%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET173^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:23:15 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 13 unt; 0 typ; 3 def)
% Number of atoms : 147 ( 33 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 149 ( 20 ~; 47 |; 14 &; 65 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 22 ( 0 sgn 8 !; 2 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vAND: $o > $o > $o ).
thf(func_def_2,type,
vOR: $o > $o > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: a > $o ).
thf(func_def_10,type,
sK3: a ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( X0
= ( ^ [X2: a] :
( ( X0 @ X2 )
& ( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_68_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( X0
= ( ^ [X2: a] :
( ( X0 @ X2 )
& ( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( X1
= ( ^ [X2: a] :
( ( X1 @ X2 )
& ( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X1: a > $o,X0: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
| ( X0 @ Y0 ) )
& ( X1 @ Y0 ) ) )
= X1 ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
| ( X0 @ Y0 ) )
& ( X1 @ Y0 ) ) )
!= X1 ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) ) )
!= sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) ) )
!= sK1 ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,definition,
( spl2_1
<=> ( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) ) )
= sK1 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f12,plain,
( ( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) ) )
!= sK1 )
| spl2_1 ),
inference(avatar_component_clause,[],[f10]) ).
thf(f13,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f7,f10]) ).
thf(f14,plain,
( ( ( sK1 @ sK3 )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) )
@ sK3 ) )
| spl2_1 ),
inference(negative_extensionality,[],[f12]) ).
thf(f15,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) )
@ sK3 ) )
| spl2_1 ),
inference(xor_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) )
@ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| spl2_1 ),
inference(xor_proxy_clausification,[],[f14]) ).
thf(f17,plain,
( ( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK1 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| spl2_1 ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
( ( $false
= ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| spl2_1 ),
inference(and_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| spl2_1 ),
inference(or_proxy_clausification,[],[f18]) ).
thf(f21,plain,
( ( ( sK1 @ sK3 )
= $false )
| spl2_1 ),
inference(duplicate_literal_removal,[],[f20]) ).
thf(f23,plain,
( ( $true
= ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK1 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $true )
| spl2_1 ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f24,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| spl2_1 ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f28,plain,
( ( ( sK1 @ sK3 )
= $true )
| spl2_1 ),
inference(duplicate_literal_removal,[],[f24]) ).
thf(f30,definition,
( spl2_2
<=> ( ( sK1 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f32,plain,
( ( ( sK1 @ sK3 )
= $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f33,plain,
( spl2_2
| spl2_1 ),
inference(avatar_split_clause,[],[f21,f10,f30]) ).
thf(f40,definition,
( spl2_4
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f42,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f48,plain,
( spl2_4
| spl2_1 ),
inference(avatar_split_clause,[],[f28,f10,f40]) ).
thf(f49,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(forward_demodulation,[],[f42,f32]) ).
thf(f50,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f51,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f50]) ).
cnf(s1,plain,
~ spl2_1,
inference(sat_conversion,[],[f13]) ).
cnf(s2,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s5,plain,
( spl2_1
| spl2_4 ),
inference(sat_conversion,[],[f48]) ).
cnf(s6,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f51]) ).
cnf(s7,plain,
spl2_4,
inference(rat,[],[s5,s1]) ).
cnf(s8,plain,
spl2_2,
inference(rat,[],[s2,s1]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s6,s7,s8]) ).
thf(f52,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET173^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:39:26 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.19/0.28 % (75002)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (75010)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=447950230:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.28 % (75010)Refutation not found, incomplete strategy
% 0.19/0.28 % (75010)------------------------------
% 0.19/0.28 % (75010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (75010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (75010)CaDiCaL version: 2.1.3
% 0.19/0.28 % (75010)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.28 % (75010)Time elapsed: 0.0000 s
% 0.19/0.28 % (75010)Peak memory usage: 12 MB
% 0.19/0.28 % (75010)------------------------------
% 0.19/0.28 % (75010)------------------------------
% 0.19/0.28 % (75011)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=196257156:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.28 % (75014)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.28 % (75014)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
% 0.19/0.28 % (75011) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-75002-75011"...
% 0.19/0.28 % (75016)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1302744273:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.28 % (75011)...printing done.
% 0.19/0.28 % (75016) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-75002-75016"...
% 0.19/0.28 % (75011)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (75011)------------------------------
% 0.19/0.28 % (75011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (75011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (75011)CaDiCaL version: 2.1.3
% 0.19/0.28 % (75011)Termination reason: Refutation
% 0.19/0.28 % (75011)Time elapsed: 0.003 s
% 0.19/0.28 % (75011)Peak memory usage: 13 MB
% 0.19/0.28 % (75011)Instructions burned: 2 (million)
% 0.19/0.28 % (75002)Success in time 0.041 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------