%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ102^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Wed Sep 30 08:20:53 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 25 unt; 0 typ; 7 def)
% Number of atoms : 258 ( 54 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 323 ( 33 ~; 42 |; 12 &; 188 @)
% ( 4 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 11 con; 0-4 aty)
% ( 18 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 50 ( 0 sgn 13 !; 1 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
s: $i > $i ).
thf(func_def_1,type,
cCKB_E2: $i > $i > $o ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vIMP: $o > $o > $o ).
thf(func_def_7,type,
vAND: $o > $o > $o ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sF3: $o ).
thf(func_def_16,type,
sK4: $i > $o ).
thf(func_def_17,type,
sK5: ( $i > $o ) > $i ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( ( X2 @ X0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ ( s @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) )
= cCKB_E2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB_E2_def) ).
thf(f2,conjecture,
! [X0: $i] : ( cCKB_E2 @ X0 @ ( s @ ( s @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB_L33000) ).
thf(f3,negated_conjecture,
~ ! [X0: $i] : ( cCKB_E2 @ X0 @ ( s @ ( s @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ! [X0: $i] : ( cCKB_E2 @ X0 @ ( s @ ( s @ X0 ) ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
~ ! [X0: $i] :
( ( cCKB_E2 @ X0 @ ( s @ ( s @ X0 ) ) )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( ( X2 @ X0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ ( s @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) )
= cCKB_E2 ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( cCKB_E2
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $i] :
( ( cCKB_E2 @ X0 @ ( s @ ( s @ X0 ) ) )
!= $true ),
inference(ennf_transformation,[],[f5]) ).
thf(f9,plain,
( ( cCKB_E2 @ sK0 @ ( s @ ( s @ sK0 ) ) )
!= $true ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f8]) ).
thf(f10,plain,
( ( cCKB_E2 @ sK0 @ ( s @ ( s @ sK0 ) ) )
!= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( cCKB_E2
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ ( s @ ( s @ sK0 ) ) )
!= $true ),
inference(definition_unfolding,[],[f10,f11]) ).
thf(f15,definition,
( sF1
= ( s @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f16,plain,
( ( s @ sK0 )
= sF1 ),
inference(reorient_equations,[],[f15]) ).
thf(f17,definition,
( sF2
= ( s @ sF1 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f18,definition,
( sF3
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sF2 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f19,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sF2 )
= sF3 ),
inference(reorient_equations,[],[f18]) ).
thf(f20,plain,
$true != sF3,
inference(definition_folding,[],[f14,f19,f17,f16]) ).
thf(f22,plain,
( ( $true = sF3 )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sF2 ) ) ),
inference(iff_proxy_clausification,[],[f19]) ).
thf(f23,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ sK0 ) )
=> ( Y0 @ sF2 ) ) ) )
| ( $true = sF3 ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( ( $true = sF3 )
| ( $false
= ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ sK0 ) )
=> ( Y0 @ sF2 ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ ( s @ Y0 ) ) ) ) )
& ( sK4 @ sK0 ) )
=> ( sK4 @ sF2 ) ) )
| ( $true = sF3 ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
( ( $true = sF3 )
| ( $false
= ( sK4 @ sF2 ) ) ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( $true = sF3 )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ ( s @ Y0 ) ) ) ) )
& ( sK4 @ sK0 ) ) ) ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f28,plain,
( ( $true = sF3 )
| ( ( sK4 @ sK0 )
= $true ) ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( $true = sF3 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ ( s @ Y0 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f30,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ ( s @ Y0 ) ) ) )
@ X1 )
= $true )
| ( $true = sF3 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X1: $i] :
( ( $true
= ( ( sK4 @ X1 )
=> ( sK4 @ ( s @ ( s @ X1 ) ) ) ) )
| ( $true = sF3 ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X1: $i] :
( ( ( sK4 @ X1 )
= $false )
| ( $true = sF3 )
| ( ( sK4 @ ( s @ ( s @ X1 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f43,definition,
( spl6_1
<=> ! [X1: $i] :
( ( ( sK4 @ X1 )
= $false )
| ( ( sK4 @ ( s @ ( s @ X1 ) ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f44,plain,
( ! [X1: $i] :
( ( ( sK4 @ ( s @ ( s @ X1 ) ) )
= $true )
| ( ( sK4 @ X1 )
= $false ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f46,definition,
( spl6_2
<=> ( $true = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f49,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f32,f46,f43]) ).
thf(f51,definition,
( spl6_3
<=> ( ( sK4 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f53,plain,
( ( ( sK4 @ sK0 )
= $true )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f54,plain,
( spl6_3
| spl6_2 ),
inference(avatar_split_clause,[],[f28,f46,f51]) ).
thf(f56,definition,
( spl6_4
<=> ( $false
= ( sK4 @ sF2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f58,plain,
( ( $false
= ( sK4 @ sF2 ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f56]) ).
thf(f59,plain,
( spl6_2
| spl6_4 ),
inference(avatar_split_clause,[],[f26,f56,f46]) ).
thf(f72,plain,
~ spl6_2,
inference(avatar_split_clause,[],[f20,f46]) ).
thf(f85,plain,
( ( ( sK4 @ sK0 )
= $false )
| ( ( sK4 @ ( s @ sF1 ) )
= $true )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f44,f16]) ).
thf(f87,plain,
( ( ( sK4 @ ( s @ sF1 ) )
= $true )
| ( $false = $true )
| ~ spl6_1
| ~ spl6_3 ),
inference(forward_demodulation,[],[f85,f53]) ).
thf(f88,plain,
( ( ( sK4 @ ( s @ sF1 ) )
= $true )
| ~ spl6_1
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f98,plain,
( ( ( sK4 @ sF2 )
= $true )
| ~ spl6_1
| ~ spl6_3 ),
inference(forward_demodulation,[],[f88,f17]) ).
thf(f99,plain,
( ( $false = $true )
| ~ spl6_1
| ~ spl6_3
| ~ spl6_4 ),
inference(forward_demodulation,[],[f98,f58]) ).
thf(f100,plain,
( $false
| ~ spl6_1
| ~ spl6_3
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f101,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4 ),
inference(avatar_contradiction_clause,[],[f100]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s2,plain,
( spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f54]) ).
cnf(s3,plain,
( spl6_2
| spl6_4 ),
inference(sat_conversion,[],[f59]) ).
cnf(s6,plain,
~ spl6_2,
inference(sat_conversion,[],[f72]) ).
cnf(s8,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f101]) ).
cnf(s9,plain,
spl6_4,
inference(rat,[],[s3,s6]) ).
cnf(s10,plain,
spl6_3,
inference(rat,[],[s2,s6]) ).
cnf(s11,plain,
~ spl6_1,
inference(rat,[],[s8,s9,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s6,s11]) ).
thf(f102,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ102^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:24:07 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.28 % (1267016)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1267027)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (1267027)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
% 0.22/0.28 % (1267027)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=3102780277:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.28 % (1267027) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1267016-1267027"...
% 0.22/0.28 % (1267027)...printing done.
% 0.22/0.28 % (1267027)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (1267027)------------------------------
% 0.22/0.28 % (1267027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1267027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1267027)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1267027)Termination reason: Refutation
% 0.22/0.28 % (1267027)Time elapsed: 0.003 s
% 0.22/0.28 % (1267027)Peak memory usage: 13 MB
% 0.22/0.28 % (1267027)Instructions burned: 5 (million)
% 0.22/0.28 % (1267016)Success in time 0.028 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------