ).
fof(f23,negated_conjecture,
join(composition(converse(sk1),sk1),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
one = join(composition(converse(sk1),sk1),one),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
composition(sk1,meet(sk2,sk3)) != meet(composition(sk1,sk2),composition(sk1,sk3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
fof(f26,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f28,plain,
! [X2,X0,X1] : complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2))) = join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2)))),
inference(definition_unfolding,[],[f20,f6,f6,f6,f6,f6]) ).
fof(f30,plain,
composition(sk1,complement(join(complement(sk2),complement(sk3)))) != complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))),
inference(definition_unfolding,[],[f25,f6,f6]) ).
fof(f31,definition,
sF0 = converse(sk1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f32,plain,
converse(sk1) = sF0,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF1 = composition(sF0,sk1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f34,plain,
composition(sF0,sk1) = sF1,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF2 = join(sF1,one),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f36,plain,
join(sF1,one) = sF2,
inference(reorient_equations,[],[f35]) ).
fof(f37,plain,
one = sF2,
inference(definition_folding,[],[f24,f36,f34,f32]) ).
fof(f38,definition,
sF3 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f39,plain,
complement(sk2) = sF3,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF4 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f41,plain,
complement(sk3) = sF4,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF5 = join(sF3,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f43,plain,
join(sF3,sF4) = sF5,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF6 = complement(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f45,plain,
complement(sF5) = sF6,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF7 = composition(sk1,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f47,plain,
composition(sk1,sF6) = sF7,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF8 = composition(sk1,sk2),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f49,plain,
composition(sk1,sk2) = sF8,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF9 = complement(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f51,plain,
complement(sF8) = sF9,
inference(reorient_equations,[],[f50]) ).
fof(f52,definition,
sF10 = composition(sk1,sk3),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f53,plain,
composition(sk1,sk3) = sF10,
inference(reorient_equations,[],[f52]) ).
fof(f54,definition,
sF11 = complement(sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f55,plain,
complement(sF10) = sF11,
inference(reorient_equations,[],[f54]) ).
fof(f56,definition,
sF12 = join(sF9,sF11),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f57,plain,
join(sF9,sF11) = sF12,
inference(reorient_equations,[],[f56]) ).
fof(f58,definition,
sF13 = complement(sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f59,plain,
complement(sF12) = sF13,
inference(reorient_equations,[],[f58]) ).
fof(f60,plain,
sF7 != sF13,
inference(definition_folding,[],[f30,f59,f57,f55,f53,f51,f49,f47,f45,f43,f41,f39]) ).
fof(f61,plain,
zero = complement(top),
inference(backward_demodulation,[],[f26,f15]) ).
fof(f62,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f64,plain,
! [X2,X0,X1] : complement(join(complement(X2),complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))))) = join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(X2),complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2))))))))),
inference(backward_demodulation,[],[f28,f1]) ).
fof(f65,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f66,plain,
one = join(sF1,one),
inference(forward_demodulation,[],[f36,f37]) ).
fof(f118,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f62,f15]) ).
fof(f119,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f118,f61]) ).
fof(f130,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f62,f1]) ).
fof(f171,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f9,f12]) ).
fof(f173,plain,
sk1 = converse(sF0),
inference(superposition,[],[f10,f32]) ).
fof(f174,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f208,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f2,f62]) ).
fof(f214,plain,
! [X0] : join(sF9,join(sF11,X0)) = join(sF12,X0),
inference(superposition,[],[f2,f57]) ).
fof(f220,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f244,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X0),complement(X0))),join(complement(top),X1)),
inference(superposition,[],[f208,f15]) ).
fof(f260,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f244,f220]) ).
fof(f272,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f260,f61]) ).
fof(f300,plain,
! [X0] : join(complement(join(complement(X0),top)),complement(join(complement(X0),zero))) = X0,
inference(superposition,[],[f62,f61]) ).
fof(f302,plain,
! [X0] : join(complement(join(complement(X0),top)),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f300,f1]) ).
fof(f304,plain,
! [X0] : join(complement(join(zero,complement(X0))),complement(join(complement(X0),top))) = X0,
inference(forward_demodulation,[],[f302,f1]) ).
fof(f306,plain,
! [X0] : join(complement(join(zero,complement(X0))),complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f304,f1]) ).
fof(f308,plain,
! [X0] : join(complement(join(top,complement(X0))),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f306,f1]) ).
fof(f316,plain,
! [X0] : composition(sF0,composition(sk1,X0)) = composition(sF1,X0),
inference(superposition,[],[f7,f34]) ).
fof(f410,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f174,f8]) ).
fof(f421,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f410,f10]) ).
fof(f440,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f171,f12]) ).
fof(f450,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f440,f11]) ).
fof(f462,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f450,f11]) ).
fof(f467,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f462,f12]) ).
fof(f497,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f130,f15]) ).
fof(f500,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),X0) = join(X0,complement(join(complement(complement(X1)),complement(X0)))),
inference(superposition,[],[f208,f130]) ).
fof(f512,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(join(complement(complement(X1)),complement(X0)))),
inference(forward_demodulation,[],[f500,f1]) ).
fof(f513,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f497,f1]) ).
fof(f537,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f513,f1]) ).
fof(f550,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f537,f61]) ).
fof(f559,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f119,f550]) ).
fof(f569,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(join(X1,complement(X0)))),
inference(backward_demodulation,[],[f512,f559]) ).
fof(f570,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f550,f559]) ).
fof(f582,plain,
! [X0,X1] : complement(join(X1,X0)) = join(zero,complement(join(X0,join(join(X1,X0),X1)))),
inference(superposition,[],[f570,f220]) ).
fof(f588,plain,
! [X0,X1] : join(complement(X0),X1) = join(zero,join(complement(join(X0,X0)),X1)),
inference(superposition,[],[f2,f570]) ).
fof(f591,plain,
! [X0,X1] : complement(join(X1,X0)) = join(zero,complement(join(X0,join(X1,join(X0,X1))))),
inference(forward_demodulation,[],[f582,f2]) ).
fof(f592,plain,
top = complement(zero),
inference(superposition,[],[f559,f61]) ).
fof(f593,plain,
sk2 = complement(sF3),
inference(superposition,[],[f559,f39]) ).
fof(f594,plain,
sk3 = complement(sF4),
inference(superposition,[],[f559,f41]) ).
fof(f595,plain,
sF5 = complement(sF6),
inference(superposition,[],[f559,f45]) ).
fof(f600,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f62,f559]) ).
fof(f604,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f130,f559]) ).
fof(f634,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f600,f1]) ).
fof(f645,plain,
complement(sF3) = join(complement(sF5),complement(join(sF3,complement(sF4)))),
inference(superposition,[],[f600,f43]) ).
fof(f673,plain,
complement(sF3) = join(complement(sF5),complement(join(sF3,sk3))),
inference(forward_demodulation,[],[f645,f594]) ).
fof(f686,plain,
complement(sF3) = join(sF6,complement(join(sF3,sk3))),
inference(forward_demodulation,[],[f673,f45]) ).
fof(f693,plain,
sk2 = join(sF6,complement(join(sF3,sk3))),
inference(forward_demodulation,[],[f686,f593]) ).
fof(f702,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(complement(X0),X1))),
inference(superposition,[],[f604,f1]) ).
fof(f736,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),complement(complement(join(complement(X1),X0)))))),
inference(superposition,[],[f600,f604]) ).
fof(f737,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),join(complement(X1),X0)))),
inference(forward_demodulation,[],[f736,f559]) ).
fof(f760,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(X0,join(complement(join(X0,X1)),complement(X1))))),
inference(forward_demodulation,[],[f737,f220]) ).
fof(f774,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f760,f1]) ).
fof(f786,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f774,f559]) ).
fof(f796,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f786,f559]) ).
fof(f817,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(complement(join(X0,X0)),complement(zero)))),
inference(superposition,[],[f634,f570]) ).
fof(f819,plain,
complement(sF4) = join(complement(sF5),complement(join(sF4,complement(sF3)))),
inference(superposition,[],[f634,f43]) ).
fof(f837,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(join(complement(join(X0,complement(X1))),join(X1,X0))),complement(complement(X0))),
inference(superposition,[],[f604,f634]) ).
fof(f849,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(complement(join(X0,complement(X1))),join(X1,X0)))),
inference(forward_demodulation,[],[f837,f1]) ).
fof(f857,plain,
complement(sF4) = join(complement(sF5),complement(join(sF4,sk2))),
inference(forward_demodulation,[],[f819,f593]) ).
fof(f858,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(complement(zero),complement(join(X0,X0))))),
inference(forward_demodulation,[],[f817,f1]) ).
fof(f870,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(join(X1,X0),complement(join(X0,complement(X1)))))),
inference(forward_demodulation,[],[f849,f1]) ).
fof(f877,plain,
complement(sF4) = join(sF6,complement(join(sF4,sk2))),
inference(forward_demodulation,[],[f857,f45]) ).
fof(f878,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f858,f592]) ).
fof(f886,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f870,f2]) ).
fof(f892,plain,
sk3 = join(sF6,complement(join(sF4,sk2))),
inference(forward_demodulation,[],[f877,f594]) ).
fof(f893,plain,
! [X0] : complement(complement(join(X0,X0))) = join(X0,complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f878,f559]) ).
fof(f900,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f886,f559]) ).
fof(f906,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f893,f559]) ).
fof(f913,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f900,f559]) ).
fof(f964,plain,
! [X0] : complement(join(complement(X0),complement(composition(sk1,complement(join(complement(sF6),complement(composition(converse(sk1),X0)))))))) = join(complement(join(complement(sF7),complement(X0))),complement(join(complement(X0),complement(composition(sk1,complement(join(complement(sF6),complement(composition(converse(sk1),X0))))))))),
inference(superposition,[],[f64,f47]) ).
fof(f966,plain,
! [X0] : complement(join(complement(X0),complement(composition(sk1,complement(join(complement(sk3),complement(composition(converse(sk1),X0)))))))) = join(complement(join(complement(sF10),complement(X0))),complement(join(complement(X0),complement(composition(sk1,complement(join(complement(sk3),complement(composition(converse(sk1),X0))))))))),
inference(superposition,[],[f64,f53]) ).
fof(f972,plain,
! [X0,X1] : complement(join(zero,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),top)))))))) = join(complement(join(complement(composition(X0,X1)),zero)),complement(join(zero,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),top))))))))),
inference(superposition,[],[f64,f61]) ).
fof(f1025,plain,
! [X0,X1] : complement(join(zero,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),top)))))))) = join(complement(join(zero,complement(composition(X0,X1)))),complement(join(zero,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),top))))))))),
inference(forward_demodulation,[],[f972,f1]) ).
fof(f1028,plain,
! [X0] : complement(join(complement(X0),complement(composition(sk1,complement(join(complement(sk3),complement(composition(sF0,X0)))))))) = join(complement(join(complement(sF10),complement(X0))),complement(join(complement(X0),complement(composition(sk1,complement(join(complement(sk3),complement(composition(sF0,X0))))))))),
inference(forward_demodulation,[],[f966,f32]) ).
fof(f1030,plain,
! [X0] : complement(join(complement(X0),complement(composition(sk1,complement(join(complement(sF6),complement(composition(sF0,X0)))))))) = join(complement(join(complement(sF7),complement(X0))),complement(join(complement(X0),complement(composition(sk1,complement(join(complement(sF6),complement(composition(sF0,X0))))))))),
inference(forward_demodulation,[],[f964,f32]) ).
fof(f1041,plain,
! [X0] : complement(join(complement(X0),complement(composition(sk1,complement(join(sF4,complement(composition(sF0,X0)))))))) = join(complement(join(complement(sF10),complement(X0))),complement(join(complement(X0),complement(composition(sk1,complement(join(sF4,complement(composition(sF0,X0))))))))),
inference(forward_demodulation,[],[f1028,f41]) ).
fof(f1043,plain,
! [X0] : complement(join(complement(X0),complement(composition(sk1,complement(join(sF5,complement(composition(sF0,X0)))))))) = join(complement(join(complement(sF7),complement(X0))),complement(join(complement(X0),complement(composition(sk1,complement(join(sF5,complement(composition(sF0,X0))))))))),
inference(forward_demodulation,[],[f1030,f595]) ).
fof(f1051,plain,
! [X0] : complement(join(complement(X0),complement(composition(sk1,complement(join(sF4,complement(composition(sF0,X0)))))))) = join(complement(join(sF11,complement(X0))),complement(join(complement(X0),complement(composition(sk1,complement(join(sF4,complement(composition(sF0,X0))))))))),
inference(forward_demodulation,[],[f1041,f55]) ).
fof(f1075,plain,
complement(join(sF9,complement(composition(sk1,complement(join(sF4,complement(composition(sF0,sF8)))))))) = join(complement(join(sF11,sF9)),complement(join(sF9,complement(composition(sk1,complement(join(sF4,complement(composition(sF0,sF8))))))))),
inference(superposition,[],[f1051,f51]) ).
fof(f1096,plain,
complement(join(sF9,complement(composition(sk1,complement(join(sF4,complement(composition(sF0,sF8)))))))) = join(complement(join(sF9,sF11)),complement(join(sF9,complement(composition(sk1,complement(join(sF4,complement(composition(sF0,sF8))))))))),
inference(forward_demodulation,[],[f1075,f1]) ).
fof(f1107,plain,
complement(join(sF9,complement(composition(sk1,complement(join(sF4,complement(composition(sF0,sF8)))))))) = join(complement(sF12),complement(join(sF9,complement(composition(sk1,complement(join(sF4,complement(composition(sF0,sF8))))))))),
inference(forward_demodulation,[],[f1096,f57]) ).
fof(f1115,plain,
complement(join(sF9,complement(composition(sk1,complement(join(sF4,complement(composition(sF0,sF8)))))))) = join(sF13,complement(join(sF9,complement(composition(sk1,complement(join(sF4,complement(composition(sF0,sF8))))))))),
inference(forward_demodulation,[],[f1107,f59]) ).
fof(f1197,plain,
complement(join(zero,complement(composition(sk1,complement(join(sF5,complement(composition(sF0,top)))))))) = join(complement(join(complement(sF7),zero)),complement(join(zero,complement(composition(sk1,complement(join(sF5,complement(composition(sF0,top))))))))),
inference(superposition,[],[f1043,f61]) ).
fof(f1232,plain,
complement(join(zero,complement(composition(sk1,complement(join(sF5,complement(composition(sF0,top)))))))) = join(complement(join(zero,complement(sF7))),complement(join(zero,complement(composition(sk1,complement(join(sF5,complement(composition(sF0,top))))))))),
inference(forward_demodulation,[],[f1197,f1]) ).
fof(f1369,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(superposition,[],[f65,f421]) ).
fof(f1379,plain,
! [X0,X1] : composition(join(converse(one),X1),X0) = join(X0,composition(X1,X0)),
inference(superposition,[],[f9,f421]) ).
fof(f1382,plain,
one = converse(one),
inference(superposition,[],[f8,f421]) ).
fof(f1386,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f421,f1382]) ).
fof(f1389,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(forward_demodulation,[],[f1379,f1382]) ).
fof(f1396,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f1369,f1386]) ).
fof(f1408,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(complement(X0)))),
inference(backward_demodulation,[],[f272,f1396]) ).
fof(f1414,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,X0)),
inference(forward_demodulation,[],[f1408,f559]) ).
fof(f1420,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X0))),
inference(backward_demodulation,[],[f588,f1414]) ).
fof(f1423,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(complement(X0),top))),
inference(backward_demodulation,[],[f906,f1420]) ).
fof(f1424,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(backward_demodulation,[],[f570,f1420]) ).
fof(f1426,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f1424,f1]) ).
fof(f1427,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(top,complement(X0)))),
inference(forward_demodulation,[],[f1423,f569]) ).
fof(f1432,plain,
! [X0] : join(complement(join(top,complement(X0))),complement(complement(X0))) = X0,
inference(backward_demodulation,[],[f308,f1426]) ).
fof(f1433,plain,
! [X0,X1] : complement(join(X1,X0)) = complement(join(X0,join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f591,f1426]) ).
fof(f1437,plain,
! [X0,X1] : complement(join(zero,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),top)))))))) = join(complement(complement(composition(X0,X1))),complement(join(zero,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),top))))))))),
inference(backward_demodulation,[],[f1025,f1426]) ).
fof(f1440,plain,
complement(complement(composition(sk1,complement(join(sF5,complement(composition(sF0,top))))))) = join(complement(join(zero,complement(sF7))),complement(complement(composition(sk1,complement(join(sF5,complement(composition(sF0,top)))))))),
inference(backward_demodulation,[],[f1232,f1426]) ).
fof(f1442,plain,
composition(sk1,complement(join(sF5,complement(composition(sF0,top))))) = join(complement(join(zero,complement(sF7))),composition(sk1,complement(join(sF5,complement(composition(sF0,top)))))),
inference(forward_demodulation,[],[f1440,f559]) ).
fof(f1445,plain,
! [X0,X1] : complement(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),top))))))) = join(complement(complement(composition(X0,X1))),complement(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),top)))))))),
inference(forward_demodulation,[],[f1437,f1426]) ).
fof(f1447,plain,
! [X0] : join(complement(complement(X0)),complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f1432,f1]) ).
fof(f1451,plain,
composition(sk1,complement(join(sF5,complement(composition(sF0,top))))) = join(complement(complement(sF7)),composition(sk1,complement(join(sF5,complement(composition(sF0,top)))))),
inference(forward_demodulation,[],[f1442,f1426]) ).
fof(f1452,plain,
! [X0,X1] : composition(X0,complement(join(complement(X1),complement(composition(converse(X0),top))))) = join(complement(complement(composition(X0,X1))),composition(X0,complement(join(complement(X1),complement(composition(converse(X0),top)))))),
inference(forward_demodulation,[],[f1445,f559]) ).
fof(f1453,plain,
! [X0] : join(X0,complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f1447,f559]) ).
fof(f1456,plain,
composition(sk1,complement(join(sF5,complement(composition(sF0,top))))) = join(sF7,composition(sk1,complement(join(sF5,complement(composition(sF0,top)))))),
inference(forward_demodulation,[],[f1451,f559]) ).
fof(f1457,plain,
! [X0,X1] : composition(X0,complement(join(complement(X1),complement(composition(converse(X0),top))))) = join(composition(X0,X1),composition(X0,complement(join(complement(X1),complement(composition(converse(X0),top)))))),
inference(forward_demodulation,[],[f1452,f559]) ).
fof(f1458,plain,
! [X0] : join(X0,X0) = X0,
inference(backward_demodulation,[],[f1427,f1453]) ).
fof(f1495,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f1426,f559]) ).
fof(f1553,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f1458]) ).
fof(f1554,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X0,X1)),
inference(superposition,[],[f220,f1458]) ).
fof(f1555,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f220,f1458]) ).
fof(f1563,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X1,join(X0,X1))),
inference(superposition,[],[f2,f1458]) ).
fof(f1578,plain,
! [X0,X1] : complement(join(X0,X1)) = complement(join(X1,X0)),
inference(backward_demodulation,[],[f1433,f1563]) ).
fof(f1667,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(X0)),
inference(superposition,[],[f1553,f604]) ).
fof(f1668,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f1553,f634]) ).
fof(f1674,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(join(X0,X1),X2)),
inference(superposition,[],[f1553,f9]) ).
fof(f1710,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = composition(join(X0,join(X0,X1)),X2),
inference(forward_demodulation,[],[f1674,f9]) ).
fof(f1711,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f1668,f1]) ).
fof(f1712,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1667,f1]) ).
fof(f1726,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = composition(join(X1,X0),X2),
inference(forward_demodulation,[],[f1710,f1554]) ).
fof(f1727,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f796,f1711]) ).
fof(f1736,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f913,f1727]) ).
fof(f1752,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1736,f1555]) ).
fof(f1779,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f1752,f1]) ).
fof(f1792,plain,
join(sF3,complement(sF4)) = join(sF3,complement(sF5)),
inference(superposition,[],[f1752,f43]) ).
fof(f1833,plain,
join(sF3,complement(sF4)) = join(sF3,sF6),
inference(forward_demodulation,[],[f1792,f45]) ).
fof(f1861,plain,
join(sF3,sk3) = join(sF3,sF6),
inference(forward_demodulation,[],[f1833,f594]) ).
fof(f1889,plain,
sk2 = join(sF6,complement(join(sF3,sF6))),
inference(backward_demodulation,[],[f693,f1861]) ).
fof(f1908,plain,
sk2 = join(sF6,complement(sF3)),
inference(forward_demodulation,[],[f1889,f1779]) ).
fof(f1921,plain,
sk2 = join(sF6,sk2),
inference(forward_demodulation,[],[f1908,f593]) ).
fof(f2028,plain,
join(sF4,complement(sF3)) = join(sF4,complement(sF5)),
inference(superposition,[],[f1779,f43]) ).
fof(f2069,plain,
join(sF4,complement(sF3)) = join(sF4,sF6),
inference(forward_demodulation,[],[f2028,f45]) ).
fof(f2099,plain,
join(sF4,sk2) = join(sF4,sF6),
inference(forward_demodulation,[],[f2069,f593]) ).
fof(f2124,plain,
sk3 = join(sF6,complement(join(sF4,sF6))),
inference(backward_demodulation,[],[f892,f2099]) ).
fof(f2140,plain,
sk3 = join(sF6,complement(sF4)),
inference(forward_demodulation,[],[f2124,f1779]) ).
fof(f2150,plain,
sk3 = join(sF6,sk3),
inference(forward_demodulation,[],[f2140,f594]) ).
fof(f2205,plain,
complement(sF6) = join(complement(sk3),complement(join(complement(sk3),sF6))),
inference(superposition,[],[f604,f2150]) ).
fof(f2210,plain,
complement(sF6) = join(complement(sk3),complement(sF6)),
inference(forward_demodulation,[],[f2205,f1752]) ).
fof(f2214,plain,
complement(sF6) = join(complement(sF6),complement(sk3)),
inference(forward_demodulation,[],[f2210,f1]) ).
fof(f2217,plain,
complement(sF6) = join(complement(sF6),sF4),
inference(forward_demodulation,[],[f2214,f41]) ).
fof(f2219,plain,
complement(sF6) = join(sF4,complement(sF6)),
inference(forward_demodulation,[],[f2217,f1]) ).
fof(f2221,plain,
sF5 = join(sF4,sF5),
inference(forward_demodulation,[],[f2219,f595]) ).
fof(f2672,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(superposition,[],[f1712,f559]) ).
fof(f3432,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f467]) ).
fof(f3451,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f3432,f10]) ).
fof(f3485,plain,
! [X0,X1] : composition(X0,complement(join(complement(X1),complement(composition(converse(X0),top))))) = composition(X0,join(X1,complement(join(complement(X1),complement(composition(converse(X0),top)))))),
inference(backward_demodulation,[],[f1457,f3451]) ).
fof(f3499,plain,
! [X0,X1] : composition(X0,X1) = composition(X0,complement(join(complement(X1),complement(composition(converse(X0),top))))),
inference(forward_demodulation,[],[f3485,f2672]) ).
fof(f3519,plain,
! [X0] : composition(sk1,join(sF6,X0)) = join(sF7,composition(sk1,X0)),
inference(superposition,[],[f3451,f47]) ).
fof(f3523,plain,
! [X0,X1] : join(composition(X0,X1),X0) = composition(X0,join(X1,one)),
inference(superposition,[],[f3451,f8]) ).
fof(f3532,plain,
! [X0] : composition(sk1,join(X0,sk2)) = join(composition(sk1,X0),sF8),
inference(superposition,[],[f3451,f49]) ).
fof(f3533,plain,
! [X0] : composition(sk1,join(X0,sk3)) = join(composition(sk1,X0),sF10),
inference(superposition,[],[f3451,f53]) ).
fof(f3562,plain,
! [X0] : join(sF10,composition(sk1,X0)) = composition(sk1,join(X0,sk3)),
inference(forward_demodulation,[],[f3533,f1]) ).
fof(f3563,plain,
! [X0] : join(sF8,composition(sk1,X0)) = composition(sk1,join(X0,sk2)),
inference(forward_demodulation,[],[f3532,f1]) ).
fof(f3570,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(X1,one)),
inference(forward_demodulation,[],[f3523,f1]) ).
fof(f3608,plain,
! [X0] : composition(X0,one) = join(X0,composition(X0,sF1)),
inference(superposition,[],[f3570,f66]) ).
fof(f3660,plain,
! [X0] : join(X0,composition(X0,sF1)) = X0,
inference(forward_demodulation,[],[f3608,f8]) ).
fof(f3721,plain,
! [X0] : composition(one,X0) = join(X0,composition(composition(one,sF1),X0)),
inference(superposition,[],[f1389,f3660]) ).
fof(f3731,plain,
! [X0] : composition(one,X0) = join(X0,composition(one,composition(sF1,X0))),
inference(forward_demodulation,[],[f3721,f7]) ).
fof(f3753,plain,
! [X0] : composition(one,X0) = join(X0,composition(sF1,X0)),
inference(forward_demodulation,[],[f3731,f1386]) ).
fof(f3762,plain,
! [X0] : join(X0,composition(sF1,X0)) = X0,
inference(forward_demodulation,[],[f3753,f1386]) ).
fof(f4099,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(composition(sF1,X0),X1)),
inference(superposition,[],[f2,f3762]) ).
fof(f4101,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(composition(sF1,X0),X1)),
inference(superposition,[],[f220,f3762]) ).
fof(f4183,plain,
! [X0,X1] : join(X0,composition(sF1,join(X0,X1))) = join(X0,composition(sF1,X1)),
inference(superposition,[],[f4099,f3451]) ).
fof(f4523,plain,
composition(sk1,sk2) = join(sF8,composition(sk1,sF6)),
inference(superposition,[],[f3563,f1921]) ).
fof(f4550,plain,
composition(sk1,sk2) = join(sF8,sF7),
inference(forward_demodulation,[],[f4523,f47]) ).
fof(f4560,plain,
sF8 = join(sF8,sF7),
inference(forward_demodulation,[],[f4550,f49]) ).
fof(f4573,plain,
complement(sF7) = join(complement(sF7),complement(sF8)),
inference(superposition,[],[f1711,f4560]) ).
fof(f4577,plain,
complement(sF7) = join(complement(sF8),complement(sF7)),
inference(forward_demodulation,[],[f4573,f1]) ).
fof(f4581,plain,
complement(sF7) = join(sF9,complement(sF7)),
inference(forward_demodulation,[],[f4577,f51]) ).
fof(f4859,plain,
composition(sk1,sk3) = join(sF10,composition(sk1,sF6)),
inference(superposition,[],[f3562,f2150]) ).
fof(f4886,plain,
composition(sk1,sk3) = join(sF10,sF7),
inference(forward_demodulation,[],[f4859,f47]) ).
fof(f4896,plain,
sF10 = join(sF10,sF7),
inference(forward_demodulation,[],[f4886,f53]) ).
fof(f4909,plain,
complement(sF7) = join(complement(sF7),complement(sF10)),
inference(superposition,[],[f1711,f4896]) ).
fof(f4913,plain,
complement(sF7) = join(complement(sF10),complement(sF7)),
inference(forward_demodulation,[],[f4909,f1]) ).
fof(f4917,plain,
complement(sF7) = join(sF11,complement(sF7)),
inference(forward_demodulation,[],[f4913,f55]) ).
fof(f5049,plain,
composition(sF0,sF8) = composition(sF1,sk2),
inference(superposition,[],[f316,f49]) ).
fof(f5051,plain,
composition(sF0,sF7) = composition(sF1,sF6),
inference(superposition,[],[f316,f47]) ).
fof(f5324,plain,
! [X0] : composition(sk1,sF6) = join(sF7,composition(sk1,complement(join(complement(sF6),X0)))),
inference(superposition,[],[f3519,f2672]) ).
fof(f5369,plain,
! [X0] : composition(sk1,sF6) = join(sF7,composition(sk1,complement(join(sF5,X0)))),
inference(forward_demodulation,[],[f5324,f595]) ).
fof(f5391,plain,
! [X0] : sF7 = join(sF7,composition(sk1,complement(join(sF5,X0)))),
inference(forward_demodulation,[],[f5369,f47]) ).
fof(f5401,plain,
sF7 = composition(sk1,complement(join(sF5,complement(composition(sF0,top))))),
inference(backward_demodulation,[],[f1456,f5391]) ).
fof(f5424,plain,
join(sF9,complement(sF7)) = join(sF12,complement(sF7)),
inference(superposition,[],[f214,f4917]) ).
fof(f5478,plain,
complement(sF7) = join(sF12,complement(sF7)),
inference(forward_demodulation,[],[f5424,f4581]) ).
fof(f5671,plain,
! [X0,X1] : join(X0,composition(sF1,join(X0,X1))) = join(composition(sF1,X1),X0),
inference(superposition,[],[f4101,f3451]) ).
fof(f5820,plain,
! [X0] : join(composition(sF1,complement(X0)),X0) = join(X0,composition(sF1,top)),
inference(superposition,[],[f5671,f15]) ).
fof(f5846,plain,
! [X0,X1] : join(complement(X0),composition(sF1,complement(X0))) = join(composition(sF1,complement(join(X0,X1))),complement(X0)),
inference(superposition,[],[f5671,f1712]) ).
fof(f5861,plain,
join(composition(sF1,sk2),sF4) = join(sF4,composition(sF1,join(sF4,sF6))),
inference(superposition,[],[f5671,f2099]) ).
fof(f5965,plain,
join(composition(sF1,sk2),sF4) = join(sF4,composition(sF1,sF6)),
inference(forward_demodulation,[],[f5861,f4183]) ).
fof(f5975,plain,
! [X0,X1] : join(complement(X0),composition(sF1,complement(X0))) = join(complement(X0),composition(sF1,complement(join(X0,X1)))),
inference(forward_demodulation,[],[f5846,f1]) ).
fof(f5995,plain,
! [X0] : join(X0,composition(sF1,complement(X0))) = join(X0,composition(sF1,top)),
inference(forward_demodulation,[],[f5820,f1]) ).
fof(f6023,plain,
join(composition(sF1,sk2),sF4) = join(sF4,composition(sF0,sF7)),
inference(forward_demodulation,[],[f5965,f5051]) ).
fof(f6031,plain,
! [X0,X1] : join(complement(X0),composition(sF1,complement(join(X0,X1)))) = composition(join(one,sF1),complement(X0)),
inference(forward_demodulation,[],[f5975,f1389]) ).
fof(f6053,plain,
join(sF4,composition(sF0,sF7)) = join(sF4,composition(sF1,sk2)),
inference(forward_demodulation,[],[f6023,f1]) ).
fof(f6057,plain,
! [X0,X1] : join(complement(X0),composition(sF1,complement(join(X0,X1)))) = composition(join(sF1,one),complement(X0)),
inference(forward_demodulation,[],[f6031,f1726]) ).
fof(f6064,plain,
join(sF4,composition(sF0,sF7)) = join(sF4,composition(sF0,sF8)),
inference(forward_demodulation,[],[f6053,f5049]) ).
fof(f6067,plain,
! [X0,X1] : composition(one,complement(X0)) = join(complement(X0),composition(sF1,complement(join(X0,X1)))),
inference(forward_demodulation,[],[f6057,f66]) ).
fof(f6071,plain,
! [X0,X1] : complement(X0) = join(complement(X0),composition(sF1,complement(join(X0,X1)))),
inference(forward_demodulation,[],[f6067,f1386]) ).
fof(f6081,plain,
complement(composition(sF0,sF7)) = join(complement(join(sF4,composition(sF0,sF8))),complement(join(composition(sF0,sF7),complement(sF4)))),
inference(superposition,[],[f634,f6064]) ).
fof(f6091,plain,
complement(composition(sF0,sF7)) = join(complement(join(sF4,composition(sF0,sF8))),complement(join(complement(sF4),composition(sF0,sF7)))),
inference(forward_demodulation,[],[f6081,f1578]) ).
fof(f6101,plain,
complement(composition(sF0,sF7)) = join(complement(join(sF4,composition(sF0,sF8))),complement(join(sk3,composition(sF0,sF7)))),
inference(forward_demodulation,[],[f6091,f594]) ).
fof(f7842,plain,
! [X0] : complement(composition(sF1,complement(X0))) = join(complement(join(X0,composition(sF1,complement(X0)))),complement(complement(X0))),
inference(superposition,[],[f702,f3762]) ).
fof(f7891,plain,
! [X0] : complement(composition(sF1,complement(X0))) = join(complement(complement(X0)),complement(join(X0,composition(sF1,complement(X0))))),
inference(forward_demodulation,[],[f7842,f1]) ).
fof(f7992,plain,
! [X0] : complement(composition(sF1,complement(X0))) = join(complement(complement(X0)),complement(join(X0,composition(sF1,top)))),
inference(forward_demodulation,[],[f7891,f5995]) ).
fof(f8061,plain,
! [X0] : complement(composition(sF1,complement(X0))) = join(X0,complement(join(X0,composition(sF1,top)))),
inference(forward_demodulation,[],[f7992,f559]) ).
fof(f8116,plain,
! [X0] : complement(composition(sF1,complement(X0))) = join(X0,complement(composition(sF1,top))),
inference(forward_demodulation,[],[f8061,f1752]) ).
fof(f12709,plain,
complement(sF12) = join(complement(sF12),complement(complement(sF7))),
inference(superposition,[],[f1712,f5478]) ).
fof(f12717,plain,
complement(sF12) = join(complement(sF12),sF7),
inference(forward_demodulation,[],[f12709,f559]) ).
fof(f12727,plain,
complement(sF12) = join(sF7,complement(sF12)),
inference(forward_demodulation,[],[f12717,f1]) ).
fof(f12734,plain,
sF13 = join(sF7,sF13),
inference(forward_demodulation,[],[f12727,f59]) ).
fof(f14083,plain,
! [X0] : composition(X0,top) = composition(X0,complement(join(zero,complement(composition(converse(X0),top))))),
inference(superposition,[],[f3499,f61]) ).
fof(f14205,plain,
! [X0] : composition(X0,top) = composition(X0,complement(complement(composition(converse(X0),top)))),
inference(forward_demodulation,[],[f14083,f1495]) ).
fof(f14251,plain,
! [X0] : composition(X0,top) = composition(X0,composition(converse(X0),top)),
inference(forward_demodulation,[],[f14205,f559]) ).
fof(f14291,plain,
composition(sF0,top) = composition(sF0,composition(sk1,top)),
inference(superposition,[],[f14251,f173]) ).
fof(f14374,plain,
composition(sF0,top) = composition(sF1,top),
inference(forward_demodulation,[],[f14291,f316]) ).
fof(f14406,plain,
! [X0] : complement(composition(sF1,complement(X0))) = join(X0,complement(composition(sF0,top))),
inference(backward_demodulation,[],[f8116,f14374]) ).
fof(f14496,plain,
sF7 = composition(sk1,complement(complement(composition(sF1,complement(sF5))))),
inference(backward_demodulation,[],[f5401,f14406]) ).
fof(f14514,plain,
sF7 = composition(sk1,composition(sF1,complement(sF5))),
inference(forward_demodulation,[],[f14496,f559]) ).
fof(f14535,plain,
sF7 = composition(sk1,composition(sF1,sF6)),
inference(forward_demodulation,[],[f14514,f45]) ).
fof(f14554,plain,
sF7 = composition(sk1,composition(sF0,sF7)),
inference(forward_demodulation,[],[f14535,f5051]) ).
fof(f17771,plain,
complement(sF4) = join(complement(sF4),composition(sF1,complement(sF5))),
inference(superposition,[],[f6071,f2221]) ).
fof(f17888,plain,
complement(sF4) = join(complement(sF4),composition(sF1,sF6)),
inference(forward_demodulation,[],[f17771,f45]) ).
fof(f17956,plain,
complement(sF4) = join(complement(sF4),composition(sF0,sF7)),
inference(forward_demodulation,[],[f17888,f5051]) ).
fof(f17998,plain,
sk3 = join(sk3,composition(sF0,sF7)),
inference(forward_demodulation,[],[f17956,f594]) ).
fof(f18018,plain,
complement(composition(sF0,sF7)) = join(complement(join(sF4,composition(sF0,sF8))),complement(sk3)),
inference(backward_demodulation,[],[f6101,f17998]) ).
fof(f18050,plain,
complement(composition(sF0,sF7)) = join(complement(sk3),complement(join(sF4,composition(sF0,sF8)))),
inference(forward_demodulation,[],[f18018,f1]) ).
fof(f18066,plain,
complement(composition(sF0,sF7)) = join(sF4,complement(join(sF4,composition(sF0,sF8)))),
inference(forward_demodulation,[],[f18050,f41]) ).
fof(f18078,plain,
join(sF4,complement(composition(sF0,sF8))) = complement(composition(sF0,sF7)),
inference(forward_demodulation,[],[f18066,f1752]) ).
fof(f18086,plain,
complement(join(sF9,complement(composition(sk1,complement(complement(composition(sF0,sF7))))))) = join(sF13,complement(join(sF9,complement(composition(sk1,complement(complement(composition(sF0,sF7)))))))),
inference(backward_demodulation,[],[f1115,f18078]) ).
fof(f18140,plain,
complement(join(sF9,complement(composition(sk1,composition(sF0,sF7))))) = join(sF13,complement(join(sF9,complement(composition(sk1,composition(sF0,sF7)))))),
inference(forward_demodulation,[],[f18086,f559]) ).
fof(f18164,plain,
complement(join(sF9,complement(sF7))) = join(sF13,complement(join(sF9,complement(sF7)))),
inference(forward_demodulation,[],[f18140,f14554]) ).
fof(f18180,plain,
complement(complement(sF7)) = join(sF13,complement(complement(sF7))),
inference(forward_demodulation,[],[f18164,f4581]) ).
fof(f18283,plain,
sF7 = join(sF13,sF7),
inference(forward_demodulation,[],[f18180,f559]) ).
fof(f18313,plain,
sF7 = join(sF7,sF13),
inference(forward_demodulation,[],[f18283,f1]) ).
fof(f18320,plain,
sF7 = sF13,
inference(backward_demodulation,[],[f12734,f18313]) ).
fof(f18396,plain,
$false,
inference(forward_subsumption_resolution,[],[f18320,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL040-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:58:39 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.50/3.74 % (2827953)Detected a unit-equality problem, will run specialized UEQ schedule.
% 20.50/3.74 % (2827963)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3836726586:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 20.50/3.74 % (2827959)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2933336681:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 20.50/3.74 % (2827962)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=519365673:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 20.50/3.74 % (2827958)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=597310000:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 20.50/3.74 % (2827960)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4017906090:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 20.50/3.74 % (2827961)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=477095947:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 20.50/3.74 % (2827964)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2165542212:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 20.50/3.74 % (2827963)Instruction limit reached!
% 20.50/3.74 % (2827963)------------------------------
% 20.50/3.74 % (2827963)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.50/3.74 % (2827963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.50/3.74 % (2827963)CaDiCaL version: 2.1.3
% 20.50/3.74 % (2827963)Termination reason: Instruction limit
% 20.50/3.74 % (2827963)Termination phase: Saturation
% 20.50/3.74 % (2827963)Time elapsed: 0.091 s
% 20.50/3.74 % (2827963)Peak memory usage: 90 MB
% 20.50/3.74 % (2827963)Instructions burned: 259 (million)
% 20.50/3.74 % (2827961)Instruction limit reached!
% 20.50/3.74 % (2827961)------------------------------
% 20.50/3.74 % (2827961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.50/3.74 % (2827961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.50/3.74 % (2827961)CaDiCaL version: 2.1.3
% 20.50/3.74 % (2827961)Termination reason: Instruction limit
% 20.50/3.74 % (2827961)Termination phase: Saturation
% 20.50/3.74 % (2827961)Time elapsed: 0.086 s
% 20.50/3.74 % (2827961)Peak memory usage: 89 MB
% 20.50/3.74 % (2827961)Instructions burned: 137 (million)
% 20.50/3.74 % (2827962)Instruction limit reached!
% 20.50/3.74 % (2827962)------------------------------
% 20.50/3.74 % (2827962)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.50/3.74 % (2827962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.50/3.74 % (2827962)CaDiCaL version: 2.1.3
% 20.50/3.74 % (2827962)Termination reason: Instruction limit
% 20.50/3.74 % (2827962)Termination phase: Saturation
% 20.50/3.74 % (2827962)Time elapsed: 0.106 s
% 20.50/3.74 % (2827962)Peak memory usage: 89 MB
% 20.50/3.74 % (2827962)Instructions burned: 182 (million)
% 20.50/3.74 % (2827972)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2200253413:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 20.50/3.74 % (2827973)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3498755137:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 20.50/3.74 % (2827974)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=650528791:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 20.50/3.74 % (2827974)Instruction limit reached!
% 20.50/3.74 % (2827974)------------------------------
% 20.50/3.74 % (2827974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.50/3.74 % (2827974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.50/3.74 % (2827974)CaDiCaL version: 2.1.3
% 20.50/3.74 % (2827974)Termination reason: Instruction limit
% 20.50/3.74 % (2827974)Termination phase: Saturation
% 20.50/3.74 % (2827974)Time elapsed: 0.124 s
% 20.50/3.74 % (2827974)Peak memory usage: 92 MB
% 20.50/3.74 % (2827974)Instructions burned: 216 (million)
% 20.50/3.74 % (2827978)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=527088474:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 20.50/3.74 % (2827964)Instruction limit reached!
% 20.50/3.74 % (2827964)------------------------------
% 20.50/3.74 % (2827964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.50/3.74 % (2827964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.50/3.74 % (2827964)CaDiCaL version: 2.1.3
% 20.50/3.74 % (2827964)Termination reason: Instruction limit
% 20.50/3.74 % (2827964)Termination phase: Saturation
% 20.50/3.74 % (2827964)Time elapsed: 0.654 s
% 20.50/3.74 % (2827964)Peak memory usage: 101 MB
% 20.50/3.74 % (2827964)Instructions burned: 1187 (million)
% 20.50/3.74 % (2827978)Instruction limit reached!
% 20.50/3.74 % (2827978)------------------------------
% 20.50/3.74 % (2827978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.50/3.75 % (2827978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.50/3.75 % (2827978)CaDiCaL version: 2.1.3
% 20.50/3.75 % (2827978)Termination reason: Instruction limit
% 20.50/3.75 % (2827978)Termination phase: Saturation
% 20.50/3.75 % (2827978)Time elapsed: 0.189 s
% 20.50/3.75 % (2827978)Peak memory usage: 92 MB
% 20.50/3.75 % (2827978)Instructions burned: 318 (million)
% 20.50/3.75 % (2827980)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=3192228990:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 20.50/3.75 % (2827981)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2191086009:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 20.50/3.75 % (2827972)Instruction limit reached!
% 20.50/3.75 % (2827972)------------------------------
% 20.50/3.75 % (2827972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.50/3.75 % (2827972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.50/3.75 % (2827972)CaDiCaL version: 2.1.3
% 20.50/3.75 % (2827972)Termination reason: Instruction limit
% 20.50/3.75 % (2827972)Termination phase: Saturation
% 20.50/3.75 % (2827972)Time elapsed: 0.724 s
% 20.50/3.75 % (2827972)Peak memory usage: 140 MB
% 20.50/3.75 % (2827972)Instructions burned: 2051 (million)
% 20.50/3.75 % (2827984)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=1011720889:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2989 on theBenchmark for (2989ds/14534Mi)
% 20.50/3.75 % (2827960)First to succeed.
% 20.50/3.75 % (2827960)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2827953"
% 20.50/3.75 % (2827981)Instruction limit reached!
% 20.50/3.75 % (2827981)------------------------------
% 20.50/3.75 % (2827981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.50/3.75 % (2827981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.50/3.75 % (2827981)CaDiCaL version: 2.1.3
% 20.50/3.75 % (2827981)Termination reason: Instruction limit
% 20.50/3.75 % (2827981)Termination phase: Saturation
% 20.50/3.75 % (2827981)Time elapsed: 1.683 s
% 20.50/3.75 % (2827981)Peak memory usage: 113 MB
% 20.50/3.75 % (2827981)Instructions burned: 2836 (million)
% 20.50/3.75 % (2827958)Also succeeded, but the first one will report.
% 20.50/3.75 % (2827960)Refutation found. Thanks to Tanya!
% 20.50/3.75 % SZS status Unsatisfiable for theBenchmark
% 20.50/3.75 % SZS output start Proof for theBenchmark
% See solution above
% 20.97/3.85 % (2827960)------------------------------
% 20.97/3.85 % (2827960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.97/3.85 % (2827960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.97/3.85 % (2827960)CaDiCaL version: 2.1.3
% 20.97/3.85 % (2827960)Termination reason: Refutation
% 20.97/3.85 % (2827960)Time elapsed: 2.456 s
% 20.97/3.85 % (2827960)Peak memory usage: 156 MB
% 20.97/3.85 % (2827960)Instructions burned: 3960 (million)
% 20.97/3.85 % (2827960)------------------------------
% 20.97/3.85 % (2827960)------------------------------
% 20.97/3.85 % (2827953)Success in time 2.896 s
% 20.97/3.85 % Vampire exiting
%------------------------------------------------------------------------------