%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL013+1 : 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 : 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 12:33:43 PM UTC 2026
% Result : Theorem 7.96s 12.22s
% Output : Refutation 9.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 16
% Syntax : Number of formulae : 137 ( 123 unt; 2 def)
% Number of atoms : 151 ( 132 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 28 ( 14 ~; 10 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 193 ( 0 sgn 192 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
fof(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) ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
fof(f14,conjecture,
! [X0] :
( composition(X0,zero) = zero
& composition(zero,X0) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0] :
( composition(X0,zero) = zero
& composition(zero,X0) = zero ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0] :
( zero != composition(X0,zero)
| zero != composition(zero,X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
( zero != composition(sK0,zero)
| zero != composition(zero,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f16]) ).
fof(f18,plain,
( zero != composition(sK0,zero)
| zero != composition(zero,sK0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f19,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f21,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f23,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f27,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f28,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f29,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f30,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f31,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f32,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f24,f27]) ).
fof(f33,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f28,f30]) ).
fof(f34,plain,
zero = complement(top),
inference(forward_demodulation,[],[f32,f25]) ).
fof(f35,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(forward_demodulation,[],[f19,f30]) ).
fof(f37,definition,
( spl1_1
<=> zero = composition(zero,sK0) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f39,plain,
( zero != composition(zero,sK0)
| spl1_1 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f41,definition,
( spl1_2
<=> zero = composition(sK0,zero) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f43,plain,
( zero != composition(sK0,zero)
| spl1_2 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f44,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f18,f41,f37]) ).
fof(f47,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f20,f31]) ).
fof(f48,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f26,f31]) ).
fof(f54,plain,
! [X0,X1] : composition(X0,X1) = composition(X0,composition(one,X1)),
inference(superposition,[],[f23,f22]) ).
fof(f68,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f29,f25]) ).
fof(f77,plain,
! [X0,X1] : top = join(X0,join(X1,complement(join(X0,X1)))),
inference(superposition,[],[f25,f29]) ).
fof(f79,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f30,f29]) ).
fof(f95,plain,
! [X2,X3,X0,X1] : composition(join(X3,composition(X0,X1)),X2) = join(composition(X3,X2),composition(X0,composition(X1,X2))),
inference(superposition,[],[f21,f23]) ).
fof(f100,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X1,X2),composition(X0,X2)),
inference(superposition,[],[f30,f21]) ).
fof(f109,plain,
! [X0] : zero = join(zero,composition(converse(X0),complement(composition(X0,top)))),
inference(superposition,[],[f35,f34]) ).
fof(f110,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(superposition,[],[f35,f31]) ).
fof(f123,plain,
! [X0,X1] : join(complement(complement(X0)),complement(join(complement(X0),complement(composition(converse(X1),complement(composition(X1,X0))))))) = X0,
inference(superposition,[],[f33,f35]) ).
fof(f127,plain,
! [X0,X1] : join(complement(join(X0,complement(X1))),complement(join(complement(X1),complement(X0)))) = X1,
inference(superposition,[],[f33,f30]) ).
fof(f130,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(join(complement(join(complement(X0),X1)),join(complement(X0),complement(X1)))),complement(X0)),
inference(superposition,[],[f33,f33]) ).
fof(f134,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f29,f33]) ).
fof(f136,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(X0),complement(join(complement(join(complement(X0),X1)),join(complement(X0),complement(X1))))),
inference(forward_demodulation,[],[f130,f30]) ).
fof(f140,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(X0),complement(join(join(complement(X0),complement(X1)),complement(join(complement(X0),X1))))),
inference(forward_demodulation,[],[f136,f30]) ).
fof(f142,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(X0),complement(join(complement(X0),join(complement(X1),complement(join(complement(X0),X1)))))),
inference(forward_demodulation,[],[f140,f29]) ).
fof(f167,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f47,f22]) ).
fof(f185,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f167,f31]) ).
fof(f202,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(superposition,[],[f54,f185]) ).
fof(f206,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[],[f202,f185]) ).
fof(f219,plain,
! [X0] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[],[f48,f25]) ).
fof(f365,plain,
! [X0,X1] : join(top,X0) = join(X1,join(X0,complement(X1))),
inference(superposition,[],[f68,f30]) ).
fof(f1089,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(converse(one),X0))),
inference(superposition,[],[f110,f206]) ).
fof(f1103,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f1089,f185]) ).
fof(f1426,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(superposition,[],[f127,f25]) ).
fof(f1486,plain,
! [X0] : join(complement(top),complement(complement(X0))) = X0,
inference(forward_demodulation,[],[f1426,f1103]) ).
fof(f1505,plain,
! [X0] : join(zero,complement(complement(X0))) = X0,
inference(forward_demodulation,[],[f1486,f34]) ).
fof(f1657,plain,
! [X0] : top = join(complement(X0),join(complement(X0),complement(complement(X0)))),
inference(superposition,[],[f77,f1103]) ).
fof(f1658,plain,
! [X0,X1] : join(X1,complement(X0)) = join(complement(X0),join(complement(X0),X1)),
inference(superposition,[],[f79,f1103]) ).
fof(f1660,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[],[f1657,f365]) ).
fof(f1746,plain,
! [X0] : top = join(X0,top),
inference(superposition,[],[f77,f1660]) ).
fof(f1849,plain,
! [X0] : top = join(top,X0),
inference(superposition,[],[f30,f1746]) ).
fof(f1971,plain,
top = converse(top),
inference(superposition,[],[f219,f1849]) ).
fof(f2713,plain,
! [X0,X1] : complement(X0) = join(complement(join(complement(complement(X0)),join(complement(X0),complement(composition(converse(X1),complement(composition(X1,X0))))))),complement(X0)),
inference(superposition,[],[f33,f123]) ).
fof(f2732,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(complement(complement(X0)),join(complement(X0),complement(composition(converse(X1),complement(composition(X1,X0)))))))),
inference(forward_demodulation,[],[f2713,f30]) ).
fof(f2755,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(complement(X0),join(complement(composition(converse(X1),complement(composition(X1,X0)))),complement(complement(X0)))))),
inference(forward_demodulation,[],[f2732,f79]) ).
fof(f2773,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(top,complement(composition(converse(X1),complement(composition(X1,X0))))))),
inference(forward_demodulation,[],[f2755,f365]) ).
fof(f2785,plain,
! [X0] : complement(X0) = join(complement(X0),complement(top)),
inference(forward_demodulation,[],[f2773,f1660]) ).
fof(f2794,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(forward_demodulation,[],[f2785,f34]) ).
fof(f2800,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f2794,f30]) ).
fof(f2819,plain,
! [X0] : complement(complement(X0)) = X0,
inference(superposition,[],[f1505,f2800]) ).
fof(f2822,plain,
top = complement(zero),
inference(superposition,[],[f25,f2800]) ).
fof(f2828,plain,
! [X0,X1] : join(X1,complement(X0)) = join(zero,join(complement(X0),X1)),
inference(superposition,[],[f79,f2800]) ).
fof(f2865,plain,
! [X2,X0,X1] : join(X1,X2) = join(complement(join(top,X0)),join(complement(join(complement(X1),complement(join(complement(complement(X1)),X0)))),X2)),
inference(superposition,[],[f134,f68]) ).
fof(f2891,plain,
! [X0,X1] : join(X1,complement(join(complement(X0),complement(complement(X1))))) = join(complement(join(complement(X1),X0)),X0),
inference(superposition,[],[f134,f127]) ).
fof(f2937,plain,
! [X0,X1] : join(X0,complement(join(complement(X1),X0))) = join(X1,complement(join(complement(X0),complement(complement(X1))))),
inference(forward_demodulation,[],[f2891,f30]) ).
fof(f2958,plain,
! [X2,X0,X1] : join(X1,X2) = join(complement(join(top,X0)),join(complement(join(complement(X1),complement(join(X1,X0)))),X2)),
inference(forward_demodulation,[],[f2865,f2819]) ).
fof(f2986,plain,
! [X0,X1] : join(X1,complement(join(complement(X0),X1))) = join(X0,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f2937,f2819]) ).
fof(f3004,plain,
! [X2,X0,X1] : join(X1,X2) = join(complement(top),join(complement(join(complement(X1),complement(join(X1,X0)))),X2)),
inference(forward_demodulation,[],[f2958,f1849]) ).
fof(f3034,plain,
! [X2,X0,X1] : join(X1,X2) = join(zero,join(complement(join(complement(X1),complement(join(X1,X0)))),X2)),
inference(forward_demodulation,[],[f3004,f34]) ).
fof(f3059,plain,
! [X2,X0,X1] : join(X1,X2) = join(X2,complement(join(complement(X1),complement(join(X1,X0))))),
inference(forward_demodulation,[],[f3034,f2828]) ).
fof(f3217,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(complement(join(complement(X0),join(complement(X1),complement(join(complement(X0),X1))))))))) = X0,
inference(superposition,[],[f33,f142]) ).
fof(f3219,plain,
! [X0,X1] : join(complement(X0),join(complement(X1),complement(join(complement(X0),X1)))) = join(complement(join(complement(X0),X1)),complement(join(complement(join(complement(X0),join(complement(X1),complement(join(complement(X0),X1))))),complement(complement(X0))))),
inference(superposition,[],[f127,f142]) ).
fof(f3229,plain,
! [X0,X1] : join(complement(X0),join(complement(X1),complement(join(complement(X0),X1)))) = join(complement(join(complement(X0),X1)),complement(join(complement(complement(X0)),complement(join(complement(X0),join(complement(X1),complement(join(complement(X0),X1)))))))),
inference(forward_demodulation,[],[f3219,f30]) ).
fof(f3231,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),join(complement(X0),join(complement(X1),complement(join(complement(X0),X1))))))) = X0,
inference(forward_demodulation,[],[f3217,f2819]) ).
fof(f3268,plain,
! [X0,X1] : join(complement(X0),join(complement(X1),complement(join(complement(X0),X1)))) = join(complement(X0),complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f3229,f3059]) ).
fof(f3269,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(join(complement(X1),complement(join(complement(X0),X1))),complement(X0)))) = X0,
inference(forward_demodulation,[],[f3231,f1658]) ).
fof(f3300,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),join(complement(X1),complement(join(complement(X0),X1)))))) = X0,
inference(forward_demodulation,[],[f3269,f30]) ).
fof(f3327,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(join(complement(X0),X1))))) = X0,
inference(forward_demodulation,[],[f3300,f3268]) ).
fof(f3352,plain,
! [X0,X1] : join(X0,complement(join(complement(complement(join(complement(X0),X1))),X0))) = X0,
inference(forward_demodulation,[],[f3327,f2986]) ).
fof(f3367,plain,
! [X0,X1] : join(X0,complement(join(X0,complement(complement(join(complement(X0),X1)))))) = X0,
inference(forward_demodulation,[],[f3352,f30]) ).
fof(f3379,plain,
! [X0,X1] : join(X0,complement(join(X0,join(complement(X0),X1)))) = X0,
inference(forward_demodulation,[],[f3367,f2819]) ).
fof(f3388,plain,
! [X0,X1] : join(X0,complement(join(top,X1))) = X0,
inference(forward_demodulation,[],[f3379,f68]) ).
fof(f3395,plain,
! [X0] : join(X0,complement(top)) = X0,
inference(forward_demodulation,[],[f3388,f1849]) ).
fof(f3402,plain,
! [X0] : join(X0,zero) = X0,
inference(forward_demodulation,[],[f3395,f34]) ).
fof(f3427,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f30,f3402]) ).
fof(f3445,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(zero)),
inference(superposition,[],[f48,f3402]) ).
fof(f3449,plain,
! [X0] : join(X0,converse(zero)) = X0,
inference(forward_demodulation,[],[f3445,f31]) ).
fof(f4073,plain,
converse(top) = converse(complement(converse(zero))),
inference(superposition,[],[f219,f3427]) ).
fof(f4075,plain,
top = converse(complement(converse(zero))),
inference(forward_demodulation,[],[f4073,f1971]) ).
fof(f4623,plain,
zero = converse(zero),
inference(superposition,[],[f3427,f3449]) ).
fof(f4947,plain,
zero = join(zero,composition(top,complement(composition(complement(converse(zero)),top)))),
inference(superposition,[],[f109,f4075]) ).
fof(f4963,plain,
zero = composition(top,complement(composition(complement(converse(zero)),top))),
inference(forward_demodulation,[],[f4947,f3427]) ).
fof(f4990,plain,
zero = composition(top,complement(composition(complement(zero),top))),
inference(forward_demodulation,[],[f4963,f4623]) ).
fof(f5012,plain,
zero = composition(top,complement(composition(top,top))),
inference(forward_demodulation,[],[f4990,f2822]) ).
fof(f7354,plain,
! [X0,X1] : composition(join(top,composition(X0,X1)),complement(composition(top,top))) = join(zero,composition(X0,composition(X1,complement(composition(top,top))))),
inference(superposition,[],[f95,f5012]) ).
fof(f7357,plain,
! [X0] : composition(join(X0,top),complement(composition(top,top))) = join(zero,composition(X0,complement(composition(top,top)))),
inference(superposition,[],[f100,f5012]) ).
fof(f7370,plain,
! [X0] : composition(join(X0,top),complement(composition(top,top))) = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f7357,f3427]) ).
fof(f7373,plain,
! [X0,X1] : composition(X0,composition(X1,complement(composition(top,top)))) = composition(join(top,composition(X0,X1)),complement(composition(top,top))),
inference(forward_demodulation,[],[f7354,f3427]) ).
fof(f7385,plain,
! [X0] : composition(top,complement(composition(top,top))) = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f7370,f1746]) ).
fof(f7388,plain,
! [X0,X1] : composition(top,complement(composition(top,top))) = composition(X0,composition(X1,complement(composition(top,top)))),
inference(forward_demodulation,[],[f7373,f1849]) ).
fof(f7398,plain,
! [X0] : zero = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f7385,f5012]) ).
fof(f7401,plain,
! [X0,X1] : zero = composition(X0,composition(X1,complement(composition(top,top)))),
inference(forward_demodulation,[],[f7388,f5012]) ).
fof(f7412,plain,
! [X0] : zero = composition(X0,zero),
inference(forward_demodulation,[],[f7401,f7398]) ).
fof(f7745,plain,
! [X0] : converse(zero) = composition(converse(zero),X0),
inference(superposition,[],[f47,f7412]) ).
fof(f7748,plain,
! [X0] : zero = composition(zero,X0),
inference(forward_demodulation,[],[f7745,f4623]) ).
fof(f8084,plain,
( zero != zero
| spl1_1 ),
inference(superposition,[],[f39,f7748]) ).
fof(f8114,plain,
( $false
| spl1_1 ),
inference(trivial_inequality_removal,[],[f8084]) ).
fof(f8115,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f8114]) ).
fof(f8178,plain,
( $false
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f43,f7412]) ).
fof(f8179,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f8178]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
spl1_1,
inference(sat_conversion,[],[f8115]) ).
cnf(s3,plain,
spl1_2,
inference(sat_conversion,[],[f8179]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f8180,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL013+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/10.44 % Computer : n016.cluster.edu
% 0.17/10.44 % Model : x86_64 x86_64
% 0.17/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.44 % Memory : 8046.5625MB
% 0.17/10.44 % OS : Linux 6.8.0-71-generic
% 0.17/10.45 % CPULimit : 300
% 0.17/10.45 % WCLimit : 300
% 0.17/10.45 % DateTime : Sun Sep 27 22:55:59 UTC 2026
% 0.17/10.45 % CPUTime :
% 0.17/10.45 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/10.50 Running first-order theorem proving
% 0.21/10.50 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
% 7.96/12.22 % (3079332)Detected formulas, will run a generic FOF schedule.
% 7.96/12.22 % (3079337)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3387510029:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.96/12.22 % (3079339)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=287048660:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.96/12.22 % (3079338)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1592665466:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.96/12.22 % (3079341)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2496616548:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.96/12.22 % (3079340)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=957439644:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.96/12.22 % (3079342)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3325336367:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.96/12.22 % (3079343)dis-21_1_sil=8000:lcm=predicate:random_seed=731381687:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 7.96/12.22 % (3079340)Refutation not found, incomplete strategy
% 7.96/12.22 % (3079340)------------------------------
% 7.96/12.22 % (3079340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.96/12.22 % (3079343)Refutation not found, incomplete strategy
% 7.96/12.22 % (3079343)------------------------------
% 7.96/12.22 % (3079343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.96/12.22 % (3079340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.96/12.22 % (3079343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.96/12.22 % (3079343)CaDiCaL version: 2.1.3
% 7.96/12.22 % (3079340)CaDiCaL version: 2.1.3
% 7.96/12.22 % (3079343)Termination reason: Refutation not found, incomplete strategy
% 7.96/12.22 % (3079343)Time elapsed: 0.002 s
% 7.96/12.22 % (3079340)Termination reason: Refutation not found, incomplete strategy
% 7.96/12.22 % (3079340)Time elapsed: 0.002 s
% 7.96/12.22 % (3079340)Peak memory usage: 88 MB
% 7.96/12.22 % (3079343)Peak memory usage: 88 MB
% 7.96/12.22 % (3079343)Instructions burned: 1 (million)
% 7.96/12.22 % (3079341)Instruction limit reached!
% 7.96/12.22 % (3079341)------------------------------
% 7.96/12.22 % (3079341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.96/12.22 % (3079341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.96/12.22 % (3079341)CaDiCaL version: 2.1.3
% 7.96/12.22 % (3079341)Termination reason: Instruction limit
% 7.96/12.22 % (3079341)Termination phase: Saturation
% 7.96/12.22 % (3079341)Time elapsed: 0.107 s
% 7.96/12.22 % (3079341)Peak memory usage: 88 MB
% 7.96/12.22 % (3079341)Instructions burned: 119 (million)
% 7.96/12.22 % (3079342)Instruction limit reached!
% 7.96/12.22 % (3079342)------------------------------
% 7.96/12.22 % (3079342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.96/12.22 % (3079342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.96/12.22 % (3079342)CaDiCaL version: 2.1.3
% 7.96/12.22 % (3079342)Termination reason: Instruction limit
% 7.96/12.22 % (3079342)Termination phase: Saturation
% 7.96/12.22 % (3079342)Time elapsed: 0.135 s
% 7.96/12.22 % (3079342)Peak memory usage: 90 MB
% 7.96/12.22 % (3079342)Instructions burned: 139 (million)
% 7.96/12.22 % (3079351)lrs+10_1_sil=8000:sp=occurrence:random_seed=3751908277:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 7.96/12.22 % (3079340)------------------------------
% 7.96/12.22 % (3079340)------------------------------
% 7.96/12.22 % (3079343)------------------------------
% 7.96/12.22 % (3079343)------------------------------
% 7.96/12.22 % (3079352)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4172402704:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 7.96/12.22 % (3079351)First to succeed.
% 7.96/12.22 % (3079351)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3079332"
% 7.96/12.22 % (3079352)Instruction limit reached!
% 7.96/12.22 % (3079352)------------------------------
% 7.96/12.22 % (3079352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.96/12.22 % (3079352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.96/12.22 % (3079352)CaDiCaL version: 2.1.3
% 7.96/12.22 % (3079352)Termination reason: Instruction limit
% 7.96/12.22 % (3079352)Termination phase: Saturation
% 7.96/12.22 % (3079352)Time elapsed: 0.154 s
% 7.96/12.22 % (3079352)Peak memory usage: 91 MB
% 7.96/12.22 % (3079352)Instructions burned: 157 (million)
% 7.96/12.22 % (3079354)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3137573061:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 7.96/12.22 % (3079355)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=81097308:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 7.96/12.22 % (3079354)Also succeeded, but the first one will report.
% 7.96/12.22 % (3079339)Refutation not found, incomplete strategy
% 7.96/12.22 % (3079339)------------------------------
% 7.96/12.22 % (3079339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.96/12.22 % (3079339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.96/12.22 % (3079339)CaDiCaL version: 2.1.3
% 7.96/12.22 % (3079339)Termination reason: Refutation not found, incomplete strategy
% 7.96/12.22 % (3079339)Time elapsed: 0.900 s
% 7.96/12.22 % (3079339)Peak memory usage: 127 MB
% 7.96/12.22 % (3079339)Instructions burned: 883 (million)
% 7.96/12.22 % (3079357)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2724217070:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2991 on theBenchmark for (2991ds/294Mi)
% 7.96/12.22 % (3079357)Refutation not found, incomplete strategy
% 7.96/12.22 % (3079357)------------------------------
% 7.96/12.22 % (3079357)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.96/12.22 % (3079357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.96/12.22 % (3079357)CaDiCaL version: 2.1.3
% 7.96/12.22 % (3079357)Termination reason: Refutation not found, incomplete strategy
% 7.96/12.22 % (3079357)Time elapsed: 0.003 s
% 7.96/12.22 % (3079357)Peak memory usage: 88 MB
% 7.96/12.22 % (3079357)Instructions burned: 1 (million)
% 7.96/12.22 % (3079351)Refutation found. Thanks to Tanya!
% 7.96/12.22 % SZS status Theorem for theBenchmark
% 7.96/12.22 % SZS output start Proof for theBenchmark
% See solution above
% 9.41/12.43 % (3079351)------------------------------
% 9.41/12.43 % (3079351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.41/12.43 % (3079351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.41/12.43 % (3079351)CaDiCaL version: 2.1.3
% 9.41/12.43 % (3079351)Termination reason: Refutation
% 9.41/12.43 % (3079351)Time elapsed: 0.237 s
% 9.41/12.43 % (3079351)Peak memory usage: 92 MB
% 9.41/12.43 % (3079351)Instructions burned: 248 (million)
% 9.41/12.43 % (3079351)------------------------------
% 9.41/12.43 % (3079351)------------------------------
% 9.41/12.43 % (3079332)Success in time 1.23 s
% 9.41/12.43 % Vampire exiting
%------------------------------------------------------------------------------