TSTP Solution File: COL076-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COL076-1 : TPTP v8.2.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 19:06:21 EDT 2024
% Result : Unsatisfiable 138.02s 20.09s
% Output : Refutation 138.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 11
% Syntax : Number of formulae : 119 ( 114 unt; 0 def)
% Number of atoms : 124 ( 123 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 11 ~; 5 |; 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 192 ( 192 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f618254,plain,
$false,
inference(unit_resulting_resolution,[],[f1133,f618227]) ).
fof(f618227,plain,
! [X0] : apply(X0,pair(X0,projection2)) != apply(eq,apply(f,pair(X0,projection2))),
inference(forward_demodulation,[],[f617381,f3232]) ).
fof(f3232,plain,
! [X0,X1] : apply(f,X0) = apply(k,apply(apply(f,X0),X1)),
inference(forward_demodulation,[],[f3168,f771]) ).
fof(f771,plain,
! [X0] : apply(f,X0) = apply(f,apply(f,X0)),
inference(unit_resulting_resolution,[],[f44,f9]) ).
fof(f9,axiom,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
fof(f44,plain,
! [X2,X0,X1] : apply(apply(f,X0),X1) = apply(apply(f,apply(f,X0)),X2),
inference(superposition,[],[f15,f11]) ).
fof(f11,axiom,
! [X0,X1] : apply(apply(f,X0),X1) = apply(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagonal_combinator) ).
fof(f15,plain,
! [X0,X1] : apply(X0,X0) = apply(apply(f,apply(f,X0)),X1),
inference(superposition,[],[f11,f11]) ).
fof(f3168,plain,
! [X0,X1] : apply(f,apply(f,X0)) = apply(k,apply(apply(f,X0),X1)),
inference(unit_resulting_resolution,[],[f44,f772]) ).
fof(f772,plain,
! [X0,X1] :
( apply(X1,n(apply(k,X0),X1)) != X0
| apply(k,X0) = X1 ),
inference(superposition,[],[f9,f1]) ).
fof(f1,axiom,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
fof(f617381,plain,
! [X0,X1] : apply(X0,pair(X0,projection2)) != apply(eq,apply(k,apply(apply(f,pair(X0,projection2)),X1))),
inference(superposition,[],[f420142,f593903]) ).
fof(f593903,plain,
! [X0,X1] : apply(apply(f,pair(X0,projection2)),X1) = pair(apply(X0,pair(X0,projection2)),projection2),
inference(forward_demodulation,[],[f593902,f591246]) ).
fof(f591246,plain,
! [X0] : apply(f,pair(X0,projection2)) = apply(f,apply(pair(apply(projection1,f),projection2),pair(X0,projection2))),
inference(forward_demodulation,[],[f591245,f3234]) ).
fof(f3234,plain,
! [X0] : apply(f,X0) = apply(k,apply(X0,X0)),
inference(forward_demodulation,[],[f3233,f771]) ).
fof(f3233,plain,
! [X0] : apply(f,apply(f,X0)) = apply(k,apply(X0,X0)),
inference(forward_demodulation,[],[f3166,f771]) ).
fof(f3166,plain,
! [X0] : apply(f,apply(f,apply(f,X0))) = apply(k,apply(X0,X0)),
inference(unit_resulting_resolution,[],[f46,f772]) ).
fof(f46,plain,
! [X0,X1] : apply(X0,X0) = apply(apply(f,apply(f,apply(f,X0))),X1),
inference(superposition,[],[f15,f11]) ).
fof(f591245,plain,
! [X0] : apply(k,apply(pair(X0,projection2),pair(X0,projection2))) = apply(f,apply(pair(apply(projection1,f),projection2),pair(X0,projection2))),
inference(forward_demodulation,[],[f591244,f132]) ).
fof(f132,plain,
! [X2,X0,X1] : apply(pair(X2,projection2),pair(X0,X1)) = pair(apply(X2,pair(X0,X1)),X1),
inference(superposition,[],[f5,f3]) ).
fof(f3,axiom,
! [X0,X1] : apply(projection2,pair(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection2) ).
fof(f5,axiom,
! [X2,X0,X1] : apply(pair(X0,X1),X2) = pair(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pairwise_application) ).
fof(f591244,plain,
! [X0] : apply(k,pair(apply(X0,pair(X0,projection2)),projection2)) = apply(f,apply(pair(apply(projection1,f),projection2),pair(X0,projection2))),
inference(forward_demodulation,[],[f590954,f118086]) ).
fof(f118086,plain,
! [X2,X0,X1] : apply(pair(apply(projection1,X0),projection2),pair(X1,X2)) = pair(apply(projection1,apply(X0,pair(X1,X2))),X2),
inference(superposition,[],[f132,f183]) ).
fof(f183,plain,
! [X0,X1] : apply(apply(projection1,X0),X1) = apply(projection1,apply(X0,X1)),
inference(superposition,[],[f143,f4]) ).
fof(f4,axiom,
! [X0] : pair(apply(projection1,X0),apply(projection2,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pairing) ).
fof(f143,plain,
! [X2,X0,X1] : apply(X0,X1) = apply(projection1,apply(pair(X0,X2),X1)),
inference(superposition,[],[f2,f5]) ).
fof(f2,axiom,
! [X0,X1] : apply(projection1,pair(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection1) ).
fof(f590954,plain,
! [X0] : apply(k,pair(apply(X0,pair(X0,projection2)),projection2)) = apply(f,pair(apply(projection1,apply(f,pair(X0,projection2))),projection2)),
inference(superposition,[],[f121188,f465390]) ).
fof(f465390,plain,
! [X0] : apply(projection1,apply(f,pair(X0,projection2))) = apply(k,apply(X0,pair(X0,projection2))),
inference(forward_demodulation,[],[f464909,f53945]) ).
fof(f53945,plain,
! [X0,X1] : pair(X1,X0) = apply(pair(projection2,projection1),pair(X0,X1)),
inference(superposition,[],[f116,f2]) ).
fof(f116,plain,
! [X2,X0,X1] : apply(pair(projection2,X2),pair(X0,X1)) = pair(X1,apply(X2,pair(X0,X1))),
inference(superposition,[],[f5,f3]) ).
fof(f464909,plain,
! [X0] : apply(projection1,apply(f,apply(pair(projection2,projection1),pair(projection2,X0)))) = apply(k,apply(X0,apply(pair(projection2,projection1),pair(projection2,X0)))),
inference(superposition,[],[f353863,f14442]) ).
fof(f14442,plain,
! [X0,X1] : apply(X0,X1) = apply(projection1,apply(apply(pair(projection2,projection1),pair(projection2,X0)),X1)),
inference(superposition,[],[f183,f14258]) ).
fof(f14258,plain,
! [X0] : apply(projection1,apply(pair(projection2,projection1),pair(projection2,X0))) = X0,
inference(superposition,[],[f8978,f1]) ).
fof(f8978,plain,
! [X0] : apply(X0,X0) = apply(projection1,apply(pair(projection2,projection1),pair(projection2,apply(X0,X0)))),
inference(forward_demodulation,[],[f8870,f131]) ).
fof(f131,plain,
! [X2,X0,X1] : apply(pair(X2,projection1),pair(X0,X1)) = pair(apply(X2,pair(X0,X1)),X0),
inference(superposition,[],[f5,f2]) ).
fof(f8870,plain,
! [X0] : apply(X0,X0) = apply(projection1,pair(apply(projection2,pair(projection2,apply(X0,X0))),projection2)),
inference(superposition,[],[f6927,f3094]) ).
fof(f3094,plain,
! [X0] : apply(apply(f,X0),n(projection1,projection2)) = apply(projection2,pair(projection2,apply(X0,X0))),
inference(superposition,[],[f142,f1010]) ).
fof(f1010,plain,
! [X0] : apply(pair(eq,apply(f,X0)),n(projection1,projection2)) = pair(projection2,apply(X0,X0)),
inference(superposition,[],[f879,f11]) ).
fof(f879,plain,
! [X0] : apply(pair(eq,X0),n(projection1,projection2)) = pair(projection2,apply(X0,n(projection1,projection2))),
inference(superposition,[],[f5,f872]) ).
fof(f872,plain,
projection2 = apply(eq,n(projection1,projection2)),
inference(forward_demodulation,[],[f867,f4]) ).
fof(f867,plain,
projection2 = apply(eq,pair(apply(projection1,n(projection1,projection2)),apply(projection2,n(projection1,projection2)))),
inference(unit_resulting_resolution,[],[f811,f8]) ).
fof(f8,axiom,
! [X0,X1] :
( projection2 = apply(eq,pair(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
fof(f811,plain,
apply(projection1,n(projection1,projection2)) != apply(projection2,n(projection1,projection2)),
inference(forward_demodulation,[],[f767,f144]) ).
fof(f144,plain,
! [X0,X1] : projection1 = apply(eq,apply(pair(X0,X0),X1)),
inference(superposition,[],[f7,f5]) ).
fof(f7,axiom,
! [X0] : projection1 = apply(eq,pair(X0,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality) ).
fof(f767,plain,
apply(apply(eq,apply(pair(k,k),projection2)),n(apply(eq,apply(pair(k,k),projection2)),projection2)) != apply(projection2,n(apply(eq,apply(pair(k,k),projection2)),projection2)),
inference(unit_resulting_resolution,[],[f140,f9]) ).
fof(f140,plain,
projection2 != apply(eq,apply(pair(k,k),projection2)),
inference(superposition,[],[f12,f5]) ).
fof(f12,axiom,
! [X1] : apply(eq,pair(apply(k,X1),apply(k,projection2))) != X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_self_referential) ).
fof(f142,plain,
! [X2,X0,X1] : apply(X2,X1) = apply(projection2,apply(pair(X0,X2),X1)),
inference(superposition,[],[f3,f5]) ).
fof(f6927,plain,
! [X0,X1] : apply(X0,X0) = apply(projection1,pair(apply(apply(f,X0),X1),projection2)),
inference(superposition,[],[f6685,f16]) ).
fof(f16,plain,
! [X2,X0,X1] : apply(apply(f,X0),X1) = apply(apply(f,X0),X2),
inference(superposition,[],[f11,f11]) ).
fof(f6685,plain,
! [X0] : apply(X0,X0) = apply(projection1,pair(apply(apply(f,X0),projection2),projection2)),
inference(forward_demodulation,[],[f6684,f152]) ).
fof(f152,plain,
! [X0,X1] : apply(pair(X1,pair(projection1,projection2)),X0) = pair(apply(X1,X0),X0),
inference(superposition,[],[f5,f138]) ).
fof(f138,plain,
! [X0] : apply(pair(projection1,projection2),X0) = X0,
inference(superposition,[],[f5,f4]) ).
fof(f6684,plain,
! [X0] : apply(X0,X0) = apply(projection1,apply(pair(apply(f,X0),pair(projection1,projection2)),projection2)),
inference(forward_demodulation,[],[f6493,f399]) ).
fof(f399,plain,
! [X2,X0,X1] : apply(pair(apply(f,X0),pair(projection1,projection2)),X1) = pair(apply(apply(f,X0),X2),X1),
inference(superposition,[],[f152,f16]) ).
fof(f6493,plain,
! [X0] : apply(X0,X0) = apply(projection1,pair(apply(apply(f,X0),apply(f,X0)),projection2)),
inference(superposition,[],[f6296,f15]) ).
fof(f6296,plain,
! [X0,X1] : apply(apply(f,X0),X1) = apply(projection1,pair(apply(X0,X0),projection2)),
inference(superposition,[],[f1095,f16]) ).
fof(f1095,plain,
! [X0] : apply(apply(f,X0),n(projection1,projection2)) = apply(projection1,pair(apply(X0,X0),projection2)),
inference(superposition,[],[f143,f932]) ).
fof(f932,plain,
! [X0] : apply(pair(apply(f,X0),eq),n(projection1,projection2)) = pair(apply(X0,X0),projection2),
inference(superposition,[],[f878,f11]) ).
fof(f878,plain,
! [X0] : apply(pair(X0,eq),n(projection1,projection2)) = pair(apply(X0,n(projection1,projection2)),projection2),
inference(superposition,[],[f5,f872]) ).
fof(f353863,plain,
! [X0] : apply(projection1,apply(f,X0)) = apply(k,apply(projection1,apply(X0,X0))),
inference(superposition,[],[f352537,f3234]) ).
fof(f352537,plain,
! [X0] : apply(projection1,apply(k,X0)) = apply(k,apply(projection1,X0)),
inference(unit_resulting_resolution,[],[f352422,f791]) ).
fof(f791,plain,
! [X0,X1] :
( apply(X1,n(X1,apply(k,X0))) != X0
| apply(k,X0) = X1 ),
inference(superposition,[],[f9,f1]) ).
fof(f352422,plain,
! [X0,X1] : apply(projection1,X1) = apply(apply(projection1,apply(k,X1)),X0),
inference(forward_demodulation,[],[f352070,f1]) ).
fof(f352070,plain,
! [X0,X1] : apply(apply(projection1,apply(k,X1)),X0) = apply(apply(apply(k,projection1),apply(k,X0)),X1),
inference(superposition,[],[f1156,f3169]) ).
fof(f3169,plain,
apply(k,projection1) = apply(abstraction,projection1),
inference(unit_resulting_resolution,[],[f1387,f772]) ).
fof(f1387,plain,
! [X0] : projection1 = apply(apply(abstraction,projection1),X0),
inference(unit_resulting_resolution,[],[f1266,f9]) ).
fof(f1266,plain,
! [X0,X1] : apply(projection1,X0) = apply(apply(apply(abstraction,projection1),X1),X0),
inference(forward_demodulation,[],[f1215,f1]) ).
fof(f1215,plain,
! [X0,X1] : apply(projection1,apply(apply(k,X0),apply(X1,X0))) = apply(apply(apply(abstraction,projection1),X1),X0),
inference(superposition,[],[f6,f183]) ).
fof(f6,axiom,
! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,apply(k,X2)),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
fof(f1156,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,X2),apply(k,X0)),X1) = apply(apply(X2,apply(k,X1)),X0),
inference(superposition,[],[f6,f1]) ).
fof(f121188,plain,
! [X0] : apply(k,pair(X0,projection2)) = apply(f,pair(apply(k,X0),projection2)),
inference(unit_resulting_resolution,[],[f118073,f3206]) ).
fof(f3206,plain,
! [X0,X1] :
( apply(X0,X0) != X1
| apply(f,X0) = apply(k,X1) ),
inference(superposition,[],[f772,f11]) ).
fof(f118073,plain,
! [X2,X0,X1] : pair(X0,X2) = apply(pair(apply(k,X0),projection2),pair(X1,X2)),
inference(superposition,[],[f132,f1]) ).
fof(f593902,plain,
! [X0,X1] : pair(apply(X0,pair(X0,projection2)),projection2) = apply(apply(f,apply(pair(apply(projection1,f),projection2),pair(X0,projection2))),X1),
inference(forward_demodulation,[],[f593901,f118086]) ).
fof(f593901,plain,
! [X0,X1] : pair(apply(X0,pair(X0,projection2)),projection2) = apply(apply(f,pair(apply(projection1,apply(f,pair(X0,projection2))),projection2)),X1),
inference(forward_demodulation,[],[f592692,f397797]) ).
fof(f397797,plain,
! [X0] : apply(projection1,apply(f,X0)) = apply(f,apply(projection1,apply(f,X0))),
inference(forward_demodulation,[],[f397567,f353863]) ).
fof(f397567,plain,
! [X0] : apply(k,apply(projection1,apply(X0,X0))) = apply(f,apply(projection1,apply(f,X0))),
inference(superposition,[],[f352541,f3234]) ).
fof(f352541,plain,
! [X0] : apply(k,apply(projection1,X0)) = apply(f,apply(projection1,apply(k,X0))),
inference(unit_resulting_resolution,[],[f352422,f3206]) ).
fof(f592692,plain,
! [X0,X1] : pair(apply(X0,pair(X0,projection2)),projection2) = apply(apply(f,pair(apply(f,apply(projection1,apply(f,pair(X0,projection2)))),projection2)),X1),
inference(superposition,[],[f540490,f398904]) ).
fof(f398904,plain,
! [X0,X1] : apply(X0,pair(X0,projection2)) = apply(apply(projection1,apply(f,pair(X0,projection2))),X1),
inference(forward_demodulation,[],[f398218,f53945]) ).
fof(f398218,plain,
! [X0,X1] : apply(X0,apply(pair(projection2,projection1),pair(projection2,X0))) = apply(apply(projection1,apply(f,apply(pair(projection2,projection1),pair(projection2,X0)))),X1),
inference(superposition,[],[f352552,f14442]) ).
fof(f352552,plain,
! [X0,X1] : apply(projection1,apply(X0,X0)) = apply(apply(projection1,apply(f,X0)),X1),
inference(superposition,[],[f352422,f3234]) ).
fof(f540490,plain,
! [X0,X1] : pair(apply(X0,X0),projection2) = apply(apply(f,pair(apply(f,X0),projection2)),X1),
inference(forward_demodulation,[],[f540489,f771]) ).
fof(f540489,plain,
! [X0,X1] : pair(apply(X0,X0),projection2) = apply(apply(f,apply(f,pair(apply(f,X0),projection2))),X1),
inference(forward_demodulation,[],[f539936,f420337]) ).
fof(f420337,plain,
! [X0] : pair(apply(f,X0),apply(k,projection2)) = apply(f,pair(apply(f,X0),projection2)),
inference(forward_demodulation,[],[f420026,f121901]) ).
fof(f121901,plain,
! [X0,X1] : apply(k,pair(apply(apply(f,X0),X1),projection2)) = apply(f,pair(apply(f,X0),projection2)),
inference(superposition,[],[f121188,f3232]) ).
fof(f420026,plain,
! [X0,X1] : pair(apply(f,X0),apply(k,projection2)) = apply(k,pair(apply(apply(f,X0),X1),projection2)),
inference(superposition,[],[f418203,f3232]) ).
fof(f418203,plain,
! [X0] : pair(apply(k,X0),apply(k,projection2)) = apply(k,pair(X0,projection2)),
inference(forward_demodulation,[],[f418202,f2]) ).
fof(f418202,plain,
! [X0] : apply(k,pair(X0,projection2)) = pair(apply(k,apply(projection1,pair(X0,projection2))),apply(k,projection2)),
inference(forward_demodulation,[],[f418149,f352537]) ).
fof(f418149,plain,
! [X0] : apply(k,pair(X0,projection2)) = pair(apply(projection1,apply(k,pair(X0,projection2))),apply(k,projection2)),
inference(superposition,[],[f4,f417832]) ).
fof(f417832,plain,
! [X0] : apply(k,projection2) = apply(projection2,apply(k,pair(X0,projection2))),
inference(superposition,[],[f417066,f121188]) ).
fof(f417066,plain,
! [X0] : apply(k,projection2) = apply(projection2,apply(f,pair(X0,projection2))),
inference(unit_resulting_resolution,[],[f416773,f791]) ).
fof(f416773,plain,
! [X0,X1] : projection2 = apply(apply(projection2,apply(f,pair(X0,projection2))),X1),
inference(forward_demodulation,[],[f415983,f771]) ).
fof(f415983,plain,
! [X0,X1] : projection2 = apply(apply(projection2,apply(f,apply(f,pair(X0,projection2)))),X1),
inference(superposition,[],[f353189,f8352]) ).
fof(f8352,plain,
! [X0,X1] : projection2 = apply(projection2,apply(apply(f,pair(X0,projection2)),X1)),
inference(superposition,[],[f3029,f927]) ).
fof(f927,plain,
! [X0] : pair(X0,projection2) = apply(pair(apply(k,X0),eq),n(projection1,projection2)),
inference(superposition,[],[f878,f1]) ).
fof(f3029,plain,
! [X0,X1] : projection2 = apply(projection2,apply(apply(f,apply(pair(X0,eq),n(projection1,projection2))),X1)),
inference(forward_demodulation,[],[f3028,f872]) ).
fof(f3028,plain,
! [X0,X1] : apply(eq,n(projection1,projection2)) = apply(projection2,apply(apply(f,apply(pair(X0,eq),n(projection1,projection2))),X1)),
inference(forward_demodulation,[],[f3027,f142]) ).
fof(f3027,plain,
! [X0,X1] : apply(projection2,apply(pair(X0,eq),n(projection1,projection2))) = apply(projection2,apply(apply(f,apply(pair(X0,eq),n(projection1,projection2))),X1)),
inference(forward_demodulation,[],[f3026,f771]) ).
fof(f3026,plain,
! [X0,X1] : apply(projection2,apply(pair(X0,eq),n(projection1,projection2))) = apply(projection2,apply(apply(f,apply(f,apply(pair(X0,eq),n(projection1,projection2)))),X1)),
inference(forward_demodulation,[],[f3012,f771]) ).
fof(f3012,plain,
! [X0,X1] : apply(projection2,apply(pair(X0,eq),n(projection1,projection2))) = apply(projection2,apply(apply(f,apply(f,apply(f,apply(pair(X0,eq),n(projection1,projection2))))),X1)),
inference(superposition,[],[f952,f46]) ).
fof(f952,plain,
! [X0,X1] : apply(projection2,X1) = apply(projection2,apply(apply(pair(X0,eq),n(projection1,projection2)),X1)),
inference(superposition,[],[f142,f878]) ).
fof(f353189,plain,
! [X0,X1] : apply(projection2,apply(X0,X0)) = apply(apply(projection2,apply(f,X0)),X1),
inference(superposition,[],[f352423,f3234]) ).
fof(f352423,plain,
! [X0,X1] : apply(projection2,X1) = apply(apply(projection2,apply(k,X1)),X0),
inference(forward_demodulation,[],[f352071,f1]) ).
fof(f352071,plain,
! [X0,X1] : apply(apply(projection2,apply(k,X1)),X0) = apply(apply(apply(k,projection2),apply(k,X0)),X1),
inference(superposition,[],[f1156,f3177]) ).
fof(f3177,plain,
apply(k,projection2) = apply(abstraction,projection2),
inference(unit_resulting_resolution,[],[f1439,f772]) ).
fof(f1439,plain,
! [X0] : projection2 = apply(apply(abstraction,projection2),X0),
inference(unit_resulting_resolution,[],[f1267,f9]) ).
fof(f1267,plain,
! [X0,X1] : apply(projection2,X0) = apply(apply(apply(abstraction,projection2),X1),X0),
inference(forward_demodulation,[],[f1216,f1]) ).
fof(f1216,plain,
! [X0,X1] : apply(projection2,apply(apply(k,X0),apply(X1,X0))) = apply(apply(apply(abstraction,projection2),X1),X0),
inference(superposition,[],[f6,f175]) ).
fof(f175,plain,
! [X0,X1] : apply(apply(projection2,X0),X1) = apply(projection2,apply(X0,X1)),
inference(superposition,[],[f142,f4]) ).
fof(f539936,plain,
! [X0,X1] : pair(apply(X0,X0),projection2) = apply(apply(f,pair(apply(f,X0),apply(k,projection2))),X1),
inference(superposition,[],[f17,f420024]) ).
fof(f420024,plain,
! [X0] : pair(apply(f,X0),apply(k,projection2)) = apply(k,pair(apply(X0,X0),projection2)),
inference(superposition,[],[f418203,f3234]) ).
fof(f17,plain,
! [X0,X1] : apply(apply(f,apply(k,X0)),X1) = X0,
inference(superposition,[],[f11,f1]) ).
fof(f420142,plain,
! [X0] : apply(eq,apply(k,pair(X0,projection2))) != X0,
inference(superposition,[],[f12,f418203]) ).
fof(f1133,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,apply(k,X0)),X2),X1) = apply(X0,apply(X2,X1)),
inference(superposition,[],[f6,f1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL076-1 : TPTP v8.2.0. Released v1.2.0.
% 0.13/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat May 18 13:05:38 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (19262)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.36 % (19263)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37 TRYING [1]
% 0.21/0.37 TRYING [2]
% 0.21/0.38 % (19265)WARNING: value z3 for option sas not known
% 0.21/0.38 % (19264)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (19266)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (19267)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.38 % (19265)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.38 % (19268)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.38 TRYING [3]
% 0.21/0.38 % (19269)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.39 TRYING [3]
% 0.21/0.40 TRYING [4]
% 0.21/0.40 TRYING [4]
% 0.21/0.44 TRYING [5]
% 0.21/0.47 TRYING [5]
% 0.21/0.50 TRYING [6]
% 1.78/0.64 TRYING [7]
% 2.22/0.70 TRYING [6]
% 3.89/0.93 TRYING [8]
% 7.40/1.41 TRYING [7]
% 7.90/1.48 TRYING [1]
% 7.90/1.48 TRYING [2]
% 7.90/1.48 TRYING [3]
% 7.90/1.49 TRYING [4]
% 8.21/1.52 TRYING [5]
% 8.45/1.58 TRYING [6]
% 9.53/1.72 TRYING [9]
% 9.53/1.74 TRYING [7]
% 12.16/2.09 TRYING [8]
% 18.10/2.94 TRYING [9]
% 30.79/4.74 TRYING [10]
% 32.24/4.96 TRYING [10]
% 34.23/5.29 TRYING [8]
% 56.00/8.43 TRYING [11]
% 63.92/9.50 TRYING [11]
% 103.42/15.16 TRYING [12]
% 138.02/20.07 % (19269)First to succeed.
% 138.02/20.08 % (19269)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19262"
% 138.02/20.09 % (19269)Refutation found. Thanks to Tanya!
% 138.02/20.09 % SZS status Unsatisfiable for theBenchmark
% 138.02/20.09 % SZS output start Proof for theBenchmark
% See solution above
% 138.02/20.09 % (19269)------------------------------
% 138.02/20.09 % (19269)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 138.02/20.09 % (19269)Termination reason: Refutation
% 138.02/20.09
% 138.02/20.09 % (19269)Memory used [KB]: 102056
% 138.02/20.09 % (19269)Time elapsed: 19.710 s
% 138.02/20.09 % (19269)Instructions burned: 47572 (million)
% 138.02/20.09 % (19262)Success in time 19.671 s
%------------------------------------------------------------------------------