%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET011^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:23:10 AM UTC 2026
% Result : Theorem 0.26s 0.36s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 33 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 211 ( 63 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 239 ( 42 ~; 31 |; 46 &; 120 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 30 ( 20 ^; 8 !; 2 ?; 30 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_4,type,
vNOT: $o > $o ).
thf(func_def_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: a > $o ).
thf(func_def_9,type,
sK2: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= ( ^ [X2: a] :
( ( X0 @ X2 )
& ~ ( ( X0 @ X2 )
& ~ ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_82_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= ( ^ [X2: a] :
( ( X0 @ X2 )
& ~ ( ( X0 @ X2 )
& ~ ( X1 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= ( ^ [X3: a] :
( ( X0 @ X3 )
& ~ ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X1: a > $o,X0: a > $o] :
( ( ^ [Y0: a] :
( ~ ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
& ( X0 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ~ ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
& ( X0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ~ ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ),
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 ) )
& ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK2 )
!= ( ^ [Y0: a] :
( ~ ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK0 @ Y0 ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f10,plain,
( ( $true
= ( ^ [Y0: a] :
( ~ ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK0 @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f11,plain,
( ( ( ^ [Y0: a] :
( ~ ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK0 @ Y0 ) )
@ sK2 )
= $false )
| ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK2 )
= $false ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f12,plain,
( ( ( ~ ( ~ ( sK1 @ sK2 )
& ( sK0 @ sK2 ) )
& ( sK0 @ sK2 ) )
= $false )
| ( ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f13,plain,
( ( ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) )
= $false )
| ( ( ~ ( ~ ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) )
= $false )
| ( ( sK0 @ sK2 )
= $false ) ),
inference(and_proxy_clausification,[],[f12]) ).
thf(f14,plain,
( ( ( sK0 @ sK2 )
= $false )
| ( ( sK1 @ sK2 )
= $false )
| ( ( ~ ( ~ ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) )
= $false )
| ( ( sK0 @ sK2 )
= $false ) ),
inference(and_proxy_clausification,[],[f13]) ).
thf(f15,plain,
( ( $true
= ( ~ ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) )
| ( ( sK1 @ sK2 )
= $false )
| ( ( sK0 @ sK2 )
= $false )
| ( ( sK0 @ sK2 )
= $false ) ),
inference(not_proxy_clausification,[],[f14]) ).
thf(f17,plain,
( ( $true
= ( ~ ( sK1 @ sK2 ) ) )
| ( ( sK0 @ sK2 )
= $false )
| ( ( sK1 @ sK2 )
= $false )
| ( ( sK0 @ sK2 )
= $false ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f18,plain,
( ( ( sK0 @ sK2 )
= $false )
| ( ( sK1 @ sK2 )
= $false )
| ( ( sK1 @ sK2 )
= $false )
| ( ( sK0 @ sK2 )
= $false ) ),
inference(not_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( ( sK0 @ sK2 )
= $false )
| ( ( sK1 @ sK2 )
= $false ) ),
inference(duplicate_literal_removal,[],[f18]) ).
thf(f21,plain,
( ( $true
= ( ~ ( ~ ( sK1 @ sK2 )
& ( sK0 @ sK2 ) )
& ( sK0 @ sK2 ) ) )
| ( $true
= ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f10]) ).
thf(f22,plain,
( ( $true
= ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( $true
= ( ~ ( ~ ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) ) )
| ( $true
= ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f24,plain,
( ( $true
= ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) )
| ( ( ~ ( sK1 @ sK2 )
& ( sK0 @ sK2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f23]) ).
thf(f26,plain,
( ( ( ~ ( sK1 @ sK2 )
& ( sK0 @ sK2 ) )
= $false )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f24]) ).
thf(f27,plain,
( ( ( sK0 @ sK2 )
= $false )
| ( $true
= ( sK1 @ sK2 ) )
| ( ( ~ ( sK1 @ sK2 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) )
| ( ( sK0 @ sK2 )
= $false ) ),
inference(not_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( ( sK0 @ sK2 )
= $false )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f28]) ).
thf(f32,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f22]) ).
thf(f34,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(duplicate_literal_removal,[],[f32]) ).
thf(f35,plain,
( ( ( sK1 @ sK2 )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f19,f34]) ).
thf(f36,plain,
( ( sK1 @ sK2 )
= $false ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f37,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f29,f34]) ).
thf(f38,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f39,plain,
$true = $false,
inference(forward_demodulation,[],[f38,f36]) ).
thf(f40,plain,
$false,
inference(trivial_inequality_removal,[],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET011^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.26 % Computer : n026.cluster.edu
% 0.13/0.26 % Model : x86_64 x86_64
% 0.13/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.26 % Memory : 8046.5625MB
% 0.13/0.26 % OS : Linux 6.8.0-71-generic
% 0.13/0.26 % CPULimit : 300
% 0.13/0.26 % WCLimit : 300
% 0.13/0.26 % DateTime : Tue Sep 29 13:38:04 UTC 2026
% 0.13/0.26 % CPUTime :
% 0.13/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.31 Running higher-order theorem proving
% 0.26/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.36 % (593989)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.36 % (593999)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4221180039:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.26/0.36 % (594001)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.26/0.36 % (594001)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
% 0.26/0.36 % (593999) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-593989-593999"...
% 0.26/0.36 % (593999)...printing done.
% 0.26/0.36 % (593999)Refutation found. Thanks to Tanya!
% 0.26/0.36 % SZS status Theorem for theBenchmark
% 0.26/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.36 % (593999)------------------------------
% 0.26/0.36 % (593999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.36 % (593999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.36 % (593999)CaDiCaL version: 2.1.3
% 0.26/0.36 % (593999)Termination reason: Refutation
% 0.26/0.36 % (593999)Time elapsed: 0.002 s
% 0.26/0.36 % (593999)Peak memory usage: 12 MB
% 0.26/0.36 % (593999)Instructions burned: 3 (million)
% 0.26/0.36 % (593989)Success in time 0.026 s
% 0.26/0.36 % Vampire exiting
%------------------------------------------------------------------------------