%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN078+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 01:49:36 PM UTC 2026
% Result : Theorem 3.48s 1.28s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 8 unt; 6 def)
% Number of atoms : 156 ( 14 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 169 ( 68 ~; 74 |; 14 &)
% ( 8 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 31 ( 0 sgn 23 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( ? [X1] :
( big_p(X1)
& X0 = f(X1) )
=> big_p(X0) )
<=> ! [X2] :
( big_p(X2)
=> big_p(f(X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel56) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( ? [X1] :
( big_p(X1)
& X0 = f(X1) )
=> big_p(X0) )
<=> ! [X2] :
( big_p(X2)
=> big_p(f(X2)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X0] :
( big_p(X0)
| ! [X1] :
( ~ big_p(X1)
| f(X1) != X0 ) )
<~> ! [X2] :
( big_p(f(X2))
| ~ big_p(X2) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ( ? [X2] :
( ~ big_p(f(X2))
& big_p(X2) )
| ? [X0] :
( ~ big_p(X0)
& ? [X1] :
( big_p(X1)
& f(X1) = X0 ) ) )
& ( ! [X2] :
( big_p(f(X2))
| ~ big_p(X2) )
| ! [X0] :
( big_p(X0)
| ! [X1] :
( ~ big_p(X1)
| f(X1) != X0 ) ) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ? [X0] :
( ~ big_p(f(X0))
& big_p(X0) )
| ? [X1] :
( ~ big_p(X1)
& ? [X2] :
( big_p(X2)
& f(X2) = X1 ) ) )
& ( ! [X3] :
( big_p(f(X3))
| ~ big_p(X3) )
| ! [X4] :
( big_p(X4)
| ! [X5] :
( ~ big_p(X5)
| f(X5) != X4 ) ) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( ( ( ~ big_p(f(sK0))
& big_p(sK0) )
| ( ~ big_p(sK1)
& big_p(sK2)
& sK1 = f(sK2) ) )
& ( ! [X3] :
( big_p(f(X3))
| ~ big_p(X3) )
| ! [X4] :
( big_p(X4)
| ! [X5] :
( ~ big_p(X5)
| f(X5) != X4 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f5]) ).
fof(f7,plain,
! [X3,X4,X5] :
( big_p(f(X3))
| ~ big_p(X3)
| big_p(X4)
| ~ big_p(X5)
| f(X5) != X4 ),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
( big_p(sK0)
| sK1 = f(sK2) ),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
( big_p(sK0)
| big_p(sK2) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
( big_p(sK0)
| ~ big_p(sK1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f11,plain,
( ~ big_p(f(sK0))
| sK1 = f(sK2) ),
inference(cnf_transformation,[],[f6]) ).
fof(f12,plain,
( ~ big_p(f(sK0))
| big_p(sK2) ),
inference(cnf_transformation,[],[f6]) ).
fof(f13,plain,
( ~ big_p(f(sK0))
| ~ big_p(sK1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f14,plain,
! [X3,X5] :
( big_p(f(X3))
| ~ big_p(X3)
| big_p(f(X5))
| ~ big_p(X5) ),
inference(equality_resolution,[],[f7]) ).
fof(f16,definition,
( spl3_1
<=> ! [X5] :
( big_p(f(X5))
| ~ big_p(X5) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f17,plain,
( ! [X5] :
( big_p(f(X5))
| ~ big_p(X5) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f18,plain,
( spl3_1
| spl3_1 ),
inference(avatar_split_clause,[],[f14,f16,f16]) ).
fof(f20,definition,
( spl3_2
<=> sK1 = f(sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f22,plain,
( sK1 = f(sK2)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f24,definition,
( spl3_3
<=> big_p(sK0) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f27,plain,
( spl3_2
| spl3_3 ),
inference(avatar_split_clause,[],[f8,f24,f20]) ).
fof(f29,definition,
( spl3_4
<=> big_p(sK2) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f31,plain,
( big_p(sK2)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,plain,
( spl3_4
| spl3_3 ),
inference(avatar_split_clause,[],[f9,f24,f29]) ).
fof(f34,definition,
( spl3_5
<=> big_p(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f36,plain,
( ~ big_p(sK1)
| spl3_5 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f37,plain,
( ~ spl3_5
| spl3_3 ),
inference(avatar_split_clause,[],[f10,f24,f34]) ).
fof(f39,definition,
( spl3_6
<=> big_p(f(sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f41,plain,
( ~ big_p(f(sK0))
| spl3_6 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,plain,
( spl3_2
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f11,f39,f20]) ).
fof(f43,plain,
( spl3_4
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f12,f39,f29]) ).
fof(f44,plain,
( ~ spl3_5
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f13,f39,f34]) ).
fof(f45,plain,
( ~ big_p(sK0)
| ~ spl3_1
| spl3_6 ),
inference(resolution,[],[f17,f41]) ).
fof(f48,plain,
( ~ spl3_3
| ~ spl3_1
| spl3_6 ),
inference(avatar_split_clause,[],[f45,f39,f16,f24]) ).
fof(f49,plain,
( big_p(sK1)
| ~ big_p(sK2)
| ~ spl3_1
| ~ spl3_2 ),
inference(superposition,[],[f17,f22]) ).
fof(f50,plain,
( ~ big_p(sK2)
| ~ spl3_1
| ~ spl3_2
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f49,f36]) ).
fof(f51,plain,
( $false
| ~ spl3_1
| ~ spl3_2
| ~ spl3_4
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f50,f31]) ).
fof(f52,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_4
| spl3_5 ),
inference(avatar_contradiction_clause,[],[f51]) ).
cnf(s1,plain,
( spl3_1
| spl3_1 ),
inference(sat_conversion,[],[f18]) ).
cnf(s2,plain,
spl3_1,
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f27]) ).
cnf(s4,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f32]) ).
cnf(s5,plain,
( spl3_3
| ~ spl3_5 ),
inference(sat_conversion,[],[f37]) ).
cnf(s6,plain,
( spl3_2
| ~ spl3_6 ),
inference(sat_conversion,[],[f42]) ).
cnf(s7,plain,
( spl3_4
| ~ spl3_6 ),
inference(sat_conversion,[],[f43]) ).
cnf(s8,plain,
( ~ spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f44]) ).
cnf(s10,plain,
( ~ spl3_1
| ~ spl3_3
| spl3_6 ),
inference(sat_conversion,[],[f48]) ).
cnf(s11,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f52]) ).
cnf(s12,plain,
spl3_2,
inference(rat,[],[s10,s3,s6,s2]) ).
cnf(s13,plain,
spl3_3,
inference(rat,[],[s11,s4,s5,s2,s12]) ).
cnf(s14,plain,
spl3_6,
inference(rat,[],[s10,s2,s13]) ).
cnf(s15,plain,
~ spl3_5,
inference(rat,[],[s8,s14]) ).
cnf(s16,plain,
spl3_4,
inference(rat,[],[s7,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s11,s12,s2,s15,s16]) ).
fof(f53,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN078+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n020.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 15:31:20 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 3.48/1.28 % (248793)Detected formulas, will run a generic FOF schedule.
% 3.48/1.28 % (248799)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1918545735:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.28 % (248803)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3119036966:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.28 % (248803)First to succeed.
% 3.48/1.28 % (248803)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-248793"
% 3.48/1.28 % (248802)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=142654644:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.28 % (248798)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=1668441480:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.28 % (248801)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1488846676:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.28 % (248804)dis-21_1_sil=8000:lcm=predicate:random_seed=4179381953:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.48/1.28 % (248800)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2378922448:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.28 % (248804)Refutation not found, incomplete strategy
% 3.48/1.28 % (248804)------------------------------
% 3.48/1.28 % (248804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.28 % (248804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.28 % (248804)CaDiCaL version: 2.1.3
% 3.48/1.28 % (248804)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.28 % (248804)Time elapsed: 0.001 s
% 3.48/1.28 % (248804)Peak memory usage: 88 MB
% 3.48/1.28 % (248802)Also succeeded, but the first one will report.
% 3.48/1.28 % (248801)Also succeeded, but the first one will report.
% 3.48/1.28 % (248804)------------------------------
% 3.48/1.28 % (248804)------------------------------
% 3.48/1.28 % (248803)Refutation found. Thanks to Tanya!
% 3.48/1.28 % SZS status Theorem for theBenchmark
% 3.48/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.28 % (248803)------------------------------
% 3.48/1.28 % (248803)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.28 % (248803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.28 % (248803)CaDiCaL version: 2.1.3
% 3.48/1.28 % (248803)Termination reason: Refutation
% 3.48/1.28 % (248803)Time elapsed: 0.003 s
% 3.48/1.28 % (248803)Peak memory usage: 90 MB
% 3.48/1.28 % (248803)Instructions burned: 1 (million)
% 3.48/1.28 % (248803)------------------------------
% 3.48/1.28 % (248803)------------------------------
% 3.48/1.28 % (248793)Success in time 0.412 s
% 3.48/1.28 % Vampire exiting
%------------------------------------------------------------------------------