TSTP Solution File: COL006-3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COL006-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.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 : Sun May 5 04:45:32 EDT 2024
% Result : Unsatisfiable 195.82s 28.35s
% Output : Refutation 195.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 38 unt; 0 def)
% Number of atoms : 42 ( 38 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 14 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 86 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f105702,plain,
$false,
inference(subsumption_resolution,[],[f105701,f3017]) ).
fof(f3017,plain,
! [X2,X3,X0,X1] : apply(apply(apply(s,X0),X0),X1) = apply(apply(apply(s,apply(apply(s,k),X2)),apply(apply(s,k),X3)),apply(X0,X1)),
inference(superposition,[],[f96,f1]) ).
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
fof(f96,plain,
! [X2,X0,X1] : apply(apply(apply(s,apply(apply(s,k),X0)),apply(apply(s,k),X2)),X1) = apply(X1,X1),
inference(superposition,[],[f21,f13]) ).
fof(f13,plain,
! [X0,X1] : apply(apply(apply(s,k),X1),X0) = X0,
inference(superposition,[],[f1,f2]) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
fof(f21,plain,
! [X2,X0,X1] : apply(apply(apply(s,X2),apply(apply(s,k),X0)),X1) = apply(apply(X2,X1),X1),
inference(superposition,[],[f1,f13]) ).
fof(f105701,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),
inference(forward_demodulation,[],[f105700,f2]) ).
fof(f105700,plain,
apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(forward_demodulation,[],[f105699,f2]) ).
fof(f105699,plain,
apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))) != apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)),apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt))),
inference(forward_demodulation,[],[f105698,f11428]) ).
fof(f11428,plain,
! [X2,X3,X0,X1] : apply(apply(apply(X0,X3),apply(X1,X3)),apply(X2,X3)) = apply(apply(apply(apply(s,X0),X1),X3),apply(X2,X3)),
inference(superposition,[],[f8,f1]) ).
fof(f8,plain,
! [X2,X3,X0,X1] : apply(apply(apply(s,apply(apply(s,X0),X1)),X3),X2) = apply(apply(apply(X0,X2),apply(X1,X2)),apply(X3,X2)),
inference(superposition,[],[f1,f1]) ).
fof(f105698,plain,
apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(apply(s,apply(k,s)),k),fixed_pt),apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt))) != apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),
inference(forward_demodulation,[],[f105697,f1]) ).
fof(f105697,plain,
apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)) != apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),
inference(forward_demodulation,[],[f105696,f2]) ).
fof(f105696,plain,
apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)) != apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),
inference(forward_demodulation,[],[f105695,f47868]) ).
fof(f47868,plain,
! [X2,X3,X0,X1,X4] : apply(apply(apply(s,X3),apply(apply(apply(s,X0),X2),X1)),X4) = apply(apply(apply(s,X3),apply(apply(X0,X1),apply(X2,X1))),X4),
inference(forward_demodulation,[],[f47342,f10]) ).
fof(f10,plain,
! [X2,X0,X1] : apply(apply(apply(s,X2),apply(k,X0)),X1) = apply(apply(X2,X1),X0),
inference(superposition,[],[f1,f2]) ).
fof(f47342,plain,
! [X2,X3,X0,X1,X4] : apply(apply(apply(apply(s,s),apply(k,apply(apply(X0,X1),apply(X2,X1)))),X3),X4) = apply(apply(apply(s,X3),apply(apply(apply(s,X0),X2),X1)),X4),
inference(superposition,[],[f1208,f45574]) ).
fof(f45574,plain,
! [X2,X3,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(k,apply(apply(X0,X2),apply(X1,X2))),X3),
inference(superposition,[],[f2,f43617]) ).
fof(f43617,plain,
! [X2,X3,X0,X1] : apply(X0,apply(apply(apply(s,X1),X2),X3)) = apply(X0,apply(apply(X1,X3),apply(X2,X3))),
inference(forward_demodulation,[],[f42232,f2]) ).
fof(f42232,plain,
! [X2,X3,X0,X1] : apply(X0,apply(apply(apply(s,X1),X2),X3)) = apply(apply(apply(k,X0),X3),apply(apply(X1,X3),apply(X2,X3))),
inference(superposition,[],[f11,f7]) ).
fof(f7,plain,
! [X2,X0,X1] : apply(X0,apply(X2,X1)) = apply(apply(apply(s,apply(k,X0)),X2),X1),
inference(superposition,[],[f1,f2]) ).
fof(f11,plain,
! [X2,X3,X0,X1] : apply(apply(apply(s,X3),apply(apply(s,X0),X1)),X2) = apply(apply(X3,X2),apply(apply(X0,X2),apply(X1,X2))),
inference(superposition,[],[f1,f1]) ).
fof(f1208,plain,
! [X2,X0,X1] : apply(apply(apply(apply(s,s),X2),X0),X1) = apply(apply(apply(s,X0),apply(X2,X0)),X1),
inference(superposition,[],[f6,f1]) ).
fof(f6,plain,
! [X2,X0,X1] : apply(apply(X0,X2),apply(apply(X1,X0),X2)) = apply(apply(apply(apply(s,s),X1),X0),X2),
inference(superposition,[],[f1,f1]) ).
fof(f105695,plain,
apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)) != apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(apply(s,apply(k,s)),k),fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),
inference(forward_demodulation,[],[f105694,f9315]) ).
fof(f9315,plain,
! [X2,X3,X0,X1] : apply(apply(apply(s,apply(s,apply(k,X3))),apply(X1,X2)),X0) = apply(X3,apply(apply(apply(apply(s,s),apply(s,X1)),apply(k,X0)),X2)),
inference(superposition,[],[f33,f1286]) ).
fof(f1286,plain,
! [X2,X0,X1] : apply(apply(apply(apply(s,s),apply(s,X0)),apply(k,X1)),X2) = apply(X1,apply(apply(X0,X2),X1)),
inference(forward_demodulation,[],[f1156,f2]) ).
fof(f1156,plain,
! [X2,X0,X1] : apply(apply(apply(apply(s,s),apply(s,X0)),apply(k,X1)),X2) = apply(apply(apply(k,X1),X2),apply(apply(X0,X2),X1)),
inference(superposition,[],[f6,f10]) ).
fof(f33,plain,
! [X2,X0,X1] : apply(apply(apply(s,apply(s,apply(k,X0))),X2),X1) = apply(X0,apply(X1,apply(X2,X1))),
inference(superposition,[],[f7,f1]) ).
fof(f105694,plain,
apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)) != apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)),
inference(forward_demodulation,[],[f105693,f17]) ).
fof(f17,plain,
! [X0,X1] : apply(X1,X0) = apply(apply(apply(s,apply(s,k)),X1),X0),
inference(superposition,[],[f13,f1]) ).
fof(f105693,plain,
apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)) != apply(apply(apply(s,apply(s,k)),fixed_pt),apply(apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)),
inference(forward_demodulation,[],[f105692,f1]) ).
fof(f105692,plain,
apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)) != apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt),
inference(forward_demodulation,[],[f105266,f1264]) ).
fof(f1264,plain,
! [X2,X0,X1] : apply(X2,apply(apply(X1,X2),apply(apply(X0,X1),X2))) = apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(apply(s,s),X0),X1)),X2),
inference(superposition,[],[f25,f6]) ).
fof(f25,plain,
! [X0,X1] : apply(X0,apply(X1,X0)) = apply(apply(apply(s,apply(s,apply(s,k))),X1),X0),
inference(superposition,[],[f17,f1]) ).
fof(f105266,plain,
apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)) != apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt))),
inference(unit_resulting_resolution,[],[f4,f14]) ).
fof(f14,plain,
! [X0,X1] :
( apply(apply(X0,fixed_pt),apply(X1,fixed_pt)) != apply(fixed_pt,apply(apply(X0,fixed_pt),apply(X1,fixed_pt)))
| fixed_point(apply(apply(s,X0),X1)) ),
inference(superposition,[],[f3,f1]) ).
fof(f3,axiom,
! [X3] :
( apply(X3,fixed_pt) != apply(fixed_pt,apply(X3,fixed_pt))
| fixed_point(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,axiom,
~ fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL006-3 : TPTP v8.1.2. Released v1.0.0.
% 0.15/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n005.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 18:33:38 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 % (28179)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (28182)WARNING: value z3 for option sas not known
% 0.22/0.38 % (28180)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (28183)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (28181)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (28185)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)
% 0.22/0.38 % (28182)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)
% 0.22/0.38 % (28186)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)
% 0.22/0.38 % (28184)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)
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.38 TRYING [3]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 TRYING [4]
% 0.22/0.40 TRYING [5]
% 0.22/0.40 TRYING [4]
% 0.22/0.43 TRYING [6]
% 0.22/0.43 TRYING [5]
% 0.22/0.50 TRYING [7]
% 0.22/0.51 TRYING [6]
% 1.56/0.62 TRYING [8]
% 2.28/0.73 TRYING [7]
% 4.83/1.04 TRYING [9]
% 7.76/1.48 TRYING [1]
% 7.76/1.48 TRYING [2]
% 7.76/1.48 TRYING [3]
% 8.02/1.48 TRYING [4]
% 8.02/1.49 TRYING [5]
% 8.02/1.52 TRYING [6]
% 8.44/1.58 TRYING [7]
% 9.38/1.72 TRYING [10]
% 9.38/1.74 TRYING [8]
% 10.25/1.81 TRYING [8]
% 11.48/2.02 TRYING [9]
% 16.29/2.76 TRYING [10]
% 21.45/3.45 TRYING [11]
% 29.63/4.59 TRYING [11]
% 33.18/5.09 TRYING [12]
% 33.18/5.14 TRYING [9]
% 51.04/7.65 TRYING [13]
% 67.39/9.97 TRYING [12]
% 82.55/12.14 TRYING [14]
% 130.16/18.94 TRYING [10]
% 173.99/25.25 TRYING [15]
% 195.82/28.31 % (28186)First to succeed.
% 195.82/28.33 % (28186)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28179"
% 195.82/28.35 % (28186)Refutation found. Thanks to Tanya!
% 195.82/28.35 % SZS status Unsatisfiable for theBenchmark
% 195.82/28.35 % SZS output start Proof for theBenchmark
% See solution above
% 195.82/28.35 % (28186)------------------------------
% 195.82/28.35 % (28186)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 195.82/28.35 % (28186)Termination reason: Refutation
% 195.82/28.35
% 195.82/28.35 % (28186)Memory used [KB]: 213097
% 195.82/28.35 % (28186)Time elapsed: 27.953 s
% 195.82/28.35 % (28186)Instructions burned: 68470 (million)
% 195.82/28.35 % (28179)Success in time 27.893 s
%------------------------------------------------------------------------------