%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV427^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:38:37 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 19 unt; 0 typ; 8 def)
% Number of atoms : 195 ( 44 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 139 ( 34 ~; 31 |; 1 &; 66 @)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 14 !; 3 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
p: $i > $o ).
thf(func_def_3,type,
q: $i > $o ).
thf(func_def_7,type,
sF1: $o ).
thf(func_def_9,type,
sF3: $o ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceax) ).
thf(f2,axiom,
! [X0: $i] :
( ( q @ X0 )
| ( p @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pq) ).
thf(f3,conjecture,
( ( q @ ( eps @ q ) )
| ( p @ ( eps @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f4,negated_conjecture,
~ ( ( q @ ( eps @ q ) )
| ( p @ ( eps @ p ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i] :
( ( q @ X0 )
| ( p @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
! [X0: $i] :
( ( ( q @ X0 )
= $true )
| ( ( p @ X0 )
= $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( ( q @ ( eps @ q ) )
| ( p @ ( eps @ p ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( ( p @ ( eps @ p ) )
= $true )
| ( ( q @ ( eps @ q ) )
= $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( ( q @ ( eps @ q ) )
!= $true )
& ( ( p @ ( eps @ p ) )
!= $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f13,plain,
! [X0: $i] :
( ( ( q @ X0 )
= $true )
| ( ( p @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( ( p @ ( eps @ p ) )
!= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( ( q @ ( eps @ q ) )
!= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( eps @ X0 ) )
= $true )
| ( ( X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f19,definition,
( sF0
= ( eps @ q ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f20,plain,
( ( eps @ q )
= sF0 ),
inference(reorient_equations,[],[f19]) ).
thf(f21,definition,
( sF1
= ( q @ sF0 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f22,plain,
$true != sF1,
inference(definition_folding,[],[f15,f21,f20]) ).
thf(f23,definition,
( sF2
= ( eps @ p ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f24,plain,
( ( eps @ p )
= sF2 ),
inference(reorient_equations,[],[f23]) ).
thf(f25,definition,
( sF3
= ( p @ sF2 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f26,plain,
( ( p @ sF2 )
= sF3 ),
inference(reorient_equations,[],[f25]) ).
thf(f27,plain,
$true != sF3,
inference(definition_folding,[],[f14,f26,f24]) ).
thf(f29,plain,
( ( ( p @ sF2 )
= $false )
| ( $true = sF3 ) ),
inference(iff_proxy_clausification,[],[f26]) ).
thf(f30,plain,
( ( $false
= ( q @ sF0 ) )
| ( $true = sF1 ) ),
inference(iff_proxy_clausification,[],[f21]) ).
thf(f33,definition,
( spl4_1
<=> ( $true = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f37,definition,
( spl4_2
<=> ( ( p @ sF2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f39,plain,
( ( ( p @ sF2 )
= $false )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f29,f37,f33]) ).
thf(f60,definition,
( spl4_7
<=> ( $false
= ( q @ sF0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f62,plain,
( ( $false
= ( q @ sF0 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f64,definition,
( spl4_8
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f67,plain,
( spl4_7
| spl4_8 ),
inference(avatar_split_clause,[],[f30,f64,f60]) ).
thf(f68,plain,
~ spl4_8,
inference(avatar_split_clause,[],[f22,f64]) ).
thf(f69,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f27,f33]) ).
thf(f95,plain,
( ( $true = $false )
| ( $true
= ( p @ sF0 ) )
| ~ spl4_7 ),
inference(constrained_superposition,[],[f62,f13]) ).
thf(f96,plain,
( ( $true
= ( p @ sF0 ) )
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f95]) ).
thf(f99,plain,
! [X0: $i] :
( ( ( p @ X0 )
!= $true )
| ( $true
= ( p @ sF2 ) ) ),
inference(constrained_superposition,[],[f16,f24]) ).
thf(f100,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( p @ X0 )
!= $true ) )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f99,f39]) ).
thf(f101,plain,
( ! [X0: $i] :
( ( p @ X0 )
!= $true )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f105,plain,
( ( $true != $true )
| ~ spl4_2
| ~ spl4_7 ),
inference(constrained_superposition,[],[f101,f96]) ).
thf(f110,plain,
( $false
| ~ spl4_2
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f105]) ).
thf(f111,plain,
( ~ spl4_2
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f110]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f40]) ).
cnf(s4,plain,
( spl4_7
| spl4_8 ),
inference(sat_conversion,[],[f67]) ).
cnf(s5,plain,
~ spl4_8,
inference(sat_conversion,[],[f68]) ).
cnf(s6,plain,
~ spl4_1,
inference(sat_conversion,[],[f69]) ).
cnf(s9,plain,
( ~ spl4_2
| ~ spl4_7 ),
inference(sat_conversion,[],[f111]) ).
cnf(s11,plain,
spl4_7,
inference(rat,[],[s4,s5]) ).
cnf(s12,plain,
~ spl4_2,
inference(rat,[],[s9,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s12,s6]) ).
thf(f112,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV427^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.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 : Tue Sep 29 15:47:34 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.28 % (3324742)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (3324753)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (3324753)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.28 % (3324753)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2763403478:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.28 % (3324753) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3324742-3324753"...
% 0.20/0.28 % (3324753)...printing done.
% 0.20/0.28 % (3324753)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 % (3324753)------------------------------
% 0.20/0.28 % (3324753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3324753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3324753)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3324753)Termination reason: Refutation
% 0.20/0.28 % (3324753)Time elapsed: 0.002 s
% 0.20/0.28 % (3324753)Peak memory usage: 13 MB
% 0.20/0.28 % (3324753)Instructions burned: 3 (million)
% 0.20/0.28 % (3324742)Success in time 0.03 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------