%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET636^5 : 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 : n003.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 08:23:26 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 1
% Syntax : Number of formulae : 54 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 417 ( 139 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 329 ( 44 ~; 77 |; 39 &; 164 @)
% ( 4 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 88 ( 54 ^; 22 !; 12 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
sK0: a > $o ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_8,type,
sK2: a ).
thf(func_def_9,type,
sK3: a ).
thf(func_def_10,type,
sK4: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ~ ? [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) )
<=> ( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X2: a] : $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_118_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ~ ? [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) )
<=> ( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X2: a] : $false ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ~ ? [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) )
<=> ( ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 ) ) )
= ( ^ [X4: a] : $false ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X1: a > $o,X0: a > $o] :
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
<=> ~ ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
<~> ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) )
& ( ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ( ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) )
& ( ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
!= $true ) )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( ( ( sK1 @ sK2 )
= $true )
& ( $true
= ( sK0 @ sK2 ) ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) )
& ( ! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( $true
!= ( sK0 @ X3 ) ) )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f7]) ).
thf(f9,plain,
! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( $true
!= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( ( sK1 @ sK2 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( ( ^ [Y0: a] : $false
@ sK3 )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK3 ) ) ),
inference(negative_extensionality,[],[f10]) ).
thf(f14,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK3 )
= $true )
| ( ( ^ [Y0: a] : $false
@ sK3 )
= $true ) ),
inference(xor_proxy_clausification,[],[f13]) ).
thf(f18,plain,
( ( $false = $true )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f19,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $false = $true )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( $false = $true )
| ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f18]) ).
thf(f21,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f20]) ).
thf(f22,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f19]) ).
thf(f23,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK4 )
!= ( ^ [Y0: a] : $false
@ sK4 ) )
| ( ( sK1 @ sK2 )
= $true ) ),
inference(negative_extensionality,[],[f11]) ).
thf(f24,plain,
( ( ( ^ [Y0: a] : $false
@ sK4 )
= $true )
| ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK4 )
= $true )
| ( ( sK1 @ sK2 )
= $true ) ),
inference(xor_proxy_clausification,[],[f23]) ).
thf(f28,plain,
( ( $false = $true )
| ( ( sK1 @ sK2 )
= $true )
| ( ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f29,plain,
( ( ( sK1 @ sK2 )
= $true )
| ( $false = $true )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( $false = $true )
| ( ( sK0 @ sK4 )
= $true )
| ( ( sK1 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f31,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( ( sK1 @ sK2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f32,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( ( sK1 @ sK2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f33,plain,
( ( $true != $true )
| ( ( sK1 @ sK2 )
= $true )
| ( ( sK0 @ sK4 )
!= $true )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(superposition,[],[f9,f32]) ).
thf(f34,plain,
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( ( sK1 @ sK2 )
= $true )
| ( ( sK0 @ sK4 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f35,plain,
( ( ( sK1 @ sK2 )
= $true )
| ( ( sK0 @ sK4 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f34,f11]) ).
thf(f36,plain,
( ( sK1 @ sK2 )
= $true ),
inference(forward_subsumption_resolution,[],[f35,f31]) ).
thf(f37,plain,
( ( $true
!= ( sK0 @ sK2 ) )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( $true != $true ) ),
inference(superposition,[],[f9,f36]) ).
thf(f38,plain,
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( $true
!= ( sK0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f39,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 )
= ( ^ [Y0: a] : $false
@ X1 ) )
| ( $true
!= ( sK0 @ sK2 ) ) ),
inference(argument_congruence,[],[f38]) ).
thf(f44,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 )
= $false )
| ( ( ^ [Y0: a] : $false
@ X1 )
= $true )
| ( $true
!= ( sK0 @ sK2 ) ) ),
inference(iff_proxy_clausification,[],[f39]) ).
thf(f45,plain,
! [X1: a] :
( ( $false = $true )
| ( $true
!= ( sK0 @ sK2 ) )
| ( $false
= ( ( sK0 @ X1 )
& ( sK1 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
! [X1: a] :
( ( $true
!= ( sK0 @ sK2 ) )
| ( $false = $true )
| ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X1: a] :
( ( $true
!= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f51,plain,
! [X0: a] :
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[],[f47,f22]) ).
thf(f52,plain,
! [X0: a] :
( ( $false
= ( sK0 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f51]) ).
thf(f57,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false = $true )
| ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(superposition,[],[f22,f52]) ).
thf(f61,plain,
( ( $false = $true )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f57]) ).
thf(f62,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f61]) ).
thf(f68,plain,
( ( $false = $true )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(forward_demodulation,[],[f62,f36]) ).
thf(f69,plain,
( $true
= ( sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f72,plain,
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( $true != $true )
| ( ( sK0 @ sK3 )
!= $true ) ),
inference(superposition,[],[f9,f69]) ).
thf(f73,plain,
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( ( sK0 @ sK3 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f76,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( ( sK0 @ sK3 )
!= $true )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] : $false ) ) ),
inference(superposition,[],[f10,f73]) ).
thf(f77,plain,
( ( ( sK0 @ sK3 )
!= $true )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f76]) ).
thf(f87,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(forward_subsumption_resolution,[],[f77,f21]) ).
thf(f89,plain,
! [X0: a] :
( ( $true != $true )
| ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) ) ),
inference(superposition,[],[f47,f87]) ).
thf(f93,plain,
! [X0: a] :
( ( $false
= ( sK0 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f89]) ).
thf(f94,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(superposition,[],[f93,f87]) ).
thf(f103,plain,
( $false
= ( sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f112,plain,
$false = $true,
inference(superposition,[],[f36,f103]) ).
thf(f114,plain,
$false,
inference(trivial_inequality_removal,[],[f112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET636^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n003.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 13:41:59 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
% 0.22/0.28 % (2514284)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (2514301)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3846918568:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.28 % (2514301) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2514284-2514301"...
% 0.22/0.28 % (2514301)...printing done.
% 0.22/0.28 % (2514303)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 % (2514303)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 % (2514301)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 % (2514301)------------------------------
% 0.22/0.28 % (2514301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (2514301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (2514301)CaDiCaL version: 2.1.3
% 0.22/0.28 % (2514301)Termination reason: Refutation
% 0.22/0.28 % (2514301)Time elapsed: 0.003 s
% 0.22/0.28 % (2514301)Peak memory usage: 12 MB
% 0.22/0.28 % (2514301)Instructions burned: 6 (million)
% 0.22/0.28 % (2514284)Success in time 0.03 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------