%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:31:13 PM UTC 2026
% Result : Unsatisfiable 0.73s 1.01s
% Output : Refutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 41 ( 39 unt; 0 def)
% Number of atoms : 43 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-8 aty)
% Number of variables : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ achievable(row(X0),squares(X1,not_covered,not_covered,X2,X3,X4,X5,X6))
| achievable(row(X0),squares(X1,covered,covered,X2,X3,X4,X5,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cover_columns_2_and_3) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ achievable(row(X0),squares(X1,X2,X3,X4,X5,X6,X7,X8))
| achievable(row(successor(X0)),squares(complement(X1),complement(X2),complement(X3),complement(X4),complement(X5),complement(X6),complement(X7),complement(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',place_vertical_pieces) ).
fof(f9,axiom,
successor(n1) = n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_1_is_2) ).
fof(f10,axiom,
successor(n2) = n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_2_is_3) ).
fof(f11,axiom,
successor(n3) = n4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_3_is_4) ).
fof(f12,axiom,
successor(n4) = n5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_4_is_5) ).
fof(f13,axiom,
successor(n5) = n6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_5_is_6) ).
fof(f14,axiom,
successor(n6) = n7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_6_is_7) ).
fof(f15,axiom,
successor(n7) = n8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_7_is_8) ).
fof(f17,axiom,
complement(covered) = not_covered,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_covered_is_not_covered) ).
fof(f18,plain,
not_covered = complement(covered),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
complement(not_covered) = covered,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_not_covered_is_covered) ).
fof(f20,plain,
covered = complement(not_covered),
inference(reorient_equations,[],[f19]) ).
fof(f21,axiom,
complement(removed) = not_covered,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_removed_is_not_covered) ).
fof(f22,plain,
not_covered = complement(removed),
inference(reorient_equations,[],[f21]) ).
fof(f23,axiom,
achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_row_initially) ).
fof(f24,negated_conjecture,
~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_row_8_can_be_covered) ).
fof(f31,plain,
achievable(row(successor(n1)),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))),
inference(resolution,[],[f8,f23]) ).
fof(f34,plain,
achievable(row(successor(n1)),squares(covered,complement(removed),complement(removed),covered,covered,covered,covered,covered)),
inference(forward_demodulation,[],[f31,f20]) ).
fof(f36,plain,
achievable(row(successor(n1)),squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered)),
inference(forward_demodulation,[],[f34,f22]) ).
fof(f38,plain,
achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered)),
inference(forward_demodulation,[],[f36,f9]) ).
fof(f59,plain,
achievable(row(n2),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(resolution,[],[f38,f2]) ).
fof(f104,plain,
achievable(row(successor(n2)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))),
inference(resolution,[],[f59,f8]) ).
fof(f105,plain,
achievable(row(successor(n2)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(forward_demodulation,[],[f104,f18]) ).
fof(f106,plain,
achievable(row(n3),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(forward_demodulation,[],[f105,f10]) ).
fof(f193,plain,
achievable(row(successor(n3)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))),
inference(resolution,[],[f106,f8]) ).
fof(f194,plain,
achievable(row(successor(n3)),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(forward_demodulation,[],[f193,f20]) ).
fof(f195,plain,
achievable(row(n4),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(forward_demodulation,[],[f194,f11]) ).
fof(f337,plain,
achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))),
inference(resolution,[],[f195,f8]) ).
fof(f338,plain,
achievable(row(successor(n4)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(forward_demodulation,[],[f337,f18]) ).
fof(f339,plain,
achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(forward_demodulation,[],[f338,f12]) ).
fof(f536,plain,
achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))),
inference(resolution,[],[f339,f8]) ).
fof(f537,plain,
achievable(row(successor(n5)),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(forward_demodulation,[],[f536,f20]) ).
fof(f538,plain,
achievable(row(n6),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(forward_demodulation,[],[f537,f13]) ).
fof(f784,plain,
achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))),
inference(resolution,[],[f538,f8]) ).
fof(f785,plain,
achievable(row(successor(n6)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(forward_demodulation,[],[f784,f18]) ).
fof(f786,plain,
achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(forward_demodulation,[],[f785,f14]) ).
fof(f1072,plain,
achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))),
inference(resolution,[],[f786,f8]) ).
fof(f1073,plain,
achievable(row(successor(n7)),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(forward_demodulation,[],[f1072,f20]) ).
fof(f1074,plain,
achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(forward_demodulation,[],[f1073,f15]) ).
fof(f1075,plain,
$false,
inference(forward_subsumption_resolution,[],[f1074,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n009.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 22:29:30 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.73/1.01 % (2472205)Input is clausal, will run a generic CNF schedule.
% 0.73/1.01 % (2472215)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2107976058:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.73/1.01 % (2472214)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=76476583:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.73/1.01 % (2472212)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=979208024:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.73/1.01 % (2472215)First to succeed.
% 0.73/1.01 % (2472215)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2472205"
% 0.73/1.01 % (2472213)lrs+10_1_sil=8000:sp=occurrence:random_seed=3364098006:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.73/1.01 % (2472211)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=465288174:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.73/1.01 % (2472216)dis-21_1_sil=8000:lcm=predicate:random_seed=2169438753:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.73/1.01 % (2472210)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=2322318198:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.73/1.01 % (2472216)Refutation not found, incomplete strategy
% 0.73/1.01 % (2472216)------------------------------
% 0.73/1.01 % (2472216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.73/1.01 % (2472216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/1.01 % (2472216)CaDiCaL version: 2.1.3
% 0.73/1.01 % (2472216)Termination reason: Refutation not found, incomplete strategy
% 0.73/1.01 % (2472216)Time elapsed: 0.002 s
% 0.73/1.01 % (2472216)Peak memory usage: 88 MB
% 0.73/1.01 % (2472216)Instructions burned: 1 (million)
% 0.73/1.01 % (2472214)Instruction limit reached!
% 0.73/1.01 % (2472214)------------------------------
% 0.73/1.01 % (2472214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.73/1.01 % (2472214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/1.01 % (2472214)CaDiCaL version: 2.1.3
% 0.73/1.01 % (2472214)Termination reason: Instruction limit
% 0.73/1.01 % (2472214)Termination phase: Saturation
% 0.73/1.01 % (2472214)Time elapsed: 0.060 s
% 0.73/1.01 % (2472214)Peak memory usage: 88 MB
% 0.73/1.01 % (2472214)Instructions burned: 114 (million)
% 0.73/1.01 % (2472213)Instruction limit reached!
% 0.73/1.01 % (2472213)------------------------------
% 0.73/1.01 % (2472213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.73/1.01 % (2472213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/1.01 % (2472213)CaDiCaL version: 2.1.3
% 0.73/1.01 % (2472213)Termination reason: Instruction limit
% 0.73/1.01 % (2472213)Termination phase: Saturation
% 0.73/1.01 % (2472213)Time elapsed: 0.057 s
% 0.73/1.01 % (2472213)Peak memory usage: 89 MB
% 0.73/1.01 % (2472213)Instructions burned: 109 (million)
% 0.73/1.01 % (2472215)Refutation found. Thanks to Tanya!
% 0.73/1.01 % SZS status Unsatisfiable for theBenchmark
% 0.73/1.01 % SZS output start Proof for theBenchmark
% See solution above
% 0.73/1.01 % (2472215)------------------------------
% 0.73/1.01 % (2472215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.73/1.01 % (2472215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/1.01 % (2472215)CaDiCaL version: 2.1.3
% 0.73/1.01 % (2472215)Termination reason: Refutation
% 0.73/1.01 % (2472215)Time elapsed: 0.013 s
% 0.73/1.01 % (2472215)Peak memory usage: 88 MB
% 0.73/1.01 % (2472215)Instructions burned: 45 (million)
% 0.73/1.01 % (2472215)------------------------------
% 0.73/1.01 % (2472215)------------------------------
% 0.73/1.01 % (2472205)Success in time 0.29 s
% 0.73/1.01 % Vampire exiting
%------------------------------------------------------------------------------