%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 12:31:54 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 40 ( 37 unt; 0 def)
% Number of atoms : 43 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 12 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Maximal term depth : 9 ( 2 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 : 23 ( 23 !; 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/sandbox/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/sandbox/benchmark/theBenchmark.p',place_vertical_pieces) ).
fof(f9,axiom,
successor(n1) = n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_1_is_2) ).
fof(f10,axiom,
successor(n2) = n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_2_is_3) ).
fof(f11,axiom,
successor(n3) = n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_3_is_4) ).
fof(f12,axiom,
successor(n4) = n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_4_is_5) ).
fof(f13,axiom,
successor(n5) = n6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_5_is_6) ).
fof(f14,axiom,
successor(n6) = n7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_6_is_7) ).
fof(f15,axiom,
successor(n7) = n8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_7_is_8) ).
fof(f17,axiom,
complement(covered) = not_covered,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',prove_row_8_can_be_covered) ).
fof(f25,plain,
not_covered = complement(complement(not_covered)),
inference(forward_demodulation,[],[f18,f20]) ).
fof(f31,plain,
! [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,complement(not_covered),complement(not_covered),X2,X3,X4,X5,X6)) ),
inference(forward_demodulation,[],[f2,f20]) ).
fof(f33,plain,
~ achievable(row(successor(n7)),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(superposition,[],[f24,f15]) ).
fof(f34,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(forward_demodulation,[],[f33,f20]) ).
fof(f35,plain,
~ achievable(row(successor(successor(n6))),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(forward_demodulation,[],[f34,f14]) ).
fof(f36,plain,
~ achievable(row(successor(successor(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(forward_demodulation,[],[f35,f13]) ).
fof(f37,plain,
~ achievable(row(successor(successor(successor(successor(n4))))),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(forward_demodulation,[],[f36,f12]) ).
fof(f38,plain,
~ achievable(row(successor(successor(successor(successor(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(forward_demodulation,[],[f37,f11]) ).
fof(f39,plain,
~ achievable(row(successor(successor(successor(successor(successor(successor(n2))))))),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(forward_demodulation,[],[f38,f10]) ).
fof(f40,plain,
~ achievable(row(successor(successor(successor(successor(successor(successor(successor(n1)))))))),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(forward_demodulation,[],[f39,f9]) ).
fof(f59,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(f72,plain,
achievable(row(successor(n1)),squares(complement(not_covered),not_covered,not_covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))),
inference(forward_demodulation,[],[f59,f22]) ).
fof(f85,plain,
achievable(row(successor(n1)),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,[],[f72,f31]) ).
fof(f131,plain,
achievable(row(successor(successor(n1))),squares(complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)))),
inference(resolution,[],[f85,f8]) ).
fof(f132,plain,
achievable(row(successor(successor(n1))),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(forward_demodulation,[],[f131,f25]) ).
fof(f140,plain,
achievable(row(successor(successor(successor(n1)))),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,[],[f132,f8]) ).
fof(f304,plain,
achievable(row(successor(successor(successor(successor(n1))))),squares(complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)))),
inference(resolution,[],[f140,f8]) ).
fof(f305,plain,
achievable(row(successor(successor(successor(successor(n1))))),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(forward_demodulation,[],[f304,f25]) ).
fof(f313,plain,
achievable(row(successor(successor(successor(successor(successor(n1)))))),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,[],[f305,f8]) ).
fof(f662,plain,
achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)))),
inference(resolution,[],[f313,f8]) ).
fof(f663,plain,
achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(forward_demodulation,[],[f662,f25]) ).
fof(f671,plain,
achievable(row(successor(successor(successor(successor(successor(successor(successor(n1)))))))),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,[],[f663,f8]) ).
fof(f672,plain,
$false,
inference(forward_subsumption_resolution,[],[f671,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n003.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 22:31:11 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.50 % (982705)Will run a generic schedule for satisfiability detection.
% 0.17/0.50 % (982720)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3763852586:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.50 % (982717)% WARNING: option uhcvi not known.
% 0.17/0.50 % (982721)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2031513044:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.50 % (982719)dis+10_1_sil=32000:sp=arity:random_seed=1857657074:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.50 % (982716)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3679490587_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.50 % (982718)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2331702819:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.50 % (982717)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1273267218:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.50 % (982722)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3080100632:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.50 % TRYING [1]
% 0.17/0.50 % TRYING [2]
% 0.17/0.50 % (982721) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-982705-982721"...
% 0.17/0.50 % (982721)...printing done.
% 0.17/0.50 % (982721)Refutation found. Thanks to Tanya!
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50 % (982721)------------------------------
% 0.17/0.50 % (982721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.50 % (982721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.50 % (982721)CaDiCaL version: 2.1.3
% 0.17/0.50 % (982721)Termination reason: Refutation
% 0.17/0.50 % (982721)Time elapsed: 0.021 s
% 0.17/0.50 % (982721)Peak memory usage: 11 MB
% 0.17/0.50 % (982721)Instructions burned: 39 (million)
% 0.17/0.50 % (982705)Success in time 0.063 s
% 0.17/0.50 % Vampire exiting
%------------------------------------------------------------------------------