%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO374^5 : 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 : n019.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 08:47:33 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 9 unt; 0 typ; 4 def)
% Number of atoms : 148 ( 36 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 199 ( 63 ~; 47 |; 3 &; 72 @)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 8 con; 0-4 aty)
% Number of variables : 25 ( 0 sgn 23 !; 2 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cN: $i > $i ).
thf(func_def_1,type,
cM: $i > $i ).
thf(func_def_3,type,
sK0: ( $i > $i ) > $o ).
thf(func_def_6,type,
vNOT: $o > $o ).
thf(func_def_9,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
db1:
!>[X0: $tType] : X0 ).
thf(f1,conjecture,
( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cM @ X0 ) )
<=> ( X1 @ ( cN @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2 @ cM )
<=> ( X2 @ cN ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT_A_LEIB2) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cM @ X0 ) )
<=> ( X1 @ ( cN @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2 @ cM )
<=> ( X2 @ cN ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cM @ X0 ) )
<=> ( X1 @ ( cN @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2 @ cM )
<=> ( X2 @ cN ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X1: $i > $o,X0: $i] :
( ( X1 @ ( cM @ X0 ) )
= ( X1 @ ( cN @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2 @ cM )
= ( X2 @ cN ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X1: $i > $o,X0: $i] :
( ( X1 @ ( cM @ X0 ) )
= ( X1 @ ( cN @ X0 ) ) )
& ? [X2: ( $i > $i ) > $o] :
( ( X2 @ cM )
!= ( X2 @ cN ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X0: $i > $o,X1: $i] :
( ( X0 @ ( cN @ X1 ) )
= ( X0 @ ( cM @ X1 ) ) )
& ? [X2: ( $i > $i ) > $o] :
( ( X2 @ cM )
!= ( X2 @ cN ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i > $o,X1: $i] :
( ( X0 @ ( cN @ X1 ) )
= ( X0 @ ( cM @ X1 ) ) )
& ( ( sK0 @ cM )
!= ( sK0 @ cN ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0)],[f6]) ).
thf(f8,plain,
( ( sK0 @ cM )
!= ( sK0 @ cN ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X0: $i > $o,X1: $i] :
( ( X0 @ ( cN @ X1 ) )
= ( X0 @ ( cM @ X1 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
( ( ( sK0 @ cM )
= $true )
| ( ( sK0 @ cN )
= $true ) ),
inference(xor_proxy_clausification,[],[f8]) ).
thf(f13,plain,
( ( ( sK0 @ cN )
= $false )
| ( ( sK0 @ cM )
= $false ) ),
inference(xor_proxy_clausification,[],[f8]) ).
thf(f14,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( cN @ X1 ) )
= $true )
| ( $false
= ( X0 @ ( cM @ X1 ) ) ) ),
inference(iff_proxy_clausification,[],[f9]) ).
thf(f17,definition,
( spl1_1
<=> ( ( sK0 @ cN )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f19,plain,
( ( ( sK0 @ cN )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f21,definition,
( spl1_2
<=> ( ( sK0 @ cM )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f23,plain,
( ( ( sK0 @ cM )
= $false )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f24,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f13,f21,f17]) ).
thf(f26,definition,
( spl1_3
<=> ( ( sK0 @ cN )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f28,plain,
( ( ( sK0 @ cN )
= $true )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f30,definition,
( spl1_4
<=> ( ( sK0 @ cM )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f32,plain,
( ( ( sK0 @ cM )
= $true )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f33,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f12,f30,f26]) ).
thf(f34,plain,
( ( $false = $true )
| ( cM != cN )
| ~ spl1_2
| ~ spl1_3 ),
inference(constrained_superposition,[],[f28,f23]) ).
thf(f36,plain,
( ( cM != cN )
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f38,plain,
( ( ( cM @ sK2 )
!= ( cN @ sK2 ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(negative_extensionality,[],[f36]) ).
thf(f39,plain,
! [X0: $i] :
( ( cM @ X0 )
= ( cN @ X0 ) ),
inference(leibniz_equality_elimination,[],[f14]) ).
thf(f61,plain,
( ( ( cM @ sK2 )
!= ( cM @ sK2 ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(constrained_superposition,[],[f38,f39]) ).
thf(f63,plain,
( $false
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f61]) ).
thf(f64,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f63]) ).
thf(f68,plain,
( ( $false = $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(constrained_superposition,[],[f28,f19]) ).
thf(f77,plain,
( $false
| ~ spl1_1
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f78,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f77]) ).
thf(f83,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_4 ),
inference(forward_demodulation,[],[f32,f23]) ).
thf(f84,plain,
( $false
| ~ spl1_2
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f85,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f84]) ).
thf(f108,plain,
( ( cM != cN )
| ( $false = $true )
| ~ spl1_1
| ~ spl1_4 ),
inference(constrained_superposition,[],[f19,f32]) ).
thf(f109,plain,
( ( cM != cN )
| ~ spl1_1
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f112,plain,
( ( ( cM @ sK3 )
!= ( cN @ sK3 ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(negative_extensionality,[],[f109]) ).
thf(f113,plain,
( $false
| ~ spl1_1
| ~ spl1_4 ),
inference(forward_subsumption_resolution,[],[f112,f39]) ).
thf(f114,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f113]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f24]) ).
cnf(s2,plain,
( spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f33]) ).
cnf(s3,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f64]) ).
cnf(s5,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(sat_conversion,[],[f78]) ).
cnf(s6,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(sat_conversion,[],[f85]) ).
cnf(s7,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(sat_conversion,[],[f114]) ).
cnf(s8,plain,
~ spl1_2,
inference(rat,[],[s2,s3,s6]) ).
cnf(s9,plain,
spl1_1,
inference(rat,[],[s1,s8]) ).
cnf(s10,plain,
~ spl1_4,
inference(rat,[],[s7,s9]) ).
cnf(s11,plain,
~ spl1_3,
inference(rat,[],[s5,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s2,s10,s11]) ).
thf(f115,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO374^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n019.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 16:49:33 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 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
% 0.22/0.28 % (1048755)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1048770)lrs+10_16_si=on:nwc=1.5:random_seed=2515386769:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.28 % (1048770) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1048755-1048770"...
% 0.22/0.28 % (1048770)...printing done.
% 0.22/0.28 % (1048770)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 % (1048770)------------------------------
% 0.22/0.28 % (1048770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1048770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1048770)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1048770)Termination reason: Refutation
% 0.22/0.28 % (1048770)Time elapsed: 0.003 s
% 0.22/0.28 % (1048770)Peak memory usage: 13 MB
% 0.22/0.28 % (1048770)Instructions burned: 6 (million)
% 0.22/0.28 % (1048755)Success in time 0.021 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------