%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN084-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:49:37 PM UTC 2026
% Result : Unsatisfiable 2.73s 1.16s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 65 ( 11 unt; 9 def)
% Number of atoms : 157 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 161 ( 69 ~; 83 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 11 ( 10 usr; 10 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 6 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
big_p(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel62_1) ).
fof(f2,negated_conjecture,
! [X0] :
( big_p(f(f(X0)))
| big_p(X0)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel62_2) ).
fof(f3,negated_conjecture,
! [X0] :
( big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel62_3) ).
fof(f4,negated_conjecture,
( ~ big_p(f(f(sk1)))
| ~ big_p(f(f(sk2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel62_4) ).
fof(f5,negated_conjecture,
( big_p(f(sk1))
| big_p(f(sk2))
| ~ big_p(sk1)
| ~ big_p(sk2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel62_5) ).
fof(f6,negated_conjecture,
( big_p(f(sk1))
| ~ big_p(sk1)
| ~ big_p(f(f(sk2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel62_6) ).
fof(f7,negated_conjecture,
( big_p(f(sk2))
| ~ big_p(sk2)
| ~ big_p(f(f(sk1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel62_7) ).
fof(f9,definition,
( spl0_1
<=> big_p(f(f(sk1))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f10,plain,
( ~ big_p(f(f(sk1)))
| spl0_1 ),
inference(avatar_component_clause,[],[f9]) ).
fof(f12,definition,
( spl0_2
<=> big_p(sk2) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f13,plain,
( ~ big_p(sk2)
| spl0_2 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f15,definition,
( spl0_3
<=> big_p(f(sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f16,plain,
( big_p(f(sk2))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f17,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f7,f15,f12,f9]) ).
fof(f19,definition,
( spl0_4
<=> big_p(f(f(sk2))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f20,plain,
( ~ big_p(f(f(sk2)))
| spl0_4 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f22,definition,
( spl0_5
<=> big_p(sk1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f23,plain,
( ~ big_p(sk1)
| spl0_5 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f25,definition,
( spl0_6
<=> big_p(f(sk1)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f26,plain,
( big_p(f(sk1))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f27,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f25,f22,f19]) ).
fof(f28,plain,
( ~ spl0_2
| ~ spl0_5
| spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f5,f25,f15,f22,f12]) ).
fof(f29,plain,
( ~ spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f4,f9,f19]) ).
fof(f31,definition,
( spl0_7
<=> big_p(a) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f32,plain,
( ~ big_p(a)
| spl0_7 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f34,definition,
( spl0_8
<=> ! [X0] :
( big_p(f(f(X0)))
| ~ big_p(f(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f35,plain,
( ! [X0] :
( big_p(f(f(X0)))
| ~ big_p(f(X0)) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f36,plain,
( ~ spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f3,f34,f31]) ).
fof(f38,definition,
( spl0_9
<=> ! [X0] :
( big_p(f(f(X0)))
| big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f39,plain,
( ! [X0] :
( big_p(f(f(X0)))
| big_p(X0) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f40,plain,
( ~ spl0_7
| spl0_9 ),
inference(avatar_split_clause,[],[f2,f38,f31]) ).
fof(f41,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f32,f1]) ).
fof(f42,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f41]) ).
fof(f43,plain,
( big_p(sk1)
| spl0_1
| ~ spl0_9 ),
inference(resolution,[],[f39,f10]) ).
fof(f44,plain,
( $false
| spl0_1
| spl0_5
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f43,f23]) ).
fof(f45,plain,
( spl0_1
| spl0_5
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f44]) ).
fof(f46,plain,
( big_p(sk2)
| spl0_4
| ~ spl0_9 ),
inference(resolution,[],[f20,f39]) ).
fof(f47,plain,
( $false
| spl0_2
| spl0_4
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f46,f13]) ).
fof(f48,plain,
( spl0_2
| spl0_4
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f47]) ).
fof(f49,plain,
( ~ big_p(f(sk1))
| spl0_1
| ~ spl0_8 ),
inference(resolution,[],[f35,f10]) ).
fof(f50,plain,
( $false
| spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f49,f26]) ).
fof(f51,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f50]) ).
fof(f52,plain,
( ~ big_p(f(sk2))
| spl0_4
| ~ spl0_8 ),
inference(resolution,[],[f20,f35]) ).
fof(f54,plain,
( $false
| ~ spl0_3
| spl0_4
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f52,f16]) ).
fof(f55,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f54]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f17]) ).
cnf(s2,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f27]) ).
cnf(s3,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f28]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f29]) ).
cnf(s5,plain,
( ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f36]) ).
cnf(s6,plain,
( ~ spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f40]) ).
cnf(s7,plain,
spl0_7,
inference(sat_conversion,[],[f42]) ).
cnf(s8,plain,
( spl0_1
| spl0_5
| ~ spl0_9 ),
inference(sat_conversion,[],[f45]) ).
cnf(s9,plain,
( spl0_2
| spl0_4
| ~ spl0_9 ),
inference(sat_conversion,[],[f48]) ).
cnf(s10,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f51]) ).
cnf(s11,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_8 ),
inference(sat_conversion,[],[f55]) ).
cnf(s12,plain,
spl0_9,
inference(rat,[],[s6,s7]) ).
cnf(s13,plain,
spl0_8,
inference(rat,[],[s5,s7]) ).
cnf(s14,plain,
( ~ spl0_5
| spl0_6 ),
inference(rat,[],[s3,s9,s11,s2,s13,s12]) ).
cnf(s15,plain,
spl0_1,
inference(rat,[],[s14,s8,s10,s12,s13]) ).
cnf(s16,plain,
~ spl0_4,
inference(rat,[],[s4,s15]) ).
cnf(s17,plain,
~ spl0_3,
inference(rat,[],[s11,s13,s16]) ).
cnf(s18,plain,
spl0_2,
inference(rat,[],[s9,s12,s16]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s15,s17,s18]) ).
fof(f56,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN084-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 15:36:17 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 2.73/1.16 % (2719780)Input is clausal, will run a generic CNF schedule.
% 2.73/1.16 % (2719828)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1484212387:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.73/1.16 % (2719828)First to succeed.
% 2.73/1.16 % (2719828)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2719780"
% 2.73/1.16 % (2719825)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=333784688:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.73/1.16 % (2719826)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1932412388:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.73/1.16 % (2719824)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=1360772589:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.73/1.16 % (2719827)lrs+10_1_sil=8000:sp=occurrence:random_seed=2344630536:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.73/1.16 % (2719827)Also succeeded, but the first one will report.
% 2.73/1.16 % (2719829)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2304555128:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.73/1.16 % (2719830)dis-21_1_sil=8000:lcm=predicate:random_seed=2553393573: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)
% 2.73/1.16 % (2719829)Also succeeded, but the first one will report.
% 2.73/1.16 % (2719830)Also succeeded, but the first one will report.
% 2.73/1.16 % (2719828)Refutation found. Thanks to Tanya!
% 2.73/1.16 % SZS status Unsatisfiable for theBenchmark
% 2.73/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.17 % (2719828)------------------------------
% 2.73/1.17 % (2719828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.17 % (2719828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.17 % (2719828)CaDiCaL version: 2.1.3
% 2.73/1.17 % (2719828)Termination reason: Refutation
% 2.73/1.17 % (2719828)Time elapsed: 0.002 s
% 2.73/1.17 % (2719828)Peak memory usage: 89 MB
% 2.73/1.17 % (2719828)Instructions burned: 1 (million)
% 2.73/1.17 % (2719828)------------------------------
% 2.73/1.17 % (2719828)------------------------------
% 2.73/1.17 % (2719780)Success in time 0.286 s
% 2.73/1.17 % Vampire exiting
%------------------------------------------------------------------------------