%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ054-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:31:23 PM UTC 2026
% Result : Satisfiable 0.19s 1.81s
% Output : Saturation 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(two_blacks_out_one_black_in,axiom,
( ~ p(X0,s(s(X1)))
| p(X0,s(X1)) ) ).
cnf(u132,axiom,
p(s(s(s(s(n0)))),s(s(s(s(s(s(n0))))))) ).
cnf(u13,axiom,
p(s(s(s(s(n0)))),s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))) ).
cnf(u149,axiom,
p(s(s(s(s(n0)))),s(s(s(s(s(n0)))))) ).
cnf(u42,axiom,
p(n0,s(s(s(s(s(s(s(s(s(s(n0))))))))))) ).
cnf(goal_state,negated_conjecture,
~ p(s(n0),n0) ).
cnf(u34,axiom,
p(n0,s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))) ).
cnf(u7,axiom,
p(s(s(s(s(s(s(s(s(n0)))))))),s(s(s(s(s(s(s(s(s(s(n0))))))))))) ).
cnf(u171,axiom,
p(s(s(s(s(n0)))),s(n0)) ).
cnf(u161,axiom,
p(s(s(s(s(n0)))),s(s(s(n0)))) ).
cnf(u46,axiom,
p(n0,s(s(s(s(s(s(s(s(s(n0)))))))))) ).
cnf(u38,axiom,
p(n0,s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))) ).
cnf(u123,axiom,
p(s(s(n0)),s(s(s(n0)))) ).
cnf(u74,axiom,
p(n0,s(s(n0))) ).
cnf(u165,axiom,
p(s(s(s(s(n0)))),s(s(n0))) ).
cnf(u84,axiom,
p(s(s(s(s(n0)))),s(s(s(s(s(s(s(s(n0))))))))) ).
cnf(u66,axiom,
p(n0,s(s(s(s(n0))))) ).
cnf(u26,axiom,
p(s(s(n0)),s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))) ).
cnf(u117,axiom,
p(s(s(n0)),s(s(s(s(n0))))) ).
cnf(u78,axiom,
p(n0,s(n0)) ).
cnf(u174,axiom,
p(s(s(s(s(n0)))),n0) ).
cnf(u69,axiom,
p(s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(s(n0)))))))) ).
cnf(u87,axiom,
p(s(s(n0)),s(s(s(s(s(s(s(s(s(n0)))))))))) ).
cnf(u70,axiom,
p(n0,s(s(s(n0)))) ).
cnf(u155,axiom,
p(s(s(s(s(n0)))),s(s(s(s(n0))))) ).
cnf(u111,axiom,
p(s(s(n0)),s(s(s(s(s(n0)))))) ).
cnf(u30,axiom,
p(n0,s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))) ).
cnf(u105,axiom,
p(s(s(n0)),s(s(s(s(s(s(n0))))))) ).
cnf(u57,axiom,
p(s(s(s(s(s(s(s(s(s(s(n0)))))))))),s(s(s(s(n0))))) ).
cnf(u8,axiom,
p(s(s(s(s(s(s(s(s(s(s(n0)))))))))),s(s(s(s(s(s(s(s(n0))))))))) ).
cnf(u10,axiom,
p(s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))) ).
cnf(u143,axiom,
p(s(s(s(s(s(s(s(s(n0)))))))),s(s(n0))) ).
cnf(u20,axiom,
p(s(s(s(s(n0)))),s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))) ).
cnf(two_whites_out_one_black_in,axiom,
( ~ p(s(s(X0)),X1)
| p(X0,s(X1)) ) ).
cnf(u61,axiom,
p(s(s(n0)),s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))) ).
cnf(u129,axiom,
p(s(s(n0)),s(s(n0))) ).
cnf(u139,axiom,
p(s(s(n0)),n0) ).
cnf(u53,axiom,
p(s(s(s(s(s(s(s(s(n0)))))))),s(s(s(s(s(s(n0))))))) ).
cnf(u14,axiom,
p(s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(s(s(s(s(n0))))))))))) ).
cnf(u135,axiom,
p(s(s(n0)),s(n0)) ).
cnf(u49,axiom,
p(s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(s(s(n0))))))))) ).
cnf(u81,axiom,
p(s(s(n0)),s(s(s(s(s(s(s(s(s(s(n0))))))))))) ).
cnf(u168,axiom,
p(s(s(s(s(s(s(n0)))))),s(s(n0))) ).
cnf(u41,axiom,
p(s(s(s(s(s(s(s(s(s(s(n0)))))))))),s(s(s(s(s(n0)))))) ).
cnf(u181,axiom,
p(s(s(s(s(s(s(n0)))))),n0) ).
cnf(u120,axiom,
p(s(s(s(s(s(s(s(s(n0)))))))),s(s(s(n0)))) ).
cnf(u93,axiom,
p(s(s(n0)),s(s(s(s(s(s(s(s(n0))))))))) ).
cnf(u99,axiom,
p(s(s(n0)),s(s(s(s(s(s(s(n0)))))))) ).
cnf(u172,axiom,
p(s(s(s(s(s(s(s(s(n0)))))))),n0) ).
cnf(two_different_balls_out_one_white_in,axiom,
( ~ p(s(X0),s(X1))
| p(s(X0),X1) ) ).
cnf(u114,axiom,
p(s(s(s(s(s(s(n0)))))),s(s(s(s(s(n0)))))) ).
cnf(u45,axiom,
p(s(s(s(s(n0)))),s(s(s(s(s(s(s(s(s(s(n0))))))))))) ).
cnf(u96,axiom,
p(s(s(s(s(s(s(s(s(n0)))))))),s(s(s(s(n0))))) ).
cnf(u37,axiom,
p(s(s(s(s(s(s(s(s(n0)))))))),s(s(s(s(s(s(s(n0)))))))) ).
cnf(u126,axiom,
p(s(s(s(s(s(s(s(s(s(s(n0)))))))))),s(n0)) ).
cnf(u73,axiom,
p(s(s(s(s(s(s(s(s(n0)))))))),s(s(s(s(s(n0)))))) ).
cnf(u152,axiom,
p(s(s(s(s(s(s(n0)))))),s(s(s(n0)))) ).
cnf(u33,axiom,
p(s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(s(s(s(n0)))))))))) ).
cnf(u65,axiom,
p(s(s(s(s(n0)))),s(s(s(s(s(s(s(s(s(n0)))))))))) ).
cnf(u108,axiom,
p(s(s(s(s(n0)))),s(s(s(s(s(s(s(n0)))))))) ).
cnf(u25,axiom,
p(n0,s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))) ).
cnf(u77,axiom,
p(s(s(s(s(s(s(s(s(s(s(n0)))))))))),s(s(s(n0)))) ).
cnf(u17,axiom,
p(s(s(s(s(s(s(s(s(s(s(n0)))))))))),s(s(s(s(s(s(s(n0)))))))) ).
cnf(u19,axiom,
p(s(s(n0)),s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))) ).
cnf(u158,axiom,
p(s(s(s(s(s(s(s(s(n0)))))))),s(n0)) ).
cnf(u29,axiom,
p(s(s(s(s(s(s(s(s(s(s(n0)))))))))),s(s(s(s(s(s(n0))))))) ).
cnf(u138,axiom,
p(s(s(s(s(s(s(n0)))))),s(s(s(s(n0))))) ).
cnf(u58,axiom,
p(n0,s(s(s(s(s(s(n0))))))) ).
cnf(u145,axiom,
p(s(s(s(s(s(s(s(s(s(s(n0)))))))))),n0) ).
cnf(u50,axiom,
p(n0,s(s(s(s(s(s(s(s(n0))))))))) ).
cnf(u23,axiom,
p(s(s(s(s(s(s(s(s(n0)))))))),s(s(s(s(s(s(s(s(n0))))))))) ).
cnf(u102,axiom,
p(s(s(s(s(s(s(s(s(s(s(n0)))))))))),s(s(n0))) ).
cnf(u62,axiom,
p(n0,s(s(s(s(s(n0)))))) ).
cnf(u54,axiom,
p(n0,s(s(s(s(s(s(s(n0)))))))) ).
cnf(u11,axiom,
p(s(s(s(s(s(s(s(s(n0)))))))),s(s(s(s(s(s(s(s(s(n0)))))))))) ).
cnf(initial_state,axiom,
p(s(s(s(s(s(s(s(s(s(s(n0)))))))))),s(s(s(s(s(s(s(s(s(n0)))))))))) ).
cnf(u90,axiom,
p(s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(n0))))))) ).
cnf(u178,axiom,
p(s(s(s(s(s(s(n0)))))),s(n0)) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ054-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 % Computer : n002.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Sun Sep 27 22:39:37 UTC 2026
% 0.10/0.41 % CPUTime :
% 0.10/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.46 Running first-order theorem proving
% 0.10/0.46 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
% 0.19/1.81 % (3957217)Input is clausal, will run a generic CNF schedule.
% 0.19/1.81 % (3957248)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2757099045:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.19/1.81 % (3957248)Refutation not found, incomplete strategy
% 0.19/1.81 % (3957248)------------------------------
% 0.19/1.81 % (3957248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.81 % (3957248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.81 % (3957248)CaDiCaL version: 2.1.3
% 0.19/1.81 % (3957248)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.81 % (3957248)Time elapsed: 0.003 s
% 0.19/1.81 % (3957248)Peak memory usage: 87 MB
% 0.19/1.81 % (3957248)Instructions burned: 4 (million)
% 0.19/1.81 % (3957246)lrs+10_1_sil=8000:sp=occurrence:random_seed=1359025194:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.19/1.81 % (3957246)First to succeed.
% 0.19/1.81 % (3957246)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3957217"
% 0.19/1.81 % (3957243)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=3061789102:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.19/1.81 % (3957250)dis-21_1_sil=8000:lcm=predicate:random_seed=1666858019: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)
% 0.19/1.81 % (3957245)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2249810118:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.19/1.81 % (3957244)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=46912214:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.19/1.81 % (3957250)Also succeeded, but the first one will report.
% 0.19/1.81 % (3957249)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3617759237:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.19/1.81 % (3957249)Instruction limit reached!
% 0.19/1.81 % (3957249)------------------------------
% 0.19/1.81 % (3957249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.81 % (3957249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.81 % (3957249)CaDiCaL version: 2.1.3
% 0.19/1.81 % (3957249)Termination reason: Instruction limit
% 0.19/1.81 % (3957249)Termination phase: Saturation
% 0.19/1.81 % (3957249)Time elapsed: 0.147 s
% 0.19/1.81 % (3957249)Peak memory usage: 88 MB
% 0.19/1.81 % (3957249)Instructions burned: 180 (million)
% 0.19/1.81 % (3957248)------------------------------
% 0.19/1.81 % (3957248)------------------------------
% 0.19/1.81 % (3957263)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2592389708:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 0.19/1.81 % (3957263)Refutation not found, incomplete strategy
% 0.19/1.81 % (3957263)------------------------------
% 0.19/1.81 % (3957263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.81 % (3957263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.81 % (3957263)CaDiCaL version: 2.1.3
% 0.19/1.81 % (3957263)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.81 % (3957263)Time elapsed: 0.001 s
% 0.19/1.81 % (3957263)Peak memory usage: 87 MB
% 0.19/1.81 % (3957265)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1334304147:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 0.19/1.81 % SZS status Satisfiable for theBenchmark
% 0.19/1.81 % SZS output start Saturation.
% See solution above
% 0.19/1.81 % SZS output start Definitions and Model Updates.
% 0.19/1.81 % SZS output end Definitions and Model Updates.
% 0.19/1.81 % (3957246)------------------------------
% 0.19/1.81 % (3957246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.81 % (3957246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.81 % (3957246)CaDiCaL version: 2.1.3
% 0.19/1.81 % (3957246)Termination reason: Satisfiable
% 0.19/1.81 % (3957246)Time elapsed: 0.005 s
% 0.19/1.81 % (3957246)Peak memory usage: 87 MB
% 0.19/1.81 % (3957246)Instructions burned: 4 (million)
% 0.19/1.81 % (3957246)------------------------------
% 0.19/1.81 % (3957246)------------------------------
% 0.19/1.81 % (3957217)Success in time 0.563 s
% 0.19/1.81 % Vampire exiting
%------------------------------------------------------------------------------