%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL026-3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:33:52 PM UTC 2026
% Result : Unsatisfiable 7.92s 2.33s
% Output : Refutation 9.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 31
% Syntax : Number of formulae : 158 ( 88 unt; 17 def)
% Number of atoms : 281 ( 132 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 241 ( 118 ~; 113 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 11 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 143 ( 0 sgn 143 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(f23,negated_conjecture,
join(sk1,one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
one = join(sk1,one),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
meet(composition(sk1,top),sk2) != composition(sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_18) ).
fof(f26,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f30,plain,
composition(sk1,sk2) != complement(join(complement(composition(sk1,top)),complement(sk2))),
inference(definition_unfolding,[],[f25,f6]) ).
fof(f31,definition,
sF0 = join(sk1,one),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f32,plain,
join(sk1,one) = sF0,
inference(reorient_equations,[],[f31]) ).
fof(f33,plain,
one = sF0,
inference(definition_folding,[],[f24,f32]) ).
fof(f34,definition,
sF1 = composition(sk1,sk2),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f35,plain,
composition(sk1,sk2) = sF1,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF2 = composition(sk1,top),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f37,plain,
composition(sk1,top) = sF2,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF3 = complement(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f39,plain,
complement(sF2) = sF3,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF4 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f41,plain,
complement(sk2) = 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,plain,
sF1 != sF6,
inference(definition_folding,[],[f30,f45,f43,f41,f39,f37,f35]) ).
fof(f47,plain,
zero = complement(top),
inference(backward_demodulation,[],[f26,f15]) ).
fof(f48,plain,
! [X0] : composition(X0,sF0) = X0,
inference(forward_demodulation,[],[f8,f33]) ).
fof(f49,plain,
sF0 = join(one,sk1),
inference(forward_demodulation,[],[f32,f1]) ).
fof(f50,plain,
sF0 = join(sF0,sk1),
inference(forward_demodulation,[],[f49,f33]) ).
fof(f58,definition,
( spl7_1
<=> zero = complement(top) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f60,plain,
( zero = complement(top)
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,plain,
spl7_1,
inference(avatar_split_clause,[],[f47,f58]) ).
fof(f63,definition,
( spl7_2
<=> sF0 = join(sF0,sk1) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f65,plain,
( sF0 = join(sF0,sk1)
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f66,plain,
spl7_2,
inference(avatar_split_clause,[],[f50,f63]) ).
fof(f75,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f4,f1]) ).
fof(f77,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(superposition,[],[f4,f1]) ).
fof(f81,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(forward_demodulation,[],[f75,f1]) ).
fof(f88,definition,
( spl7_3
<=> complement(sF5) = sF6 ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
fof(f90,plain,
( complement(sF5) = sF6
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
spl7_3,
inference(avatar_split_clause,[],[f45,f88]) ).
fof(f102,plain,
! [X0,X1] : complement(X1) = join(composition(X0,complement(composition(converse(X0),X1))),complement(X1)),
inference(superposition,[],[f14,f10]) ).
fof(f109,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(forward_demodulation,[],[f102,f1]) ).
fof(f111,definition,
( spl7_5
<=> composition(sk1,sk2) = sF1 ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
fof(f113,plain,
( composition(sk1,sk2) = sF1
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
spl7_5,
inference(avatar_split_clause,[],[f35,f111]) ).
fof(f124,plain,
! [X0] : join(complement(join(complement(X0),complement(complement(complement(X0))))),complement(top)) = X0,
inference(superposition,[],[f4,f15]) ).
fof(f125,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f124,f1]) ).
fof(f127,plain,
( ! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0
| ~ spl7_1 ),
inference(forward_demodulation,[],[f125,f60]) ).
fof(f129,definition,
( spl7_6
<=> sF1 = sF6 ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
fof(f131,plain,
( sF1 != sF6
| spl7_6 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
~ spl7_6,
inference(avatar_split_clause,[],[f46,f129]) ).
fof(f134,definition,
( spl7_7
<=> complement(sk2) = sF4 ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
fof(f136,plain,
( complement(sk2) = sF4
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,plain,
spl7_7,
inference(avatar_split_clause,[],[f41,f134]) ).
fof(f147,definition,
( spl7_8
<=> composition(sk1,top) = sF2 ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
fof(f149,plain,
( composition(sk1,top) = sF2
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f150,plain,
spl7_8,
inference(avatar_split_clause,[],[f37,f147]) ).
fof(f160,definition,
( spl7_9
<=> join(sF3,sF4) = sF5 ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
fof(f162,plain,
( join(sF3,sF4) = sF5
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f163,plain,
spl7_9,
inference(avatar_split_clause,[],[f43,f160]) ).
fof(f165,definition,
( spl7_10
<=> complement(sF2) = sF3 ),
introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition]) ).
fof(f167,plain,
( complement(sF2) = sF3
| ~ spl7_10 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f168,plain,
spl7_10,
inference(avatar_split_clause,[],[f39,f165]) ).
fof(f228,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f282,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f81,f15]) ).
fof(f293,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f282,f1]) ).
fof(f309,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f293,f1]) ).
fof(f315,plain,
( ! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0)))))
| ~ spl7_1 ),
inference(forward_demodulation,[],[f309,f60]) ).
fof(f319,plain,
( ! [X0] : complement(complement(X0)) = X0
| ~ spl7_1 ),
inference(backward_demodulation,[],[f127,f315]) ).
fof(f336,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1))))
| ~ spl7_1 ),
inference(superposition,[],[f77,f319]) ).
fof(f339,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0)))
| ~ spl7_1 ),
inference(superposition,[],[f81,f319]) ).
fof(f353,plain,
( ! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0))))
| ~ spl7_1 ),
inference(superposition,[],[f336,f1]) ).
fof(f424,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f427,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(f435,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f427,f12]) ).
fof(f446,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f435,f11]) ).
fof(f449,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f446,f11]) ).
fof(f451,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f449,f12]) ).
fof(f464,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f451]) ).
fof(f476,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f464,f10]) ).
fof(f528,plain,
( ! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(complement(X0),X1)))
| ~ spl7_1 ),
inference(superposition,[],[f339,f1]) ).
fof(f552,plain,
( ! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),join(complement(X1),X0))))
| ~ spl7_1 ),
inference(superposition,[],[f4,f339]) ).
fof(f561,plain,
( ! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),complement(join(X0,join(complement(join(X0,X1)),complement(X1)))))
| ~ spl7_1 ),
inference(forward_demodulation,[],[f552,f228]) ).
fof(f578,plain,
( ! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),complement(join(X0,join(complement(X1),complement(join(X0,X1))))))
| ~ spl7_1 ),
inference(forward_demodulation,[],[f561,f1]) ).
fof(f591,plain,
( ! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1))))))
| ~ spl7_1 ),
inference(forward_demodulation,[],[f578,f319]) ).
fof(f1119,plain,
! [X0] : converse(converse(X0)) = composition(converse(sF0),X0),
inference(superposition,[],[f424,f48]) ).
fof(f1137,plain,
! [X0] : composition(converse(sF0),X0) = X0,
inference(forward_demodulation,[],[f1119,f10]) ).
fof(f1159,plain,
! [X0] : complement(X0) = join(complement(X0),composition(sF0,complement(X0))),
inference(superposition,[],[f109,f1137]) ).
fof(f1162,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(converse(sF0),X1),X0),
inference(superposition,[],[f9,f1137]) ).
fof(f1172,plain,
sF0 = converse(sF0),
inference(superposition,[],[f48,f1137]) ).
fof(f1177,plain,
! [X0] : composition(sF0,X0) = X0,
inference(backward_demodulation,[],[f1137,f1172]) ).
fof(f1188,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(sF0,X1),X0),
inference(forward_demodulation,[],[f1162,f1172]) ).
fof(f1192,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f1159,f1177]) ).
fof(f1238,plain,
( ! [X0] : join(X0,X0) = X0
| ~ spl7_1 ),
inference(superposition,[],[f1192,f319]) ).
fof(f1310,plain,
( ! [X0] : composition(sF0,X0) = join(X0,composition(sk1,X0))
| ~ spl7_2 ),
inference(superposition,[],[f1188,f65]) ).
fof(f1354,plain,
( ! [X0] : join(X0,composition(sk1,X0)) = X0
| ~ spl7_2 ),
inference(forward_demodulation,[],[f1310,f1177]) ).
fof(f1389,plain,
( ! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1))
| ~ spl7_1 ),
inference(superposition,[],[f2,f1238]) ).
fof(f1480,plain,
( ! [X0,X1] : join(X0,X1) = join(X0,join(composition(sk1,X0),X1))
| ~ spl7_2 ),
inference(superposition,[],[f2,f1354]) ).
fof(f1540,plain,
( ! [X0,X1] : join(X0,composition(sk1,X1)) = join(X0,composition(sk1,join(X0,X1)))
| ~ spl7_2 ),
inference(superposition,[],[f1480,f476]) ).
fof(f1634,plain,
( ! [X0] : join(X0,composition(sk1,complement(X0))) = join(X0,composition(sk1,top))
| ~ spl7_2 ),
inference(superposition,[],[f1540,f15]) ).
fof(f1705,plain,
( ! [X0] : join(X0,sF2) = join(X0,composition(sk1,complement(X0)))
| ~ spl7_2
| ~ spl7_8 ),
inference(forward_demodulation,[],[f1634,f149]) ).
fof(f1725,plain,
( ! [X0] : join(complement(X0),sF2) = join(complement(X0),composition(sk1,X0))
| ~ spl7_1
| ~ spl7_2
| ~ spl7_8 ),
inference(superposition,[],[f1705,f319]) ).
fof(f1777,plain,
( ! [X0] : join(sF2,complement(X0)) = join(complement(X0),composition(sk1,X0))
| ~ spl7_1
| ~ spl7_2
| ~ spl7_8 ),
inference(forward_demodulation,[],[f1725,f1]) ).
fof(f1810,plain,
( ! [X0] : complement(composition(sk1,X0)) = join(complement(X0),complement(join(complement(X0),composition(sk1,X0))))
| ~ spl7_1
| ~ spl7_2 ),
inference(superposition,[],[f528,f1354]) ).
fof(f1898,plain,
( ! [X0] : complement(composition(sk1,X0)) = join(complement(X0),complement(join(sF2,complement(X0))))
| ~ spl7_1
| ~ spl7_2
| ~ spl7_8 ),
inference(forward_demodulation,[],[f1810,f1777]) ).
fof(f2047,plain,
( ! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(complement(complement(join(X1,X0))),complement(join(X0,complement(X1))))))
| ~ spl7_1 ),
inference(superposition,[],[f528,f353]) ).
fof(f2049,plain,
( ! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(join(X1,X0),complement(join(X0,complement(X1))))))
| ~ spl7_1 ),
inference(forward_demodulation,[],[f2047,f319]) ).
fof(f2088,plain,
( ! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,complement(join(X0,complement(X1)))))))
| ~ spl7_1 ),
inference(forward_demodulation,[],[f2049,f2]) ).
fof(f2121,plain,
( ! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1)))))))
| ~ spl7_1 ),
inference(forward_demodulation,[],[f2088,f319]) ).
fof(f2146,plain,
( ! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1)))))))
| ~ spl7_1 ),
inference(forward_demodulation,[],[f2121,f319]) ).
fof(f2547,plain,
( ! [X0,X1] : join(X0,X1) = join(X1,join(X0,X1))
| ~ spl7_1 ),
inference(superposition,[],[f1389,f1]) ).
fof(f2566,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0))
| ~ spl7_1 ),
inference(superposition,[],[f1389,f353]) ).
fof(f2611,plain,
( ! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0)))
| ~ spl7_1 ),
inference(forward_demodulation,[],[f2566,f1]) ).
fof(f2627,plain,
( ! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1))))
| ~ spl7_1 ),
inference(backward_demodulation,[],[f591,f2611]) ).
fof(f2633,plain,
( ! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1))))
| ~ spl7_1 ),
inference(backward_demodulation,[],[f2146,f2627]) ).
fof(f2640,plain,
( ! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1)))
| ~ spl7_1 ),
inference(forward_demodulation,[],[f2633,f2547]) ).
fof(f2668,plain,
( ! [X0,X1] : join(X1,complement(X0)) = join(X1,complement(join(X0,X1)))
| ~ spl7_1 ),
inference(superposition,[],[f2640,f1]) ).
fof(f2765,plain,
( ! [X0] : join(complement(X0),complement(sF2)) = complement(composition(sk1,X0))
| ~ spl7_1
| ~ spl7_2
| ~ spl7_8 ),
inference(backward_demodulation,[],[f1898,f2668]) ).
fof(f2796,plain,
( ! [X0] : join(complement(X0),sF3) = complement(composition(sk1,X0))
| ~ spl7_1
| ~ spl7_2
| ~ spl7_8
| ~ spl7_10 ),
inference(forward_demodulation,[],[f2765,f167]) ).
fof(f2818,plain,
( ! [X0] : join(sF3,complement(X0)) = complement(composition(sk1,X0))
| ~ spl7_1
| ~ spl7_2
| ~ spl7_8
| ~ spl7_10 ),
inference(forward_demodulation,[],[f2796,f1]) ).
fof(f3629,plain,
( complement(sF1) = join(sF3,complement(sk2))
| ~ spl7_1
| ~ spl7_2
| ~ spl7_5
| ~ spl7_8
| ~ spl7_10 ),
inference(superposition,[],[f2818,f113]) ).
fof(f3661,plain,
( join(sF3,sF4) = complement(sF1)
| ~ spl7_1
| ~ spl7_2
| ~ spl7_5
| ~ spl7_7
| ~ spl7_8
| ~ spl7_10 ),
inference(forward_demodulation,[],[f3629,f136]) ).
fof(f3669,plain,
( sF5 = complement(sF1)
| ~ spl7_1
| ~ spl7_2
| ~ spl7_5
| ~ spl7_7
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(forward_demodulation,[],[f3661,f162]) ).
fof(f3693,definition,
( spl7_19
<=> sF5 = complement(sF1) ),
introduced(definition,[new_symbols(definition,[spl7_19])],[avatar_definition]) ).
fof(f3695,plain,
( sF5 = complement(sF1)
| ~ spl7_19 ),
inference(avatar_component_clause,[],[f3693]) ).
fof(f3696,plain,
( spl7_19
| ~ spl7_1
| ~ spl7_2
| ~ spl7_5
| ~ spl7_7
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(avatar_split_clause,[],[f3669,f165,f160,f147,f134,f111,f63,f58,f3693]) ).
fof(f3697,plain,
( ! [X0] : sF1 = join(complement(join(sF5,complement(X0))),complement(join(sF5,X0)))
| ~ spl7_19 ),
inference(superposition,[],[f4,f3695]) ).
fof(f3718,plain,
( ! [X0] : sF1 = join(complement(join(sF5,X0)),complement(join(sF5,complement(X0))))
| ~ spl7_19 ),
inference(forward_demodulation,[],[f3697,f1]) ).
fof(f3723,plain,
( sF1 = complement(sF5)
| ~ spl7_1
| ~ spl7_19 ),
inference(forward_demodulation,[],[f3718,f336]) ).
fof(f3727,plain,
( sF1 = sF6
| ~ spl7_1
| ~ spl7_3
| ~ spl7_19 ),
inference(forward_demodulation,[],[f3723,f90]) ).
fof(f3729,plain,
( $false
| ~ spl7_1
| ~ spl7_3
| spl7_6
| ~ spl7_19 ),
inference(forward_subsumption_resolution,[],[f3727,f131]) ).
fof(f3730,plain,
( ~ spl7_1
| ~ spl7_3
| spl7_6
| ~ spl7_19 ),
inference(avatar_contradiction_clause,[],[f3729]) ).
cnf(s1,plain,
spl7_1,
inference(sat_conversion,[],[f61]) ).
cnf(s2,plain,
spl7_2,
inference(sat_conversion,[],[f66]) ).
cnf(s3,plain,
spl7_3,
inference(sat_conversion,[],[f91]) ).
cnf(s5,plain,
spl7_5,
inference(sat_conversion,[],[f114]) ).
cnf(s6,plain,
~ spl7_6,
inference(sat_conversion,[],[f132]) ).
cnf(s7,plain,
spl7_7,
inference(sat_conversion,[],[f137]) ).
cnf(s8,plain,
spl7_8,
inference(sat_conversion,[],[f150]) ).
cnf(s9,plain,
spl7_9,
inference(sat_conversion,[],[f163]) ).
cnf(s10,plain,
spl7_10,
inference(sat_conversion,[],[f168]) ).
cnf(s19,plain,
( ~ spl7_1
| ~ spl7_2
| ~ spl7_5
| ~ spl7_7
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10
| spl7_19 ),
inference(sat_conversion,[],[f3696]) ).
cnf(s21,plain,
( ~ spl7_1
| ~ spl7_3
| spl7_6
| ~ spl7_19 ),
inference(sat_conversion,[],[f3730]) ).
cnf(s22,plain,
~ spl7_19,
inference(rat,[],[s21,s3,s6,s1]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s19,s2,s10,s9,s8,s7,s5,s22,s1]) ).
fof(f3732,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL026-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 % Computer : n016.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 27 22:57:47 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.92/2.33 % (3081686)Detected a unit-equality problem, will run specialized UEQ schedule.
% 7.92/2.33 % (3081691)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=3608138736:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 7.92/2.33 % (3081696)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1687259068:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 7.92/2.33 % (3081694)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=846090150:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 7.92/2.33 % (3081693)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4088731010:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 7.92/2.33 % (3081692)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=3800197252:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 7.92/2.33 % (3081695)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1892104820:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 7.92/2.33 % (3081697)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2857959129:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 7.92/2.33 % (3081696)Instruction limit reached!
% 7.92/2.33 % (3081696)------------------------------
% 7.92/2.33 % (3081696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.92/2.33 % (3081696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.92/2.33 % (3081696)CaDiCaL version: 2.1.3
% 7.92/2.33 % (3081696)Termination reason: Instruction limit
% 7.92/2.33 % (3081696)Termination phase: Saturation
% 7.92/2.33 % (3081696)Time elapsed: 0.209 s
% 7.92/2.33 % (3081696)Peak memory usage: 90 MB
% 7.92/2.33 % (3081696)Instructions burned: 257 (million)
% 7.92/2.33 % (3081694)Instruction limit reached!
% 7.92/2.33 % (3081694)------------------------------
% 7.92/2.33 % (3081694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.92/2.33 % (3081694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.92/2.33 % (3081694)CaDiCaL version: 2.1.3
% 7.92/2.33 % (3081694)Termination reason: Instruction limit
% 7.92/2.33 % (3081694)Termination phase: Saturation
% 7.92/2.33 % (3081694)Time elapsed: 0.136 s
% 7.92/2.33 % (3081694)Peak memory usage: 89 MB
% 7.92/2.33 % (3081694)Instructions burned: 136 (million)
% 7.92/2.33 % (3081695)Instruction limit reached!
% 7.92/2.33 % (3081695)------------------------------
% 7.92/2.33 % (3081695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.92/2.33 % (3081695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.92/2.33 % (3081695)CaDiCaL version: 2.1.3
% 7.92/2.33 % (3081695)Termination reason: Instruction limit
% 7.92/2.33 % (3081695)Termination phase: Saturation
% 7.92/2.33 % (3081695)Time elapsed: 0.182 s
% 7.92/2.33 % (3081695)Peak memory usage: 89 MB
% 7.92/2.33 % (3081695)Instructions burned: 182 (million)
% 7.92/2.33 % (3081706)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3027650764:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 7.92/2.33 % (3081705)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3933161931:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 7.92/2.33 % (3081707)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2952284912:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 7.92/2.33 % (3081707)Instruction limit reached!
% 7.92/2.33 % (3081707)------------------------------
% 7.92/2.33 % (3081707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.92/2.33 % (3081707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.92/2.33 % (3081707)CaDiCaL version: 2.1.3
% 7.92/2.33 % (3081707)Termination reason: Instruction limit
% 7.92/2.33 % (3081707)Termination phase: Saturation
% 7.92/2.33 % (3081707)Time elapsed: 0.210 s
% 7.92/2.33 % (3081707)Peak memory usage: 92 MB
% 7.92/2.33 % (3081707)Instructions burned: 216 (million)
% 7.92/2.33 % (3081691)First to succeed.
% 7.92/2.33 % (3081691)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3081686"
% 7.92/2.33 % (3081711)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=2093603612:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2990 on theBenchmark for (2990ds/317Mi)
% 7.92/2.33 % (3081691)Refutation found. Thanks to Tanya!
% 7.92/2.33 % SZS status Unsatisfiable for theBenchmark
% 7.92/2.33 % SZS output start Proof for theBenchmark
% See solution above
% 9.75/2.56 % (3081691)------------------------------
% 9.75/2.56 % (3081691)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.75/2.56 % (3081691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.75/2.56 % (3081691)CaDiCaL version: 2.1.3
% 9.75/2.56 % (3081691)Termination reason: Refutation
% 9.75/2.56 % (3081691)Time elapsed: 0.842 s
% 9.75/2.56 % (3081691)Peak memory usage: 134 MB
% 9.75/2.56 % (3081691)Instructions burned: 1444 (million)
% 9.75/2.56 % (3081691)------------------------------
% 9.75/2.56 % (3081691)------------------------------
% 9.75/2.56 % (3081686)Success in time 1.274 s
% 9.75/2.56 % Vampire exiting
%------------------------------------------------------------------------------