%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN098-1.002 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 01:49:39 PM UTC 2026
% Result : Unsatisfiable 2.77s 1.15s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 30
% Syntax : Number of formulae : 71 ( 11 unt; 14 def)
% Number of atoms : 156 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 141 ( 56 ~; 71 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 30 ( 29 usr; 30 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
( u_1
| ~ p_0
| ~ q_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_s3_goal_1) ).
fof(f2,axiom,
~ u_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_1_s3_goal_1) ).
fof(f3,axiom,
( u_2
| p_0
| ~ p_1
| ~ p_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_s3_type11_1) ).
fof(f4,axiom,
( p_0
| ~ u_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_2_s3_type11_1) ).
fof(f7,axiom,
( u_4
| p_1
| ~ p_2
| ~ p_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_s3_type11_3) ).
fof(f8,axiom,
( p_1
| ~ u_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_4_s3_type11_3) ).
fof(f13,axiom,
( u_7
| q_0
| ~ q_1
| ~ p_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_s3_type12_2) ).
fof(f14,axiom,
( q_0
| ~ u_7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_7_s3_type12_2) ).
fof(f17,axiom,
( u_9
| q_1
| ~ q_2
| ~ p_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_s3_type12_4) ).
fof(f18,axiom,
( q_1
| ~ u_9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_9_s3_type12_4) ).
fof(f27,axiom,
( u_14
| p_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_t3_1) ).
fof(f28,axiom,
( p_2
| ~ u_14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_14_t3_1) ).
fof(f29,axiom,
( u_15
| p_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_t3_2) ).
fof(f30,axiom,
( p_3
| ~ u_15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_15_t3_2) ).
fof(f31,axiom,
( u_16
| q_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_t3_3) ).
fof(f32,axiom,
( q_2
| ~ u_16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_16_t3_3) ).
fof(f74,definition,
( spl0_2
<=> p_3 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f79,definition,
( spl0_3
<=> u_15 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f82,plain,
( spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f29,f79,f74]) ).
fof(f83,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f30,f74,f79]) ).
fof(f100,definition,
( spl0_7
<=> p_2 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f104,definition,
( spl0_8
<=> u_14 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f107,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f27,f104,f100]) ).
fof(f108,plain,
( ~ spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f28,f100,f104]) ).
fof(f110,definition,
( spl0_9
<=> p_1 ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f114,definition,
( spl0_10
<=> u_4 ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f117,plain,
( ~ spl0_2
| ~ spl0_7
| spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f7,f114,f110,f100,f74]) ).
fof(f118,plain,
( ~ spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f8,f110,f114]) ).
fof(f126,definition,
( spl0_12
<=> q_2 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f131,definition,
( spl0_13
<=> u_16 ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f134,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f31,f131,f126]) ).
fof(f135,plain,
( ~ spl0_13
| spl0_12 ),
inference(avatar_split_clause,[],[f32,f126,f131]) ).
fof(f137,definition,
( spl0_14
<=> q_1 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f147,definition,
( spl0_16
<=> u_9 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f150,plain,
( ~ spl0_2
| ~ spl0_12
| spl0_14
| spl0_16 ),
inference(avatar_split_clause,[],[f17,f147,f137,f126,f74]) ).
fof(f151,plain,
( ~ spl0_16
| spl0_14 ),
inference(avatar_split_clause,[],[f18,f137,f147]) ).
fof(f154,definition,
( spl0_17
<=> q_0 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f164,definition,
( spl0_19
<=> u_7 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f167,plain,
( ~ spl0_7
| ~ spl0_14
| spl0_17
| spl0_19 ),
inference(avatar_split_clause,[],[f13,f164,f154,f137,f100]) ).
fof(f168,plain,
( ~ spl0_19
| spl0_17 ),
inference(avatar_split_clause,[],[f14,f154,f164]) ).
fof(f170,definition,
( spl0_20
<=> p_0 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f174,definition,
( spl0_21
<=> u_2 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f177,plain,
( ~ spl0_7
| ~ spl0_9
| spl0_20
| spl0_21 ),
inference(avatar_split_clause,[],[f3,f174,f170,f110,f100]) ).
fof(f178,plain,
( ~ spl0_21
| spl0_20 ),
inference(avatar_split_clause,[],[f4,f170,f174]) ).
fof(f185,plain,
( ~ p_0
| ~ q_0 ),
inference(forward_subsumption_resolution,[],[f1,f2]) ).
fof(f186,plain,
( ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f185,f170,f154]) ).
cnf(s2,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f82]) ).
cnf(s3,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f83]) ).
cnf(s7,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f107]) ).
cnf(s8,plain,
( spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f108]) ).
cnf(s9,plain,
( ~ spl0_2
| ~ spl0_7
| spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f117]) ).
cnf(s10,plain,
( spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f118]) ).
cnf(s14,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f134]) ).
cnf(s15,plain,
( spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f135]) ).
cnf(s18,plain,
( ~ spl0_2
| ~ spl0_12
| spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f150]) ).
cnf(s19,plain,
( spl0_14
| ~ spl0_16 ),
inference(sat_conversion,[],[f151]) ).
cnf(s23,plain,
( ~ spl0_7
| ~ spl0_14
| spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f167]) ).
cnf(s24,plain,
( spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f168]) ).
cnf(s25,plain,
( ~ spl0_7
| ~ spl0_9
| spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f177]) ).
cnf(s26,plain,
( spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f178]) ).
cnf(s29,plain,
( ~ spl0_17
| ~ spl0_20 ),
inference(sat_conversion,[],[f186]) ).
cnf(s30,plain,
spl0_2,
inference(rat,[],[s2,s3]) ).
cnf(s32,plain,
spl0_7,
inference(rat,[],[s7,s8]) ).
cnf(s33,plain,
spl0_9,
inference(rat,[],[s9,s10,s30,s32]) ).
cnf(s34,plain,
spl0_12,
inference(rat,[],[s14,s15]) ).
cnf(s35,plain,
spl0_14,
inference(rat,[],[s18,s19,s30,s34]) ).
cnf(s36,plain,
spl0_17,
inference(rat,[],[s23,s24,s32,s35]) ).
cnf(s37,plain,
~ spl0_20,
inference(rat,[],[s29,s36]) ).
cnf(s39,plain,
~ spl0_21,
inference(rat,[],[s26,s37]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s25,s33,s32,s39,s37]) ).
fof(f187,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN098-1.002 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n004.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 15:33:07 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 2.77/1.15 % (462829)Input is clausal, will run a generic CNF schedule.
% 2.77/1.15 % (462837)lrs+10_1_sil=8000:sp=occurrence:random_seed=1521378589:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.77/1.15 % (462837)First to succeed.
% 2.77/1.15 % (462837)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-462829"
% 2.77/1.15 % (462838)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=454779814:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.77/1.15 % (462835)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3923309310:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.77/1.15 % (462834)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=2970966627:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.77/1.15 % (462836)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3122253393:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.77/1.15 % (462840)dis-21_1_sil=8000:lcm=predicate:random_seed=3234255045: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)
% 2.77/1.15 % (462838)Refutation not found, incomplete strategy
% 2.77/1.15 % (462838)------------------------------
% 2.77/1.15 % (462838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.15 % (462838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.15 % (462838)CaDiCaL version: 2.1.3
% 2.77/1.15 % (462838)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.15 % (462838)Time elapsed: 0.001 s
% 2.77/1.15 % (462838)Peak memory usage: 86 MB
% 2.77/1.15 % (462840)Also succeeded, but the first one will report.
% 2.77/1.15 % (462839)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4061398268:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.77/1.15 % (462839)Also succeeded, but the first one will report.
% 2.77/1.15 % (462837)Refutation found. Thanks to Tanya!
% 2.77/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.77/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.15 % (462837)------------------------------
% 2.77/1.15 % (462837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.15 % (462837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.15 % (462837)CaDiCaL version: 2.1.3
% 2.77/1.15 % (462837)Termination reason: Refutation
% 2.77/1.15 % (462837)Time elapsed: 0.001 s
% 2.77/1.15 % (462837)Peak memory usage: 88 MB
% 2.77/1.15 % (462837)Instructions burned: 2 (million)
% 2.77/1.15 % (462837)------------------------------
% 2.77/1.15 % (462837)------------------------------
% 2.77/1.15 % (462829)Success in time 0.295 s
% 2.77/1.15 % Vampire exiting
%------------------------------------------------------------------------------