%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% 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 02:06:42 PM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 8 unt; 6 def)
% Number of atoms : 148 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 150 ( 63 ~; 72 |; 2 &)
% ( 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 : 18 ( 0 sgn 16 !; 2 ?)
% 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,
( ~ big_p(f(sK1))
| sK0 = f(sK2) ),
inference(cnf_transformation,[],[f3]) ).
fof(f5,plain,
( ~ big_p(f(sK1))
| big_p(sK2) ),
inference(cnf_transformation,[],[f3]) ).
fof(f6,plain,
( big_p(sK1)
| sK0 = f(sK2) ),
inference(cnf_transformation,[],[f3]) ).
fof(f7,plain,
( big_p(sK1)
| big_p(sK2) ),
inference(cnf_transformation,[],[f3]) ).
fof(f8,plain,
! [X2,X0,X1] :
( ~ big_p(X2)
| big_p(f(X2))
| f(X1) != X0
| ~ big_p(X1)
| big_p(X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f9,plain,
( big_p(sK1)
| ~ big_p(sK0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f10,plain,
( ~ big_p(f(sK1))
| ~ big_p(sK0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f11,plain,
! [X2,X1] :
( ~ big_p(X2)
| big_p(f(X2))
| ~ big_p(X1)
| big_p(f(X1)) ),
inference(equality_resolution,[],[f8]) ).
fof(f12,plain,
( big_p(f(sK1))
| big_p(sK0) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f13,plain,
( ~ big_p(sK1)
| big_p(sK0) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f14,plain,
! [X2,X1] :
( big_p(X2)
| ~ big_p(f(X2))
| big_p(X1)
| ~ big_p(f(X1)) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f15,plain,
( ~ big_p(sK1)
| ~ big_p(sK2) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f16,plain,
( ~ big_p(sK1)
| sK0 = f(sK2) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f17,plain,
( big_p(f(sK1))
| ~ big_p(sK2) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f18,plain,
( big_p(f(sK1))
| sK0 = f(sK2) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f20,definition,
( spl3_1
<=> sK0 = f(sK2) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f22,plain,
( sK0 = f(sK2)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f24,definition,
( spl3_2
<=> big_p(f(sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f26,plain,
( big_p(f(sK1))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f27,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f18,f24,f20]) ).
fof(f29,definition,
( spl3_3
<=> big_p(sK2) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f31,plain,
( ~ big_p(sK2)
| spl3_3 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,plain,
( ~ spl3_3
| spl3_2 ),
inference(avatar_split_clause,[],[f17,f24,f29]) ).
fof(f34,definition,
( spl3_4
<=> big_p(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f36,plain,
( ~ big_p(sK1)
| spl3_4 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f37,plain,
( spl3_1
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f16,f34,f20]) ).
fof(f38,plain,
( ~ spl3_3
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f15,f34,f29]) ).
fof(f40,definition,
( spl3_5
<=> ! [X1] :
( big_p(X1)
| ~ big_p(f(X1)) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f41,plain,
( ! [X1] :
( ~ big_p(f(X1))
| big_p(X1) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f42,plain,
( spl3_5
| spl3_5 ),
inference(avatar_split_clause,[],[f14,f40,f40]) ).
fof(f44,definition,
( spl3_6
<=> big_p(sK0) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f46,plain,
( big_p(sK0)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,plain,
( spl3_6
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f13,f34,f44]) ).
fof(f48,plain,
( spl3_6
| spl3_2 ),
inference(avatar_split_clause,[],[f12,f24,f44]) ).
fof(f49,plain,
( big_p(sK1)
| ~ spl3_2
| ~ spl3_5 ),
inference(resolution,[],[f41,f26]) ).
fof(f50,plain,
( $false
| ~ spl3_2
| spl3_4
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f49,f36]) ).
fof(f51,plain,
( ~ spl3_2
| spl3_4
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f50]) ).
fof(f52,plain,
( ~ big_p(sK0)
| big_p(sK2)
| ~ spl3_1
| ~ spl3_5 ),
inference(superposition,[],[f41,f22]) ).
fof(f53,plain,
( big_p(sK2)
| ~ spl3_1
| ~ spl3_5
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f52,f46]) ).
fof(f54,plain,
( $false
| ~ spl3_1
| spl3_3
| ~ spl3_5
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f53,f31]) ).
fof(f55,plain,
( ~ spl3_1
| spl3_3
| ~ spl3_5
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[],[f54]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f27]) ).
cnf(s2,plain,
( spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f32]) ).
cnf(s3,plain,
( spl3_1
| ~ spl3_4 ),
inference(sat_conversion,[],[f37]) ).
cnf(s4,plain,
( ~ spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s5,plain,
( spl3_5
| spl3_5 ),
inference(sat_conversion,[],[f42]) ).
cnf(s6,plain,
spl3_5,
inference(rat,[],[s5]) ).
cnf(s7,plain,
( ~ spl3_4
| spl3_6 ),
inference(sat_conversion,[],[f47]) ).
cnf(s8,plain,
( spl3_2
| spl3_6 ),
inference(sat_conversion,[],[f48]) ).
cnf(s9,plain,
( ~ spl3_2
| spl3_4
| ~ spl3_5 ),
inference(sat_conversion,[],[f51]) ).
cnf(s10,plain,
( ~ spl3_1
| spl3_3
| ~ spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f55]) ).
cnf(s11,plain,
spl3_1,
inference(rat,[],[s9,s1,s3,s6]) ).
cnf(s12,plain,
spl3_2,
inference(rat,[],[s10,s2,s8,s6,s11]) ).
cnf(s13,plain,
spl3_4,
inference(rat,[],[s9,s6,s12]) ).
cnf(s14,plain,
spl3_6,
inference(rat,[],[s7,s13]) ).
cnf(s15,plain,
~ spl3_3,
inference(rat,[],[s4,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s10,s11,s6,s14,s15]) ).
fof(f56,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 15:30:22 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25 % (459403)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (459409)% WARNING: option uhcvi not known.
% 0.08/0.25 % (459409)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4290330782:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.25 % (459409) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-459403-459409"...
% 0.08/0.25 % (459409)...printing done.
% 0.08/0.25 % (459409)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (459409)------------------------------
% 0.08/0.25 % (459409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (459409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (459409)CaDiCaL version: 2.1.3
% 0.08/0.25 % (459409)Termination reason: Refutation
% 0.08/0.25 % (459409)Time elapsed: 0.001 s
% 0.08/0.25 % (459409)Peak memory usage: 12 MB
% 0.08/0.25 % (459409)Instructions burned: 1 (million)
% 0.08/0.25 % (459403)Success in time 0.03 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------