%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL029-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:33:54 PM UTC 2026
% Result : Unsatisfiable 6.42s 2.81s
% Output : Refutation 13.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 15
% Syntax : Number of formulae : 152 ( 152 unt; 0 def)
% Number of atoms : 152 ( 151 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 232 ( 232 !; 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,axiom,
! [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,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
fof(f23,negated_conjecture,
join(sk1,one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
one = join(sk1,one),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
join(sk2,one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
fof(f26,plain,
one = join(sk2,one),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
tuple(join(meet(composition(sk1,sk3),composition(sk2,sk3)),composition(meet(sk1,sk2),sk3)),join(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3)))) != tuple(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_19) ).
fof(f32,plain,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(join(complement(sk1),complement(sk2))),sk3)),join(composition(complement(join(complement(sk1),complement(sk2))),sk3),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))))) != tuple(composition(complement(join(complement(sk1),complement(sk2))),sk3),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(definition_unfolding,[],[f27,f6,f6,f6,f6,f6,f6]) ).
fof(f37,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f4,f1]) ).
fof(f38,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(join(complement(join(complement(X0),complement(X1))),complement(complement(join(complement(X0),X1))))),complement(X0)),
inference(superposition,[],[f4,f4]) ).
fof(f44,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(superposition,[],[f1,f4]) ).
fof(f47,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(X0),complement(join(complement(join(complement(X0),complement(X1))),complement(complement(join(complement(X0),X1)))))),
inference(forward_demodulation,[],[f38,f1]) ).
fof(f48,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(forward_demodulation,[],[f37,f1]) ).
fof(f51,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(X0),complement(join(complement(complement(join(complement(X0),X1))),complement(join(complement(X0),complement(X1)))))),
inference(forward_demodulation,[],[f47,f1]) ).
fof(f120,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f12,f10]) ).
fof(f122,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(f126,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f120,f8]) ).
fof(f134,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f126,f10]) ).
fof(f139,plain,
! [X0,X1] : complement(X1) = join(composition(X0,complement(composition(converse(X0),X1))),complement(X1)),
inference(superposition,[],[f14,f10]) ).
fof(f150,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(forward_demodulation,[],[f139,f1]) ).
fof(f187,plain,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X1,join(X0,X2)),
inference(superposition,[],[f2,f1]) ).
fof(f188,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f15]) ).
fof(f190,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),complement(X1))),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f2,f4]) ).
fof(f203,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f206,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(X2,complement(join(complement(X0),complement(X1))))),
inference(forward_demodulation,[],[f190,f203]) ).
fof(f599,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f122,f12]) ).
fof(f609,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f599,f11]) ).
fof(f616,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f609,f11]) ).
fof(f620,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f616,f12]) ).
fof(f774,plain,
! [X2,X3,X0,X1] : composition(join(X3,composition(X0,X1)),X2) = join(composition(X3,X2),composition(X0,composition(X1,X2))),
inference(superposition,[],[f9,f7]) ).
fof(f910,plain,
! [X0,X1] : composition(join(converse(one),X1),X0) = join(X0,composition(X1,X0)),
inference(superposition,[],[f9,f134]) ).
fof(f913,plain,
one = converse(one),
inference(superposition,[],[f8,f134]) ).
fof(f919,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(forward_demodulation,[],[f910,f913]) ).
fof(f930,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f134,f913]) ).
fof(f955,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(converse(one),X0))),
inference(superposition,[],[f150,f930]) ).
fof(f958,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f955,f134]) ).
fof(f983,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(X0,complement(join(complement(X0),complement(X1)))),
inference(superposition,[],[f206,f958]) ).
fof(f990,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f983,f44]) ).
fof(f1048,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),X0) = join(X0,X0),
inference(superposition,[],[f206,f990]) ).
fof(f1086,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,X0),
inference(forward_demodulation,[],[f1048,f1]) ).
fof(f1228,plain,
! [X0,X1] : join(X1,X1) = join(X1,complement(join(X0,complement(X1)))),
inference(superposition,[],[f1086,f1]) ).
fof(f1231,plain,
! [X0,X1] : join(X1,X1) = join(X1,complement(join(top,X0))),
inference(superposition,[],[f1086,f188]) ).
fof(f1244,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f990,f1086]) ).
fof(f1252,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X0))),complement(join(complement(X0),join(complement(complement(X0)),X1)))) = X0,
inference(superposition,[],[f4,f1086]) ).
fof(f1281,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X0))),complement(join(top,X1))) = X0,
inference(forward_demodulation,[],[f1252,f188]) ).
fof(f1296,plain,
! [X0,X1] : join(X1,complement(join(top,X0))) = X1,
inference(forward_demodulation,[],[f1231,f1244]) ).
fof(f1299,plain,
! [X0,X1] : join(X1,complement(join(X0,complement(X1)))) = X1,
inference(forward_demodulation,[],[f1228,f1244]) ).
fof(f1323,plain,
! [X0,X1] : join(complement(complement(X0)),complement(join(top,X1))) = X0,
inference(forward_demodulation,[],[f1281,f958]) ).
fof(f1343,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f1323,f1296]) ).
fof(f1374,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f48,f1343]) ).
fof(f1375,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(complement(complement(join(X0,X1))),complement(join(X0,complement(X1)))))),
inference(superposition,[],[f51,f1343]) ).
fof(f1394,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(join(X0,X1),complement(join(X0,complement(X1)))))),
inference(forward_demodulation,[],[f1375,f1343]) ).
fof(f1405,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,join(X1,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f1394,f2]) ).
fof(f1407,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1405,f1299]) ).
fof(f1410,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(superposition,[],[f1299,f1343]) ).
fof(f1433,plain,
! [X0,X1] : join(X1,X0) = join(complement(join(complement(X1),X0)),X0),
inference(superposition,[],[f206,f1299]) ).
fof(f1445,plain,
! [X0,X1] : join(X1,complement(complement(X0))) = join(complement(join(complement(join(X1,complement(complement(X0)))),X0)),complement(complement(X0))),
inference(superposition,[],[f48,f1299]) ).
fof(f1467,plain,
! [X0,X1] : join(X1,complement(complement(X0))) = join(complement(complement(X0)),complement(join(complement(join(X1,complement(complement(X0)))),X0))),
inference(forward_demodulation,[],[f1445,f1]) ).
fof(f1474,plain,
! [X0,X1] : join(X1,X0) = join(X0,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f1433,f1]) ).
fof(f1492,plain,
! [X0,X1] : join(X1,complement(complement(X0))) = join(complement(complement(X0)),complement(join(X0,complement(join(X1,complement(complement(X0))))))),
inference(forward_demodulation,[],[f1467,f1]) ).
fof(f1500,plain,
! [X0,X1] : join(X1,X0) = join(X0,complement(join(X0,complement(join(X1,X0))))),
inference(forward_demodulation,[],[f1492,f1343]) ).
fof(f1504,plain,
! [X0,X1] : join(X1,X0) = join(X0,complement(complement(join(X1,X0)))),
inference(forward_demodulation,[],[f1500,f1407]) ).
fof(f1506,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(forward_demodulation,[],[f1504,f1343]) ).
fof(f1544,plain,
! [X0,X1] : join(X0,X1) = join(X1,join(X1,X0)),
inference(superposition,[],[f203,f1506]) ).
fof(f1617,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f1407,f1]) ).
fof(f1952,plain,
join(one,complement(one)) = join(one,complement(sk1)),
inference(superposition,[],[f1617,f24]) ).
fof(f1968,plain,
! [X2,X0,X1] : join(X2,join(X0,complement(X1))) = join(X0,join(complement(join(X1,X0)),X2)),
inference(superposition,[],[f203,f1617]) ).
fof(f2022,plain,
top = join(one,complement(sk1)),
inference(forward_demodulation,[],[f1952,f15]) ).
fof(f2167,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X1))),
inference(superposition,[],[f1474,f1343]) ).
fof(f2206,plain,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X1,join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f2,f1474]) ).
fof(f2255,plain,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X2,join(X1,complement(complement(X0)))),
inference(forward_demodulation,[],[f2206,f1968]) ).
fof(f2313,plain,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X2,join(X1,X0)),
inference(forward_demodulation,[],[f2255,f1343]) ).
fof(f2412,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X0,X1))),
inference(superposition,[],[f2167,f1]) ).
fof(f4489,plain,
! [X2,X0,X1] : join(complement(join(X1,X0)),X2) = join(X2,complement(join(join(X0,X1),X2))),
inference(superposition,[],[f2412,f2313]) ).
fof(f4517,plain,
! [X2,X0,X1] : join(complement(join(X1,X0)),X2) = join(X2,complement(join(X0,X1))),
inference(forward_demodulation,[],[f4489,f1617]) ).
fof(f9277,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f620]) ).
fof(f9296,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f9277,f10]) ).
fof(f9332,plain,
! [X0,X1] : join(composition(X0,X1),X0) = composition(X0,join(X1,one)),
inference(superposition,[],[f9296,f8]) ).
fof(f9361,plain,
! [X2,X3,X0,X1] : join(composition(X0,join(X1,X2)),X3) = join(X3,join(composition(X0,X2),composition(X0,X1))),
inference(superposition,[],[f2313,f9296]) ).
fof(f9373,plain,
! [X2,X3,X0,X1] : join(composition(X0,join(X1,X2)),X3) = join(X3,composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f9361,f9296]) ).
fof(f9383,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(X1,one)),
inference(forward_demodulation,[],[f9332,f1]) ).
fof(f11253,plain,
! [X0] : composition(X0,one) = join(X0,composition(X0,sk1)),
inference(superposition,[],[f9383,f24]) ).
fof(f11254,plain,
! [X0] : composition(X0,one) = join(X0,composition(X0,sk2)),
inference(superposition,[],[f9383,f26]) ).
fof(f11355,plain,
! [X0] : join(X0,composition(X0,sk2)) = X0,
inference(forward_demodulation,[],[f11254,f8]) ).
fof(f11356,plain,
! [X0] : join(X0,composition(X0,sk1)) = X0,
inference(forward_demodulation,[],[f11253,f8]) ).
fof(f11459,plain,
! [X0] : composition(one,X0) = join(X0,composition(composition(one,sk2),X0)),
inference(superposition,[],[f919,f11355]) ).
fof(f11467,plain,
! [X0] : composition(one,X0) = join(X0,composition(one,composition(sk2,X0))),
inference(forward_demodulation,[],[f11459,f7]) ).
fof(f11507,plain,
! [X0] : composition(one,X0) = join(X0,composition(sk2,X0)),
inference(forward_demodulation,[],[f11467,f930]) ).
fof(f11528,plain,
! [X0] : join(X0,composition(sk2,X0)) = X0,
inference(forward_demodulation,[],[f11507,f930]) ).
fof(f11587,plain,
! [X0] : composition(one,X0) = join(X0,composition(composition(one,sk1),X0)),
inference(superposition,[],[f919,f11356]) ).
fof(f11595,plain,
! [X0] : composition(one,X0) = join(X0,composition(one,composition(sk1,X0))),
inference(forward_demodulation,[],[f11587,f7]) ).
fof(f11635,plain,
! [X0] : composition(one,X0) = join(X0,composition(sk1,X0)),
inference(forward_demodulation,[],[f11595,f930]) ).
fof(f11656,plain,
! [X0] : join(X0,composition(sk1,X0)) = X0,
inference(forward_demodulation,[],[f11635,f930]) ).
fof(f11932,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(composition(sk2,X0),X1)),
inference(superposition,[],[f2,f11528]) ).
fof(f11942,plain,
! [X0] : complement(composition(sk2,X0)) = join(complement(composition(sk2,X0)),complement(X0)),
inference(superposition,[],[f1410,f11528]) ).
fof(f11963,plain,
! [X0] : complement(composition(sk2,complement(X0))) = join(complement(join(composition(sk2,complement(X0)),X0)),complement(complement(X0))),
inference(superposition,[],[f1374,f11528]) ).
fof(f11978,plain,
! [X0] : complement(composition(sk2,complement(X0))) = join(complement(complement(X0)),complement(join(X0,composition(sk2,complement(X0))))),
inference(forward_demodulation,[],[f11963,f4517]) ).
fof(f11997,plain,
! [X0] : complement(composition(sk2,X0)) = join(complement(X0),complement(composition(sk2,X0))),
inference(forward_demodulation,[],[f11942,f1]) ).
fof(f12014,plain,
! [X0] : complement(composition(sk2,complement(X0))) = join(X0,complement(join(X0,composition(sk2,complement(X0))))),
inference(forward_demodulation,[],[f11978,f1343]) ).
fof(f12035,plain,
! [X0] : complement(composition(sk2,complement(X0))) = join(X0,complement(composition(sk2,complement(X0)))),
inference(forward_demodulation,[],[f12014,f1407]) ).
fof(f12282,plain,
! [X0] : complement(composition(sk1,complement(X0))) = join(complement(join(composition(sk1,complement(X0)),X0)),complement(complement(X0))),
inference(superposition,[],[f1374,f11656]) ).
fof(f12297,plain,
! [X0] : complement(composition(sk1,complement(X0))) = join(complement(complement(X0)),complement(join(X0,composition(sk1,complement(X0))))),
inference(forward_demodulation,[],[f12282,f4517]) ).
fof(f12333,plain,
! [X0] : complement(composition(sk1,complement(X0))) = join(X0,complement(join(X0,composition(sk1,complement(X0))))),
inference(forward_demodulation,[],[f12297,f1343]) ).
fof(f12354,plain,
! [X0] : complement(composition(sk1,complement(X0))) = join(X0,complement(composition(sk1,complement(X0)))),
inference(forward_demodulation,[],[f12333,f1407]) ).
fof(f13298,plain,
! [X0,X1] : join(X0,composition(sk2,join(X0,X1))) = join(X0,composition(sk2,X1)),
inference(superposition,[],[f11932,f9296]) ).
fof(f13581,plain,
! [X0] : join(X0,composition(sk2,complement(X0))) = join(X0,composition(sk2,top)),
inference(superposition,[],[f13298,f15]) ).
fof(f13665,plain,
! [X0,X1] : join(composition(sk2,join(X0,X1)),X0) = join(X0,join(X0,composition(sk2,X1))),
inference(superposition,[],[f1544,f13298]) ).
fof(f13719,plain,
! [X0,X1] : join(composition(sk2,X1),X0) = join(composition(sk2,join(X0,X1)),X0),
inference(forward_demodulation,[],[f13665,f1544]) ).
fof(f13800,plain,
! [X0,X1] : join(composition(sk2,X1),X0) = join(X0,composition(sk2,join(X1,X0))),
inference(forward_demodulation,[],[f13719,f9373]) ).
fof(f13845,plain,
! [X0] : join(complement(X0),composition(sk2,X0)) = join(complement(X0),composition(sk2,top)),
inference(superposition,[],[f13581,f1343]) ).
fof(f13863,plain,
! [X0] : join(X0,complement(composition(sk2,complement(X0)))) = join(X0,complement(join(X0,composition(sk2,top)))),
inference(superposition,[],[f1407,f13581]) ).
fof(f13928,plain,
! [X0] : join(X0,complement(composition(sk2,complement(X0)))) = join(X0,complement(composition(sk2,top))),
inference(forward_demodulation,[],[f13863,f1407]) ).
fof(f13965,plain,
! [X0] : complement(composition(sk2,complement(X0))) = join(X0,complement(composition(sk2,top))),
inference(forward_demodulation,[],[f13928,f12035]) ).
fof(f14064,plain,
! [X0,X1] : complement(composition(sk2,complement(join(X0,X1)))) = join(X1,join(X0,complement(composition(sk2,top)))),
inference(superposition,[],[f187,f13965]) ).
fof(f14128,plain,
! [X0,X1] : complement(composition(sk2,complement(join(X0,X1)))) = join(X1,complement(composition(sk2,complement(X0)))),
inference(forward_demodulation,[],[f14064,f13965]) ).
fof(f14616,plain,
! [X0,X1] : join(X1,complement(composition(sk2,X0))) = complement(composition(sk2,complement(join(complement(X0),X1)))),
inference(superposition,[],[f14128,f1343]) ).
fof(f15043,plain,
! [X0] : join(complement(composition(sk1,complement(complement(X0)))),complement(composition(sk2,X0))) = complement(composition(sk2,complement(complement(composition(sk1,complement(complement(X0))))))),
inference(superposition,[],[f14616,f12354]) ).
fof(f15185,plain,
! [X0] : join(complement(composition(sk1,complement(complement(X0)))),complement(composition(sk2,X0))) = complement(composition(sk2,composition(sk1,complement(complement(X0))))),
inference(forward_demodulation,[],[f15043,f1343]) ).
fof(f15285,plain,
! [X0] : join(complement(composition(sk1,X0)),complement(composition(sk2,X0))) = complement(composition(sk2,composition(sk1,X0))),
inference(forward_demodulation,[],[f15185,f1343]) ).
fof(f20800,plain,
join(composition(sk2,one),complement(sk1)) = join(complement(sk1),composition(sk2,top)),
inference(superposition,[],[f13800,f2022]) ).
fof(f20939,plain,
join(composition(sk2,one),complement(sk1)) = join(complement(sk1),composition(sk2,sk1)),
inference(forward_demodulation,[],[f20800,f13845]) ).
fof(f21032,plain,
join(complement(sk1),composition(sk2,sk1)) = join(complement(sk1),composition(sk2,one)),
inference(forward_demodulation,[],[f20939,f1]) ).
fof(f21090,plain,
join(complement(sk1),composition(sk2,sk1)) = join(complement(sk1),sk2),
inference(forward_demodulation,[],[f21032,f8]) ).
fof(f21127,plain,
join(complement(sk1),composition(sk2,sk1)) = join(sk2,complement(sk1)),
inference(forward_demodulation,[],[f21090,f1]) ).
fof(f21223,plain,
join(complement(sk1),complement(composition(sk2,sk1))) = join(complement(sk1),complement(join(sk2,complement(sk1)))),
inference(superposition,[],[f1407,f21127]) ).
fof(f21257,plain,
join(complement(sk1),complement(sk2)) = join(complement(sk1),complement(composition(sk2,sk1))),
inference(forward_demodulation,[],[f21223,f1617]) ).
fof(f21291,plain,
join(complement(sk1),complement(sk2)) = complement(composition(sk2,sk1)),
inference(forward_demodulation,[],[f21257,f11997]) ).
fof(f21350,plain,
tuple(composition(complement(complement(composition(sk2,sk1))),sk3),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))) != tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(complement(composition(sk2,sk1))),sk3)),join(composition(complement(complement(composition(sk2,sk1))),sk3),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))))),
inference(superposition,[],[f32,f21291]) ).
fof(f21457,plain,
tuple(composition(complement(complement(composition(sk2,sk1))),sk3),complement(complement(composition(sk2,composition(sk1,sk3))))) != tuple(join(complement(complement(composition(sk2,composition(sk1,sk3)))),composition(complement(complement(composition(sk2,sk1))),sk3)),join(composition(complement(complement(composition(sk2,sk1))),sk3),complement(complement(composition(sk2,composition(sk1,sk3)))))),
inference(forward_demodulation,[],[f21350,f15285]) ).
fof(f21499,plain,
tuple(composition(complement(complement(composition(sk2,sk1))),sk3),complement(complement(composition(sk2,composition(sk1,sk3))))) != tuple(join(complement(complement(composition(sk2,composition(sk1,sk3)))),composition(complement(complement(composition(sk2,sk1))),sk3)),join(complement(complement(composition(sk2,composition(sk1,sk3)))),composition(complement(complement(composition(sk2,sk1))),sk3))),
inference(forward_demodulation,[],[f21457,f1]) ).
fof(f21527,plain,
tuple(composition(composition(sk2,sk1),sk3),complement(complement(composition(sk2,composition(sk1,sk3))))) != tuple(join(complement(complement(composition(sk2,composition(sk1,sk3)))),composition(composition(sk2,sk1),sk3)),join(complement(complement(composition(sk2,composition(sk1,sk3)))),composition(composition(sk2,sk1),sk3))),
inference(forward_demodulation,[],[f21499,f1343]) ).
fof(f21542,plain,
tuple(composition(composition(sk2,sk1),sk3),complement(complement(composition(sk2,composition(sk1,sk3))))) != tuple(join(composition(composition(sk2,sk1),sk3),complement(complement(composition(sk2,composition(sk1,sk3))))),join(composition(composition(sk2,sk1),sk3),complement(complement(composition(sk2,composition(sk1,sk3)))))),
inference(forward_demodulation,[],[f21527,f1]) ).
fof(f21549,plain,
tuple(composition(composition(sk2,sk1),sk3),composition(sk2,composition(sk1,sk3))) != tuple(join(composition(composition(sk2,sk1),sk3),composition(sk2,composition(sk1,sk3))),join(composition(composition(sk2,sk1),sk3),composition(sk2,composition(sk1,sk3)))),
inference(forward_demodulation,[],[f21542,f1343]) ).
fof(f21552,plain,
tuple(composition(composition(sk2,sk1),sk3),composition(sk2,composition(sk1,sk3))) != tuple(composition(join(composition(sk2,sk1),composition(sk2,sk1)),sk3),composition(join(composition(sk2,sk1),composition(sk2,sk1)),sk3)),
inference(forward_demodulation,[],[f21549,f774]) ).
fof(f21555,plain,
tuple(composition(composition(sk2,sk1),sk3),composition(sk2,composition(sk1,sk3))) != tuple(composition(composition(join(sk2,sk2),sk1),sk3),composition(composition(join(sk2,sk2),sk1),sk3)),
inference(forward_demodulation,[],[f21552,f9]) ).
fof(f21558,plain,
tuple(composition(composition(sk2,sk1),sk3),composition(sk2,composition(sk1,sk3))) != tuple(composition(join(sk2,sk2),composition(sk1,sk3)),composition(join(sk2,sk2),composition(sk1,sk3))),
inference(forward_demodulation,[],[f21555,f7]) ).
fof(f21561,plain,
tuple(composition(composition(sk2,sk1),sk3),composition(sk2,composition(sk1,sk3))) != tuple(composition(sk2,composition(sk1,sk3)),composition(sk2,composition(sk1,sk3))),
inference(forward_demodulation,[],[f21558,f1244]) ).
fof(f21563,plain,
tuple(composition(sk2,composition(sk1,sk3)),composition(sk2,composition(sk1,sk3))) != tuple(composition(sk2,composition(sk1,sk3)),composition(sk2,composition(sk1,sk3))),
inference(forward_demodulation,[],[f21561,f7]) ).
fof(f21564,plain,
$false,
inference(trivial_inequality_removal,[],[f21563]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL029-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n010.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 22:53:47 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.49 Running first-order theorem proving
% 0.20/0.49 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
% 6.42/2.81 % (1391007)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.42/2.81 % (1391013)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=519621821:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.42/2.81 % (1391017)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1847394585:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.42/2.81 % (1391012)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=1190747472:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.42/2.81 % (1391015)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1836303867:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.42/2.81 % (1391014)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2214472166:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.42/2.81 % (1391016)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3043447301:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.42/2.81 % (1391018)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1226157257:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.42/2.81 % (1391015)Instruction limit reached!
% 6.42/2.81 % (1391015)------------------------------
% 6.42/2.81 % (1391015)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/2.81 % (1391015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/2.81 % (1391015)CaDiCaL version: 2.1.3
% 6.42/2.81 % (1391015)Termination reason: Instruction limit
% 6.42/2.81 % (1391015)Termination phase: Saturation
% 6.42/2.81 % (1391015)Time elapsed: 0.138 s
% 6.42/2.81 % (1391015)Peak memory usage: 89 MB
% 6.42/2.81 % (1391015)Instructions burned: 137 (million)
% 6.42/2.81 % (1391016)Instruction limit reached!
% 6.42/2.81 % (1391016)------------------------------
% 6.42/2.81 % (1391016)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/2.81 % (1391016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/2.81 % (1391016)CaDiCaL version: 2.1.3
% 6.42/2.81 % (1391016)Termination reason: Instruction limit
% 6.42/2.81 % (1391016)Termination phase: Saturation
% 6.42/2.81 % (1391016)Time elapsed: 0.172 s
% 6.42/2.81 % (1391016)Peak memory usage: 89 MB
% 6.42/2.81 % (1391016)Instructions burned: 181 (million)
% 6.42/2.81 % (1391017)Instruction limit reached!
% 6.42/2.81 % (1391017)------------------------------
% 6.42/2.81 % (1391017)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/2.81 % (1391017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/2.81 % (1391017)CaDiCaL version: 2.1.3
% 6.42/2.81 % (1391017)Termination reason: Instruction limit
% 6.42/2.81 % (1391017)Termination phase: Saturation
% 6.42/2.81 % (1391017)Time elapsed: 0.278 s
% 6.42/2.81 % (1391017)Peak memory usage: 90 MB
% 6.42/2.81 % (1391017)Instructions burned: 258 (million)
% 6.42/2.81 % (1391027)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=885816346:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 6.42/2.81 % (1391026)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=612579658:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 6.42/2.81 % (1391028)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2390989556:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 6.42/2.81 % (1391028)Instruction limit reached!
% 6.42/2.81 % (1391028)------------------------------
% 6.42/2.81 % (1391028)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/2.81 % (1391028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/2.81 % (1391028)CaDiCaL version: 2.1.3
% 6.42/2.81 % (1391028)Termination reason: Instruction limit
% 6.42/2.81 % (1391028)Termination phase: Saturation
% 6.42/2.81 % (1391028)Time elapsed: 0.199 s
% 6.42/2.81 % (1391028)Peak memory usage: 92 MB
% 6.42/2.81 % (1391028)Instructions burned: 216 (million)
% 6.42/2.81 % (1391032)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=226630302:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2989 on theBenchmark for (2989ds/317Mi)
% 6.42/2.81 % (1391018)Instruction limit reached!
% 6.42/2.81 % (1391018)------------------------------
% 6.42/2.81 % (1391018)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/2.81 % (1391018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/2.81 % (1391018)CaDiCaL version: 2.1.3
% 6.42/2.81 % (1391018)Termination reason: Instruction limit
% 6.42/2.81 % (1391018)Termination phase: Saturation
% 6.42/2.81 % (1391018)Time elapsed: 1.112 s
% 6.42/2.81 % (1391018)Peak memory usage: 101 MB
% 6.42/2.81 % (1391018)Instructions burned: 1187 (million)
% 6.42/2.81 % (1391032)Instruction limit reached!
% 6.42/2.81 % (1391032)------------------------------
% 6.42/2.81 % (1391032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/2.81 % (1391032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/2.81 % (1391032)CaDiCaL version: 2.1.3
% 6.42/2.81 % (1391032)Termination reason: Instruction limit
% 6.42/2.81 % (1391032)Termination phase: Saturation
% 6.42/2.81 % (1391032)Time elapsed: 0.274 s
% 6.42/2.81 % (1391032)Peak memory usage: 92 MB
% 6.42/2.81 % (1391032)Instructions burned: 317 (million)
% 6.42/2.81 % (1391013)First to succeed.
% 6.42/2.81 % (1391013)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1391007"
% 6.42/2.81 % (1391034)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=123020505:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2985 on theBenchmark for (2985ds/12125Mi)
% 6.42/2.81 % (1391013)Refutation found. Thanks to Tanya!
% 6.42/2.81 % SZS status Unsatisfiable for theBenchmark
% 6.42/2.81 % SZS output start Proof for theBenchmark
% See solution above
% 13.83/3.02 % (1391013)------------------------------
% 13.83/3.02 % (1391013)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.83/3.02 % (1391013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.83/3.02 % (1391013)CaDiCaL version: 2.1.3
% 13.83/3.02 % (1391013)Termination reason: Refutation
% 13.83/3.02 % (1391013)Time elapsed: 1.420 s
% 13.83/3.02 % (1391013)Peak memory usage: 143 MB
% 13.83/3.02 % (1391013)Instructions burned: 2489 (million)
% 13.83/3.02 % (1391013)------------------------------
% 13.83/3.02 % (1391013)------------------------------
% 13.83/3.02 % (1391007)Success in time 1.876 s
% 13.83/3.02 % Vampire exiting
%------------------------------------------------------------------------------