%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN375^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 : Wed Sep 30 08:41:52 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 6 unt; 0 typ; 3 def)
% Number of atoms : 250 ( 64 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 202 ( 42 ~; 38 |; 20 &; 81 @)
% ( 7 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn 43 !; 30 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cP: $i > $o ).
thf(f1,conjecture,
( ( ( ? [X1: $i] : ( cP @ X1 )
=> ! [X0: $i] : ( cP @ X0 ) )
& ( ! [X0: $i] : ( cP @ X0 )
=> ? [X1: $i] : ( cP @ X1 ) ) )
=> ( ? [X1: $i] : ( cP @ X1 )
<=> ! [X0: $i] : ( cP @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX2126_BUG) ).
thf(f2,negated_conjecture,
~ ( ( ( ? [X1: $i] : ( cP @ X1 )
=> ! [X0: $i] : ( cP @ X0 ) )
& ( ! [X0: $i] : ( cP @ X0 )
=> ? [X1: $i] : ( cP @ X1 ) ) )
=> ( ? [X1: $i] : ( cP @ X1 )
<=> ! [X0: $i] : ( cP @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ? [X0: $i] : ( cP @ X0 )
=> ! [X1: $i] : ( cP @ X1 ) )
& ( ! [X2: $i] : ( cP @ X2 )
=> ? [X3: $i] : ( cP @ X3 ) ) )
=> ( ? [X4: $i] : ( cP @ X4 )
<=> ! [X5: $i] : ( cP @ X5 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ? [X0: $i] :
( ( cP @ X0 )
= $true )
=> ! [X1: $i] :
( ( cP @ X1 )
= $true ) )
& ( ! [X2: $i] :
( ( cP @ X2 )
= $true )
=> ? [X3: $i] :
( ( cP @ X3 )
= $true ) ) )
=> ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
<=> ! [X5: $i] :
( ( cP @ X5 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
<~> ! [X5: $i] :
( ( cP @ X5 )
= $true ) )
& ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cP @ X0 )
!= $true ) )
& ( ? [X3: $i] :
( ( cP @ X3 )
= $true )
| ? [X2: $i] :
( ( cP @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
<~> ! [X5: $i] :
( ( cP @ X5 )
= $true ) )
& ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cP @ X0 )
!= $true ) )
& ( ? [X3: $i] :
( ( cP @ X3 )
= $true )
| ? [X2: $i] :
( ( cP @ X2 )
!= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( ? [X5: $i] :
( ( cP @ X5 )
!= $true )
| ! [X4: $i] :
( ( cP @ X4 )
!= $true ) )
& ( ! [X5: $i] :
( ( cP @ X5 )
= $true )
| ? [X4: $i] :
( ( cP @ X4 )
= $true ) )
& ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cP @ X0 )
!= $true ) )
& ( ? [X3: $i] :
( ( cP @ X3 )
= $true )
| ? [X2: $i] :
( ( cP @ X2 )
!= $true ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f8,plain,
( ( ? [X5: $i] :
( ( cP @ X5 )
!= $true )
| ! [X4: $i] :
( ( cP @ X4 )
!= $true ) )
& ( ! [X5: $i] :
( ( cP @ X5 )
= $true )
| ? [X4: $i] :
( ( cP @ X4 )
= $true ) )
& ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cP @ X0 )
!= $true ) )
& ( ? [X3: $i] :
( ( cP @ X3 )
= $true )
| ? [X2: $i] :
( ( cP @ X2 )
!= $true ) ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
( ( ? [X0: $i] :
( ( cP @ X0 )
!= $true )
| ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ! [X2: $i] :
( ( cP @ X2 )
= $true )
| ? [X3: $i] :
( ( cP @ X3 )
= $true ) )
& ( ! [X4: $i] :
( ( cP @ X4 )
= $true )
| ! [X5: $i] :
( ( cP @ X5 )
!= $true ) )
& ( ? [X6: $i] :
( $true
= ( cP @ X6 ) )
| ? [X7: $i] :
( $true
!= ( cP @ X7 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
( ( ( $true
!= ( cP @ sK0 ) )
| ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ! [X2: $i] :
( ( cP @ X2 )
= $true )
| ( $true
= ( cP @ sK1 ) ) )
& ( ! [X4: $i] :
( ( cP @ X4 )
= $true )
| ! [X5: $i] :
( ( cP @ X5 )
!= $true ) )
& ( ( $true
= ( cP @ sK2 ) )
| ( $true
!= ( cP @ sK3 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X3,sK1),skolemize(X6,sK2),skolemize(X7,sK3)],[f9]) ).
thf(f12,plain,
! [X4: $i,X5: $i] :
( ( ( cP @ X4 )
= $true )
| ( ( cP @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
! [X2: $i] :
( ( ( cP @ X2 )
= $true )
| ( $true
= ( cP @ sK1 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f14,plain,
! [X1: $i] :
( ( $true
!= ( cP @ sK0 ) )
| ( ( cP @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f18,definition,
( spl4_1
<=> ! [X1: $i] :
( ( cP @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f19,plain,
( ! [X1: $i] :
( ( cP @ X1 )
!= $true )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f21,definition,
( spl4_2
<=> ( $true
= ( cP @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f23,plain,
( ( $true
!= ( cP @ sK0 ) )
| spl4_2 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f24,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f14,f21,f18]) ).
thf(f25,plain,
( ! [X2: $i] :
( ( cP @ X2 )
= $true )
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f13,f19]) ).
thf(f26,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f25,f19]) ).
thf(f27,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f26]) ).
thf(f38,definition,
( spl4_5
<=> ! [X4: $i] :
( ( cP @ X4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f39,plain,
( ! [X4: $i] :
( ( cP @ X4 )
= $true )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f38]) ).
thf(f40,plain,
( spl4_1
| spl4_5 ),
inference(avatar_split_clause,[],[f12,f38,f18]) ).
thf(f41,plain,
( ( $true != $true )
| spl4_2
| ~ spl4_5 ),
inference(constrained_superposition,[],[f23,f39]) ).
thf(f45,plain,
( $false
| spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f46,plain,
( spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f45]) ).
cnf(s8,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f24]) ).
cnf(s12,plain,
~ spl4_1,
inference(sat_conversion,[],[f27]) ).
cnf(s23,plain,
( spl4_1
| spl4_5 ),
inference(sat_conversion,[],[f40]) ).
cnf(s27,plain,
( spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f46]) ).
cnf(s28,plain,
spl4_5,
inference(rat,[],[s23,s12]) ).
cnf(s29,plain,
spl4_2,
inference(rat,[],[s27,s28]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s8,s29,s12]) ).
thf(f47,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN375^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n016.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:20:05 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.20/0.28 % (544723)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (544738)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=272174600:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (544738) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-544723-544738"...
% 0.20/0.28 % (544738)...printing done.
% 0.20/0.28 % (544738)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (544738)------------------------------
% 0.20/0.28 % (544738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (544738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (544738)CaDiCaL version: 2.1.3
% 0.20/0.28 % (544738)Termination reason: Refutation
% 0.20/0.28 % (544738)Time elapsed: 0.002 s
% 0.20/0.28 % (544738)Peak memory usage: 12 MB
% 0.20/0.28 % (544738)Instructions burned: 2 (million)
% 0.20/0.28 % (544723)Success in time 0.034 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------