%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL044-2 : 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 : 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 : Tue Sep 29 12:34:07 PM UTC 2026
% Result : Unsatisfiable 7.08s 1.65s
% Output : Refutation 8.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 22
% Syntax : Number of formulae : 177 ( 177 unt; 7 def)
% Number of atoms : 177 ( 176 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 : 18 ( 18 usr; 13 con; 0-2 aty)
% Number of variables : 230 ( 230 !; 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(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(f21,axiom,
! [X2,X0,X1] : join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) = meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law_2_16) ).
fof(f22,plain,
! [X2,X0,X1] : meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2) = join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
join(composition(complement(sk1),sk2),complement(sk3)) = complement(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
complement(sk3) = join(composition(complement(sk1),sk2),complement(sk3)),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
join(composition(sk3,converse(sk2)),sk1) != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
fof(f26,plain,
sk1 != join(composition(sk3,converse(sk2)),sk1),
inference(reorient_equations,[],[f25]) ).
fof(f27,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f30,plain,
! [X2,X0,X1] : complement(join(complement(composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),X1)),complement(X2))) = join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),X1)),complement(X2)))),
inference(definition_unfolding,[],[f22,f6,f6,f6,f6,f6]) ).
fof(f31,definition,
sF0 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f32,plain,
complement(sk3) = sF0,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF1 = complement(sk1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f34,plain,
complement(sk1) = sF1,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF2 = composition(sF1,sk2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f36,plain,
composition(sF1,sk2) = sF2,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF3 = join(sF2,sF0),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f38,plain,
join(sF2,sF0) = sF3,
inference(reorient_equations,[],[f37]) ).
fof(f39,plain,
sF0 = sF3,
inference(definition_folding,[],[f24,f38,f32,f36,f34,f32]) ).
fof(f40,definition,
sF4 = converse(sk2),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f41,plain,
converse(sk2) = sF4,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF5 = composition(sk3,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f43,plain,
composition(sk3,sF4) = sF5,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF6 = join(sF5,sk1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f45,plain,
join(sF5,sk1) = sF6,
inference(reorient_equations,[],[f44]) ).
fof(f46,plain,
sk1 != sF6,
inference(definition_folding,[],[f26,f45,f43,f41]) ).
fof(f47,plain,
zero = complement(top),
inference(backward_demodulation,[],[f27,f15]) ).
fof(f48,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f49,plain,
! [X2,X0,X1] : complement(join(complement(X2),complement(composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),X1)))) = join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(X2),complement(composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),X1))))),
inference(backward_demodulation,[],[f30,f1]) ).
fof(f51,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f52,plain,
sF0 = join(sF2,sF0),
inference(forward_demodulation,[],[f38,f39]) ).
fof(f76,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f48,f15]) ).
fof(f77,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f76,f47]) ).
fof(f88,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f48,f1]) ).
fof(f90,plain,
sk2 = converse(sF4),
inference(superposition,[],[f10,f41]) ).
fof(f91,plain,
! [X0,X1] : converse(join(X1,converse(X0))) = join(converse(X1),X0),
inference(superposition,[],[f11,f10]) ).
fof(f106,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f118,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f15]) ).
fof(f120,plain,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X1,join(X0,X2)),
inference(superposition,[],[f2,f1]) ).
fof(f122,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f2,f48]) ).
fof(f133,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f149,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X0),complement(X0))),join(complement(top),X1)),
inference(superposition,[],[f122,f15]) ).
fof(f165,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f149,f133]) ).
fof(f173,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f165,f47]) ).
fof(f187,plain,
! [X0] : zero = join(zero,composition(converse(X0),complement(composition(X0,top)))),
inference(superposition,[],[f51,f47]) ).
fof(f259,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(X1,top),
inference(superposition,[],[f133,f15]) ).
fof(f334,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f88,f15]) ).
fof(f350,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f334,f1]) ).
fof(f366,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f350,f1]) ).
fof(f375,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f366,f47]) ).
fof(f380,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f77,f375]) ).
fof(f391,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f375,f380]) ).
fof(f403,plain,
! [X0,X1] : complement(join(X1,X0)) = join(zero,complement(join(X0,join(join(X1,X0),X1)))),
inference(superposition,[],[f391,f133]) ).
fof(f409,plain,
! [X0,X1] : join(complement(X0),X1) = join(zero,join(complement(join(X0,X0)),X1)),
inference(superposition,[],[f2,f391]) ).
fof(f412,plain,
! [X0,X1] : complement(join(X1,X0)) = join(zero,complement(join(X0,join(X1,join(X0,X1))))),
inference(forward_demodulation,[],[f403,f2]) ).
fof(f414,plain,
sk1 = complement(sF1),
inference(superposition,[],[f380,f34]) ).
fof(f417,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f48,f380]) ).
fof(f421,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f88,f380]) ).
fof(f442,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f417,f1]) ).
fof(f541,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,[],[f417,f421]) ).
fof(f542,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,[],[f541,f380]) ).
fof(f564,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,[],[f542,f133]) ).
fof(f578,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,[],[f564,f1]) ).
fof(f589,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f578,f380]) ).
fof(f597,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f589,f380]) ).
fof(f662,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f106,f8]) ).
fof(f677,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f662,f10]) ).
fof(f689,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(superposition,[],[f51,f677]) ).
fof(f694,plain,
! [X0,X1] : composition(join(X1,converse(one)),X0) = join(composition(X1,X0),X0),
inference(superposition,[],[f9,f677]) ).
fof(f695,plain,
! [X0,X1] : composition(join(converse(one),X1),X0) = join(X0,composition(X1,X0)),
inference(superposition,[],[f9,f677]) ).
fof(f697,plain,
one = converse(one),
inference(superposition,[],[f8,f677]) ).
fof(f698,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f677,f697]) ).
fof(f701,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(forward_demodulation,[],[f695,f697]) ).
fof(f702,plain,
! [X0,X1] : composition(join(X1,converse(one)),X0) = join(X0,composition(X1,X0)),
inference(forward_demodulation,[],[f694,f1]) ).
fof(f706,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f689,f698]) ).
fof(f708,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(X1,one),X0),
inference(forward_demodulation,[],[f702,f697]) ).
fof(f711,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(complement(X0)))),
inference(backward_demodulation,[],[f173,f706]) ).
fof(f713,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,X0)),
inference(forward_demodulation,[],[f711,f380]) ).
fof(f717,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X0))),
inference(backward_demodulation,[],[f409,f713]) ).
fof(f718,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(backward_demodulation,[],[f391,f717]) ).
fof(f720,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f718,f1]) ).
fof(f724,plain,
! [X0,X1] : complement(join(X1,X0)) = complement(join(X0,join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f412,f720]) ).
fof(f746,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f720,f380]) ).
fof(f773,plain,
! [X0] : zero = composition(converse(X0),complement(composition(X0,top))),
inference(backward_demodulation,[],[f187,f746]) ).
fof(f788,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f1,f746]) ).
fof(f814,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f706,f380]) ).
fof(f856,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f814]) ).
fof(f857,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X0,X1)),
inference(superposition,[],[f133,f814]) ).
fof(f858,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f133,f814]) ).
fof(f864,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X1,join(X0,X1))),
inference(superposition,[],[f2,f814]) ).
fof(f873,plain,
! [X0,X1] : complement(join(X0,X1)) = complement(join(X1,X0)),
inference(backward_demodulation,[],[f724,f864]) ).
fof(f942,plain,
! [X0] : converse(join(X0,one)) = join(converse(X0),one),
inference(superposition,[],[f11,f697]) ).
fof(f957,plain,
! [X0] : join(one,converse(X0)) = converse(join(X0,one)),
inference(forward_demodulation,[],[f942,f1]) ).
fof(f991,plain,
! [X0] : top = join(X0,top),
inference(superposition,[],[f856,f15]) ).
fof(f1037,plain,
! [X0,X1] : top = join(X0,join(complement(X0),X1)),
inference(backward_demodulation,[],[f259,f991]) ).
fof(f1046,plain,
! [X1] : top = join(top,X1),
inference(backward_demodulation,[],[f118,f1037]) ).
fof(f1649,plain,
complement(sk1) = join(complement(sF6),complement(join(sk1,complement(sF5)))),
inference(superposition,[],[f442,f45]) ).
fof(f1668,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,[],[f421,f442]) ).
fof(f1676,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f856,f442]) ).
fof(f1677,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f1676,f1]) ).
fof(f1684,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,[],[f1668,f1]) ).
fof(f1695,plain,
sF1 = join(complement(sF6),complement(join(sk1,complement(sF5)))),
inference(forward_demodulation,[],[f1649,f34]) ).
fof(f1707,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f597,f1677]) ).
fof(f1714,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,[],[f1684,f873]) ).
fof(f1733,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,[],[f1714,f2]) ).
fof(f1748,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,X1)))),
inference(forward_demodulation,[],[f1733,f1707]) ).
fof(f1761,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1748,f858]) ).
fof(f1770,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1761,f380]) ).
fof(f1776,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1770,f380]) ).
fof(f1795,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f1776,f1]) ).
fof(f1803,plain,
! [X2,X0,X1] : join(join(X1,X0),complement(X2)) = join(join(X1,X0),complement(join(X0,join(X1,X2)))),
inference(superposition,[],[f1776,f120]) ).
fof(f1821,plain,
! [X2,X0,X1] : join(join(X0,complement(X1)),X2) = join(complement(join(X0,X1)),join(X0,X2)),
inference(superposition,[],[f120,f1776]) ).
fof(f1847,plain,
! [X2,X0,X1] : join(join(X0,complement(X1)),X2) = join(X0,join(X2,complement(join(X0,X1)))),
inference(forward_demodulation,[],[f1821,f133]) ).
fof(f1861,plain,
! [X2,X0,X1] : join(join(X1,X0),complement(X2)) = join(X1,join(X0,complement(join(X0,join(X1,X2))))),
inference(forward_demodulation,[],[f1803,f2]) ).
fof(f1876,plain,
! [X2,X0,X1] : join(X0,join(complement(X1),X2)) = join(X0,join(X2,complement(join(X0,X1)))),
inference(forward_demodulation,[],[f1847,f2]) ).
fof(f1888,plain,
! [X2,X0,X1] : join(join(X1,X0),complement(X2)) = join(X1,join(X0,complement(join(X1,X2)))),
inference(forward_demodulation,[],[f1861,f1776]) ).
fof(f1911,plain,
! [X2,X0,X1] : join(X1,join(complement(X2),X0)) = join(join(X1,X0),complement(X2)),
inference(forward_demodulation,[],[f1888,f1876]) ).
fof(f1922,plain,
! [X2,X0,X1] : join(X1,join(complement(X2),X0)) = join(X1,join(X0,complement(X2))),
inference(forward_demodulation,[],[f1911,f2]) ).
fof(f1955,plain,
join(sF0,complement(sF0)) = join(sF0,complement(sF2)),
inference(superposition,[],[f1795,f52]) ).
fof(f1997,plain,
top = join(sF0,complement(sF2)),
inference(forward_demodulation,[],[f1955,f15]) ).
fof(f2230,plain,
! [X0] : complement(join(complement(X0),complement(composition(complement(join(complement(sk3),complement(composition(X0,converse(sF4))))),sF4)))) = join(complement(join(complement(sF5),complement(X0))),complement(join(complement(X0),complement(composition(complement(join(complement(sk3),complement(composition(X0,converse(sF4))))),sF4))))),
inference(superposition,[],[f49,f43]) ).
fof(f2302,plain,
! [X0] : complement(join(complement(X0),complement(composition(complement(join(complement(sk3),complement(composition(X0,sk2)))),sF4)))) = join(complement(join(complement(sF5),complement(X0))),complement(join(complement(X0),complement(composition(complement(join(complement(sk3),complement(composition(X0,sk2)))),sF4))))),
inference(forward_demodulation,[],[f2230,f90]) ).
fof(f2322,plain,
! [X0] : complement(join(complement(X0),complement(composition(complement(join(sF0,complement(composition(X0,sk2)))),sF4)))) = join(complement(join(complement(sF5),complement(X0))),complement(join(complement(X0),complement(composition(complement(join(sF0,complement(composition(X0,sk2)))),sF4))))),
inference(forward_demodulation,[],[f2302,f32]) ).
fof(f2501,plain,
complement(join(complement(sF1),complement(composition(complement(join(sF0,complement(sF2))),sF4)))) = join(complement(join(complement(sF5),complement(sF1))),complement(join(complement(sF1),complement(composition(complement(join(sF0,complement(sF2))),sF4))))),
inference(superposition,[],[f2322,f36]) ).
fof(f2522,plain,
complement(join(complement(sF1),complement(composition(complement(top),sF4)))) = join(complement(join(complement(sF5),complement(sF1))),complement(join(complement(sF1),complement(composition(complement(top),sF4))))),
inference(forward_demodulation,[],[f2501,f1997]) ).
fof(f2536,plain,
complement(join(complement(sF1),complement(composition(zero,sF4)))) = join(complement(join(complement(sF5),complement(sF1))),complement(join(complement(sF1),complement(composition(zero,sF4))))),
inference(forward_demodulation,[],[f2522,f47]) ).
fof(f2547,plain,
complement(join(sk1,complement(composition(zero,sF4)))) = join(complement(join(complement(sF5),sk1)),complement(join(sk1,complement(composition(zero,sF4))))),
inference(forward_demodulation,[],[f2536,f414]) ).
fof(f2555,plain,
complement(join(sk1,complement(composition(zero,sF4)))) = join(complement(join(sk1,complement(sF5))),complement(join(sk1,complement(composition(zero,sF4))))),
inference(forward_demodulation,[],[f2547,f873]) ).
fof(f2601,plain,
! [X0] : converse(converse(X0)) = join(converse(zero),X0),
inference(superposition,[],[f91,f746]) ).
fof(f2622,plain,
! [X0] : join(converse(zero),X0) = X0,
inference(forward_demodulation,[],[f2601,f10]) ).
fof(f2672,plain,
zero = converse(zero),
inference(superposition,[],[f788,f2622]) ).
fof(f2856,plain,
! [X0,X1] : join(complement(join(X1,X0)),X0) = join(X0,join(X0,complement(X1))),
inference(superposition,[],[f857,f1795]) ).
fof(f2890,plain,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X1,join(join(X1,X0),X2)),
inference(superposition,[],[f2,f857]) ).
fof(f2923,plain,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X1,join(X1,join(X0,X2))),
inference(forward_demodulation,[],[f2890,f2]) ).
fof(f2943,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(join(X1,X0)),X0),
inference(forward_demodulation,[],[f2856,f857]) ).
fof(f2959,plain,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(join(X0,X2),X1),
inference(forward_demodulation,[],[f2923,f857]) ).
fof(f2975,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X1,X0))),
inference(forward_demodulation,[],[f2943,f1]) ).
fof(f2984,plain,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X0,join(X2,X1)),
inference(forward_demodulation,[],[f2959,f2]) ).
fof(f4707,plain,
join(complement(join(sk1,complement(composition(zero,sF4)))),complement(complement(join(sk1,complement(composition(zero,sF4)))))) = join(complement(complement(join(sk1,complement(sF5)))),complement(join(sk1,complement(composition(zero,sF4))))),
inference(superposition,[],[f2975,f2555]) ).
fof(f4709,plain,
join(complement(join(sk1,complement(composition(zero,sF4)))),complement(complement(join(sk1,complement(composition(zero,sF4)))))) = join(join(sk1,complement(sF5)),complement(join(sk1,complement(composition(zero,sF4))))),
inference(forward_demodulation,[],[f4707,f380]) ).
fof(f4718,plain,
join(complement(join(sk1,complement(composition(zero,sF4)))),complement(complement(join(sk1,complement(composition(zero,sF4)))))) = join(sk1,join(complement(sF5),complement(join(sk1,complement(composition(zero,sF4)))))),
inference(forward_demodulation,[],[f4709,f2]) ).
fof(f4724,plain,
join(complement(join(sk1,complement(composition(zero,sF4)))),complement(complement(join(sk1,complement(composition(zero,sF4)))))) = join(sk1,join(complement(complement(composition(zero,sF4))),complement(sF5))),
inference(forward_demodulation,[],[f4718,f1876]) ).
fof(f4730,plain,
join(complement(join(sk1,complement(composition(zero,sF4)))),complement(complement(join(sk1,complement(composition(zero,sF4)))))) = join(sk1,join(complement(sF5),complement(complement(composition(zero,sF4))))),
inference(forward_demodulation,[],[f4724,f1922]) ).
fof(f4736,plain,
join(complement(join(sk1,complement(composition(zero,sF4)))),complement(complement(join(sk1,complement(composition(zero,sF4)))))) = join(sk1,join(complement(sF5),composition(zero,sF4))),
inference(forward_demodulation,[],[f4730,f380]) ).
fof(f4742,plain,
top = join(sk1,join(complement(sF5),composition(zero,sF4))),
inference(forward_demodulation,[],[f4736,f15]) ).
fof(f7622,plain,
! [X0] : zero = composition(converse(join(X0,one)),complement(join(top,composition(X0,top)))),
inference(superposition,[],[f773,f708]) ).
fof(f7670,plain,
! [X0] : zero = composition(converse(join(X0,one)),complement(top)),
inference(forward_demodulation,[],[f7622,f1046]) ).
fof(f7695,plain,
! [X0] : zero = composition(converse(join(X0,one)),zero),
inference(forward_demodulation,[],[f7670,f47]) ).
fof(f7717,plain,
! [X0] : zero = composition(join(one,converse(X0)),zero),
inference(forward_demodulation,[],[f7695,f957]) ).
fof(f7731,plain,
! [X0] : zero = join(zero,composition(converse(X0),zero)),
inference(forward_demodulation,[],[f7717,f701]) ).
fof(f7740,plain,
! [X0] : zero = composition(converse(X0),zero),
inference(forward_demodulation,[],[f7731,f746]) ).
fof(f8201,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X0,join(X2,X1)),
inference(superposition,[],[f2,f2984]) ).
fof(f9141,plain,
! [X0] : converse(zero) = composition(converse(zero),X0),
inference(superposition,[],[f106,f7740]) ).
fof(f9179,plain,
! [X0] : zero = composition(zero,X0),
inference(forward_demodulation,[],[f9141,f2672]) ).
fof(f9241,plain,
top = join(sk1,join(complement(sF5),zero)),
inference(backward_demodulation,[],[f4742,f9179]) ).
fof(f9277,plain,
top = join(sk1,join(zero,complement(sF5))),
inference(forward_demodulation,[],[f9241,f8201]) ).
fof(f9309,plain,
top = join(sk1,complement(sF5)),
inference(forward_demodulation,[],[f9277,f746]) ).
fof(f9328,plain,
sF1 = join(complement(sF6),complement(top)),
inference(backward_demodulation,[],[f1695,f9309]) ).
fof(f9346,plain,
sF1 = join(complement(sF6),zero),
inference(forward_demodulation,[],[f9328,f47]) ).
fof(f9361,plain,
sF1 = join(zero,complement(sF6)),
inference(forward_demodulation,[],[f9346,f1]) ).
fof(f9375,plain,
sF1 = complement(sF6),
inference(forward_demodulation,[],[f9361,f746]) ).
fof(f9438,plain,
sF6 = complement(sF1),
inference(superposition,[],[f380,f9375]) ).
fof(f9468,plain,
sk1 = sF6,
inference(forward_demodulation,[],[f9438,f414]) ).
fof(f9476,plain,
$false,
inference(forward_subsumption_resolution,[],[f9468,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : REL044-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 22:56:34 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 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
% 7.08/1.65 % (2850455)Detected a unit-equality problem, will run specialized UEQ schedule.
% 7.08/1.65 % (2850462)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3471612113:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 7.08/1.65 % (2850465)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2959840795:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 7.08/1.65 % (2850461)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=3562285858:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 7.08/1.65 % (2850463)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3299432772:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 7.08/1.65 % (2850464)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2638916250:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 7.08/1.65 % (2850460)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=2016184467:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 7.08/1.65 % (2850466)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2875749760:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 7.08/1.65 % (2850463)Instruction limit reached!
% 7.08/1.65 % (2850463)------------------------------
% 7.08/1.65 % (2850463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.08/1.65 % (2850463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.08/1.65 % (2850463)CaDiCaL version: 2.1.3
% 7.08/1.65 % (2850463)Termination reason: Instruction limit
% 7.08/1.65 % (2850463)Termination phase: Saturation
% 7.08/1.65 % (2850463)Time elapsed: 0.045 s
% 7.08/1.65 % (2850463)Peak memory usage: 89 MB
% 7.08/1.65 % (2850463)Instructions burned: 139 (million)
% 7.08/1.65 % (2850464)Instruction limit reached!
% 7.08/1.65 % (2850464)------------------------------
% 7.08/1.65 % (2850464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.08/1.65 % (2850464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.08/1.65 % (2850464)CaDiCaL version: 2.1.3
% 7.08/1.65 % (2850464)Termination reason: Instruction limit
% 7.08/1.65 % (2850464)Termination phase: Saturation
% 7.08/1.65 % (2850464)Time elapsed: 0.056 s
% 7.08/1.65 % (2850464)Peak memory usage: 89 MB
% 7.08/1.65 % (2850464)Instructions burned: 181 (million)
% 7.08/1.65 % (2850465)Instruction limit reached!
% 7.08/1.65 % (2850465)------------------------------
% 7.08/1.65 % (2850465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.08/1.65 % (2850465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.08/1.65 % (2850465)CaDiCaL version: 2.1.3
% 7.08/1.65 % (2850465)Termination reason: Instruction limit
% 7.08/1.65 % (2850465)Termination phase: Saturation
% 7.08/1.65 % (2850465)Time elapsed: 0.092 s
% 7.08/1.65 % (2850465)Peak memory usage: 90 MB
% 7.08/1.65 % (2850465)Instructions burned: 258 (million)
% 7.08/1.65 % (2850474)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=22756413:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 7.08/1.65 % (2850475)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=742480693:i=4948:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/4948Mi)
% 7.08/1.65 % (2850476)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3313338235:i=215:ep=RSTC_2998 on theBenchmark for (2998ds/215Mi)
% 7.08/1.65 % (2850476)Instruction limit reached!
% 7.08/1.65 % (2850476)------------------------------
% 7.08/1.65 % (2850476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.08/1.65 % (2850476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.08/1.65 % (2850476)CaDiCaL version: 2.1.3
% 7.08/1.65 % (2850476)Termination reason: Instruction limit
% 7.08/1.65 % (2850476)Termination phase: Saturation
% 7.08/1.65 % (2850476)Time elapsed: 0.066 s
% 7.08/1.65 % (2850476)Peak memory usage: 92 MB
% 7.08/1.65 % (2850476)Instructions burned: 216 (million)
% 7.08/1.65 % (2850480)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=823120553:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2996 on theBenchmark for (2996ds/317Mi)
% 7.08/1.65 % (2850466)Instruction limit reached!
% 7.08/1.65 % (2850466)------------------------------
% 7.08/1.65 % (2850466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.08/1.65 % (2850466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.08/1.65 % (2850466)CaDiCaL version: 2.1.3
% 7.08/1.65 % (2850466)Termination reason: Instruction limit
% 7.08/1.65 % (2850466)Termination phase: Saturation
% 7.08/1.65 % (2850466)Time elapsed: 0.358 s
% 7.08/1.65 % (2850466)Peak memory usage: 101 MB
% 7.08/1.65 % (2850466)Instructions burned: 1189 (million)
% 7.08/1.65 % (2850480)Instruction limit reached!
% 7.08/1.65 % (2850480)------------------------------
% 7.08/1.65 % (2850480)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.08/1.65 % (2850480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.08/1.65 % (2850480)CaDiCaL version: 2.1.3
% 7.08/1.65 % (2850480)Termination reason: Instruction limit
% 7.08/1.65 % (2850480)Termination phase: Saturation
% 7.08/1.65 % (2850480)Time elapsed: 0.111 s
% 7.08/1.65 % (2850480)Peak memory usage: 93 MB
% 7.08/1.65 % (2850480)Instructions burned: 318 (million)
% 7.08/1.65 % (2850482)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=4188374173:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2995 on theBenchmark for (2995ds/12125Mi)
% 7.08/1.65 % (2850483)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2748728696:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2994 on theBenchmark for (2994ds/2836Mi)
% 7.08/1.65 % (2850462)First to succeed.
% 7.08/1.65 % (2850462)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2850455"
% 7.08/1.65 % (2850474)Instruction limit reached!
% 7.08/1.65 % (2850474)------------------------------
% 7.08/1.65 % (2850474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.08/1.65 % (2850474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.08/1.65 % (2850474)CaDiCaL version: 2.1.3
% 7.08/1.65 % (2850474)Termination reason: Instruction limit
% 7.08/1.65 % (2850474)Termination phase: Saturation
% 7.08/1.65 % (2850474)Time elapsed: 0.728 s
% 7.08/1.65 % (2850474)Peak memory usage: 141 MB
% 7.08/1.65 % (2850474)Instructions burned: 2051 (million)
% 7.08/1.65 % (2850486)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=872175364:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2990 on theBenchmark for (2990ds/14534Mi)
% 7.08/1.65 % (2850462)Refutation found. Thanks to Tanya!
% 7.08/1.65 % SZS status Unsatisfiable for theBenchmark
% 7.08/1.65 % SZS output start Proof for theBenchmark
% See solution above
% 8.12/1.74 % (2850462)------------------------------
% 8.12/1.74 % (2850462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.12/1.74 % (2850462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.12/1.74 % (2850462)CaDiCaL version: 2.1.3
% 8.12/1.74 % (2850462)Termination reason: Refutation
% 8.12/1.74 % (2850462)Time elapsed: 0.864 s
% 8.12/1.74 % (2850462)Peak memory usage: 142 MB
% 8.12/1.74 % (2850462)Instructions burned: 2521 (million)
% 8.12/1.74 % (2850462)------------------------------
% 8.12/1.74 % (2850462)------------------------------
% 8.12/1.74 % (2850455)Success in time 1.127 s
% 8.12/1.74 % Vampire exiting
%------------------------------------------------------------------------------