%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MSC006-1 : 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 : 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 12:04:46 PM UTC 2026
% Result : Unsatisfiable 2.68s 1.35s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 9 unt; 3 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 89 ( 47 ~; 39 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( p(X0,X2)
| ~ p(X1,X2)
| ~ p(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_transitivity) ).
fof(f2,axiom,
! [X2,X0,X1] :
( q(X0,X2)
| ~ q(X1,X2)
| ~ q(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_transitivity) ).
fof(f3,axiom,
! [X0,X1] :
( q(X1,X0)
| ~ q(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_symmetry) ).
fof(f4,axiom,
! [X0,X1] :
( q(X0,X1)
| p(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',all_related) ).
fof(f5,axiom,
~ p(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_is_not_total) ).
fof(f6,negated_conjecture,
~ q(c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_q_is_total) ).
fof(f7,plain,
~ q(d,c),
inference(resolution,[],[f3,f6]) ).
fof(f8,plain,
p(c,d),
inference(resolution,[],[f4,f6]) ).
fof(f9,plain,
p(d,c),
inference(resolution,[],[f7,f4]) ).
fof(f11,plain,
! [X0] :
( ~ p(a,X0)
| ~ p(X0,b) ),
inference(resolution,[],[f1,f5]) ).
fof(f12,plain,
! [X0] :
( ~ q(c,X0)
| ~ q(X0,d) ),
inference(resolution,[],[f2,f6]) ).
fof(f15,plain,
! [X0] :
( ~ q(X0,d)
| p(c,X0) ),
inference(resolution,[],[f12,f4]) ).
fof(f16,plain,
! [X0] :
( ~ q(X0,d)
| ~ q(X0,c) ),
inference(resolution,[],[f12,f3]) ).
fof(f20,plain,
! [X0,X1] :
( ~ p(a,X1)
| ~ p(X1,X0)
| ~ p(X0,b) ),
inference(resolution,[],[f11,f1]) ).
fof(f23,plain,
! [X0] :
( ~ q(d,X0)
| p(c,X0) ),
inference(resolution,[],[f15,f3]) ).
fof(f25,plain,
! [X0] :
( ~ q(X0,c)
| p(X0,d) ),
inference(resolution,[],[f16,f4]) ).
fof(f39,plain,
! [X0] :
( p(d,X0)
| p(c,X0) ),
inference(resolution,[],[f23,f4]) ).
fof(f42,plain,
! [X0] :
( p(X0,d)
| p(X0,c) ),
inference(resolution,[],[f25,f4]) ).
fof(f62,plain,
( p(a,c)
| ~ p(d,b) ),
inference(resolution,[],[f42,f11]) ).
fof(f64,definition,
( spl0_1
<=> p(d,b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f65,plain,
( ~ p(d,b)
| spl0_1 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,definition,
( spl0_2
<=> p(a,c) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f68,plain,
( p(a,c)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f69,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f62,f67,f64]) ).
fof(f71,definition,
( spl0_3
<=> ! [X0] :
( ~ p(d,X0)
| ~ p(X0,b) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f72,plain,
( ! [X0] :
( ~ p(d,X0)
| ~ p(X0,b) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,plain,
( ! [X0] :
( ~ p(c,X0)
| ~ p(X0,b) )
| ~ spl0_2 ),
inference(resolution,[],[f68,f20]) ).
fof(f98,plain,
( ~ p(d,b)
| ~ spl0_2 ),
inference(resolution,[],[f74,f8]) ).
fof(f106,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f98,f67,f64]) ).
fof(f111,plain,
( p(c,b)
| spl0_1 ),
inference(resolution,[],[f65,f39]) ).
fof(f113,plain,
( ! [X0] :
( ~ p(X0,b)
| ~ p(d,X0) )
| spl0_1 ),
inference(resolution,[],[f65,f1]) ).
fof(f114,plain,
( spl0_3
| spl0_1 ),
inference(avatar_split_clause,[],[f113,f64,f71]) ).
fof(f129,plain,
( ~ p(c,b)
| ~ spl0_3 ),
inference(resolution,[],[f72,f9]) ).
fof(f135,plain,
( $false
| spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f129,f111]) ).
fof(f136,plain,
( spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f135]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f69]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f106]) ).
cnf(s5,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f114]) ).
cnf(s9,plain,
( spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f136]) ).
cnf(s10,plain,
spl0_1,
inference(rat,[],[s5,s9]) ).
cnf(s11,plain,
~ spl0_2,
inference(rat,[],[s4,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s11,s10]) ).
fof(f137,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MSC006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n004.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 17:40:22 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.68/1.35 % (3776294)Input is clausal, will run a generic CNF schedule.
% 2.68/1.35 % (3776303)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2089472225:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.68/1.35 % (3776303)First to succeed.
% 2.68/1.35 % (3776303)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3776294"
% 2.68/1.35 % (3776299)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=582234411:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.68/1.35 % (3776305)dis-21_1_sil=8000:lcm=predicate:random_seed=821474681: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)
% 2.68/1.35 % (3776301)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1092206362:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.68/1.35 % (3776302)lrs+10_1_sil=8000:sp=occurrence:random_seed=2299827452:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.68/1.35 % (3776300)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4077195093:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.68/1.35 % (3776304)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=398014318:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.68/1.35 % (3776304)Also succeeded, but the first one will report.
% 2.68/1.35 % (3776302)Also succeeded, but the first one will report.
% 2.68/1.35 % (3776305)Also succeeded, but the first one will report.
% 2.68/1.35 % (3776303)Refutation found. Thanks to Tanya!
% 2.68/1.35 % SZS status Unsatisfiable for theBenchmark
% 2.68/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.35 % (3776303)------------------------------
% 2.68/1.35 % (3776303)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.35 % (3776303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.35 % (3776303)CaDiCaL version: 2.1.3
% 2.68/1.35 % (3776303)Termination reason: Refutation
% 2.68/1.35 % (3776303)Time elapsed: 0.003 s
% 2.68/1.35 % (3776303)Peak memory usage: 89 MB
% 2.68/1.35 % (3776303)Instructions burned: 4 (million)
% 2.68/1.35 % (3776303)------------------------------
% 2.68/1.35 % (3776303)------------------------------
% 2.68/1.35 % (3776294)Success in time 0.294 s
% 2.68/1.35 % Vampire exiting
%------------------------------------------------------------------------------