%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN161-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 01:49:48 PM UTC 2026
% Result : Unsatisfiable 5.74s 1.98s
% Output : Refutation 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 49 ( 16 unt; 5 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 106 ( 55 ~; 46 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 6 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0] : p0(b,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
fof(f17,axiom,
! [X0] : q0(X0,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
fof(f19,axiom,
! [X0,X1] : m0(X0,d,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
fof(f148,axiom,
! [X2,X0,X1] :
( ~ m0(X1,X2,X0)
| q1(X0,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_110) ).
fof(f163,axiom,
! [X0] :
( ~ p0(X0,X0)
| s1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_125) ).
fof(f164,axiom,
! [X2,X0,X1] :
( s1(X0)
| ~ q0(X0,X1)
| ~ s1(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_126) ).
fof(f192,axiom,
! [X0] :
( ~ q1(X0,X0,X0)
| p2(X0,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_154) ).
fof(f243,axiom,
! [X0,X1] :
( ~ p2(X1,X0,X0)
| k3(X0,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_205) ).
fof(f325,axiom,
! [X0,X1] :
( ~ k3(X0,X0,X1)
| p4(X0,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_287) ).
fof(f354,axiom,
! [X2,X0,X1] :
( n5(X0,X0)
| ~ p4(X1,X0,X0)
| ~ s1(X0)
| ~ p4(b,b,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_316) ).
fof(f369,negated_conjecture,
! [X0] : ~ n5(c,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f466,definition,
( spl0_23
<=> ! [X0] : p2(X0,X0,X0) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f467,plain,
( ! [X0] : p2(X0,X0,X0)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f583,definition,
( spl0_51
<=> ! [X2] : ~ s1(X2) ),
introduced(definition,[new_symbols(definition,[spl0_51])],[avatar_definition]) ).
fof(f584,plain,
( ! [X2] : ~ s1(X2)
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f586,definition,
( spl0_52
<=> ! [X0,X1] :
( s1(X0)
| ~ q0(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_52])],[avatar_definition]) ).
fof(f587,plain,
( ! [X0,X1] :
( ~ q0(X0,X1)
| s1(X0) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f588,plain,
( spl0_51
| spl0_52 ),
inference(avatar_split_clause,[],[f164,f586,f583]) ).
fof(f624,definition,
( spl0_61
<=> ! [X2] : ~ p4(b,b,X2) ),
introduced(definition,[new_symbols(definition,[spl0_61])],[avatar_definition]) ).
fof(f625,plain,
( ! [X2] : ~ p4(b,b,X2)
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f627,definition,
( spl0_62
<=> ! [X0,X1] :
( n5(X0,X0)
| ~ s1(X0)
| ~ p4(X1,X0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_62])],[avatar_definition]) ).
fof(f628,plain,
( ! [X0,X1] :
( n5(X0,X0)
| ~ s1(X0)
| ~ p4(X1,X0,X0) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f629,plain,
( spl0_61
| spl0_62 ),
inference(avatar_split_clause,[],[f354,f627,f624]) ).
fof(f709,plain,
s1(b),
inference(resolution,[],[f163,f14]) ).
fof(f710,plain,
( $false
| ~ spl0_51 ),
inference(forward_subsumption_resolution,[],[f709,f584]) ).
fof(f711,plain,
~ spl0_51,
inference(avatar_contradiction_clause,[],[f710]) ).
fof(f712,plain,
( ! [X0] : s1(X0)
| ~ spl0_52 ),
inference(resolution,[],[f587,f17]) ).
fof(f779,plain,
! [X0] : q1(X0,X0,X0),
inference(resolution,[],[f148,f19]) ).
fof(f795,plain,
! [X0] : p2(X0,X0,X0),
inference(resolution,[],[f192,f779]) ).
fof(f806,plain,
spl0_23,
inference(avatar_split_clause,[],[f795,f466]) ).
fof(f821,plain,
( ! [X0] : k3(X0,X0,X0)
| ~ spl0_23 ),
inference(resolution,[],[f243,f467]) ).
fof(f838,plain,
( ! [X0] : p4(X0,X0,X0)
| ~ spl0_23 ),
inference(resolution,[],[f325,f821]) ).
fof(f905,plain,
( $false
| ~ spl0_23
| ~ spl0_61 ),
inference(resolution,[],[f838,f625]) ).
fof(f906,plain,
( ~ spl0_23
| ~ spl0_61 ),
inference(avatar_contradiction_clause,[],[f905]) ).
fof(f907,plain,
( ! [X0,X1] :
( ~ p4(X1,X0,X0)
| n5(X0,X0) )
| ~ spl0_52
| ~ spl0_62 ),
inference(forward_subsumption_resolution,[],[f628,f712]) ).
fof(f908,plain,
( ! [X0] : n5(X0,X0)
| ~ spl0_23
| ~ spl0_52
| ~ spl0_62 ),
inference(resolution,[],[f907,f838]) ).
fof(f909,plain,
( $false
| ~ spl0_23
| ~ spl0_52
| ~ spl0_62 ),
inference(resolution,[],[f908,f369]) ).
fof(f910,plain,
( ~ spl0_23
| ~ spl0_52
| ~ spl0_62 ),
inference(avatar_contradiction_clause,[],[f909]) ).
cnf(s29,plain,
( spl0_51
| spl0_52 ),
inference(sat_conversion,[],[f588]) ).
cnf(s34,plain,
( spl0_61
| spl0_62 ),
inference(sat_conversion,[],[f629]) ).
cnf(s57,plain,
~ spl0_51,
inference(sat_conversion,[],[f711]) ).
cnf(s63,plain,
spl0_23,
inference(sat_conversion,[],[f806]) ).
cnf(s75,plain,
( ~ spl0_23
| ~ spl0_61 ),
inference(sat_conversion,[],[f906]) ).
cnf(s76,plain,
( ~ spl0_23
| ~ spl0_52
| ~ spl0_62 ),
inference(sat_conversion,[],[f910]) ).
cnf(s77,plain,
~ spl0_61,
inference(rat,[],[s75,s63]) ).
cnf(s81,plain,
spl0_62,
inference(rat,[],[s34,s77]) ).
cnf(s82,plain,
~ spl0_52,
inference(rat,[],[s76,s63,s81]) ).
cnf(s84,plain,
$false,
inference(rat,[],[s29,s82,s57]) ).
fof(f911,plain,
$false,
inference(avatar_sat_refutation,[],[s84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN161-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.28 % Computer : n009.cluster.edu
% 0.12/0.28 % Model : x86_64 x86_64
% 0.12/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.28 % Memory : 8046.5625MB
% 0.12/0.28 % OS : Linux 6.8.0-71-generic
% 0.12/0.28 % CPULimit : 300
% 0.12/0.28 % WCLimit : 300
% 0.12/0.28 % DateTime : Mon Sep 28 15:37:15 UTC 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.29/0.35 Running first-order theorem proving
% 0.29/0.35 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.74/1.98 % (3160748)Input is clausal, will run a generic CNF schedule.
% 5.74/1.98 % (3160754)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2680005619:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.74/1.98 % (3160753)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=1814876781:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.74/1.98 % (3160755)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=639416565:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.74/1.98 % (3160756)lrs+10_1_sil=8000:sp=occurrence:random_seed=263111525:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.74/1.98 % (3160757)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=708245445:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.74/1.98 % (3160758)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3562210339:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.74/1.98 % (3160759)dis-21_1_sil=8000:lcm=predicate:random_seed=2367942724: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)
% 5.74/1.98 % (3160756)First to succeed.
% 5.74/1.98 % (3160756)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3160748"
% 5.74/1.98 % (3160757)Also succeeded, but the first one will report.
% 5.74/1.98 % (3160758)Also succeeded, but the first one will report.
% 5.74/1.98 % (3160759)Also succeeded, but the first one will report.
% 5.74/1.98 % (3160756)Refutation found. Thanks to Tanya!
% 5.74/1.98 % SZS status Unsatisfiable for theBenchmark
% 5.74/1.98 % SZS output start Proof for theBenchmark
% See solution above
% 5.74/1.98 % (3160756)------------------------------
% 5.74/1.98 % (3160756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.98 % (3160756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.98 % (3160756)CaDiCaL version: 2.1.3
% 5.74/1.98 % (3160756)Termination reason: Refutation
% 5.74/1.98 % (3160756)Time elapsed: 0.014 s
% 5.74/1.98 % (3160756)Peak memory usage: 89 MB
% 5.74/1.98 % (3160756)Instructions burned: 10 (million)
% 5.74/1.98 % (3160756)------------------------------
% 5.74/1.98 % (3160756)------------------------------
% 5.74/1.98 % (3160748)Success in time 0.681 s
% 5.74/1.98 % Vampire exiting
%------------------------------------------------------------------------------