%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO304^5 : 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 : n020.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 08:47:24 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 15 unt; 0 typ; 4 def)
% Number of atoms : 188 ( 71 equ; 5 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 250 ( 46 ~; 45 |; 2 &; 112 @)
% ( 4 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 17 usr; 10 con; 0-4 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 70 ( 0 sgn 12 !; 1 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
vIMP: $o > $o > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_10,type,
sK0: ( a > a > $o ) > $o ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(func_def_12,type,
sK1: a ).
thf(func_def_13,type,
sK2: a ).
thf(func_def_14,type,
sK3: a > $o ).
thf(f1,conjecture,
! [X0: ( a > a > $o ) > $o] :
( ( X0
@ ^ [X1: a,X2: a] :
! [X3: a > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
=> ( X0
@ ^ [X1: a,X2: a] : ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cE2_eq__pme) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > a > $o ) > $o] :
( ( X0
@ ^ [X1: a,X2: a] :
! [X3: a > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
=> ( X0
@ ^ [X1: a,X2: a] : ( X1 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: ( a > a > $o ) > $o] :
( ( X0
@ ^ [X1: a,X2: a] :
! [X3: a > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
=> ( X0
@ ^ [X4: a,X5: a] : ( X4 = X5 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: ( a > a > $o ) > $o] :
( ( $true
= ( X0
@ ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( $true
= ( X0
@ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: ( a > a > $o ) > $o] :
( ( $true
= ( X0
@ ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) )
& ( $true
!= ( X0
@ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( $true
= ( sK0
@ ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) )
& ( $true
!= ( sK0
@ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f5]) ).
thf(f7,plain,
( $true
!= ( sK0
@ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( $true
= ( sK0
@ ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
( $true
!= ( sK0 @ (=) ) ),
inference(beta-eta_normalization,[],[f7]) ).
thf(f12,plain,
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) )
!= (=) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f11,f8]) ).
thf(f13,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) )
!= (=) ),
inference(trivial_inequality_removal,[],[f12]) ).
thf(f14,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK1 )
!= ( (=) @ sK1 ) ),
inference(negative_extensionality,[],[f13]) ).
thf(f15,plain,
( ( (=) @ sK1 )
!= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK1 )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f16,plain,
( ( sK1 = sK2 )
!= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK1 )
=> ( Y1 @ Y0 ) ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f15]) ).
thf(f17,plain,
( ( $true
= ( sK1 = sK2 ) )
| ( $true
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK1 )
=> ( Y1 @ Y0 ) ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( $false
= ( sK1 = sK2 ) )
| ( $false
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK1 )
=> ( Y1 @ Y0 ) ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f19,plain,
( ( sK1 != sK2 )
| ( $false
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK1 )
=> ( Y1 @ Y0 ) ) )
@ sK2 ) ) ),
inference(equality_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK2 ) ) ) )
| ( sK1 != sK2 ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( sK1 != sK2 )
| ( ( ^ [Y0: a > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK2 ) )
@ sK3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( sK1 != sK2 )
| ( $false
= ( ( sK3 @ sK1 )
=> ( sK3 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
( ( $false
= ( sK3 @ sK2 ) )
| ( sK1 != sK2 ) ),
inference(imp_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( sK1 != sK2 )
| ( $true
= ( sK3 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f22]) ).
thf(f25,plain,
( ( $true
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK1 )
=> ( Y1 @ Y0 ) ) )
@ sK2 ) )
| ( sK1 = sK2 ) ),
inference(equality_proxy_clausification,[],[f17]) ).
thf(f26,plain,
( ( sK1 = sK2 )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
! [X1: a > $o] :
( ( sK1 = sK2 )
| ( $true
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK2 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X1: a > $o] :
( ( $true
= ( ( X1 @ sK1 )
=> ( X1 @ sK2 ) ) )
| ( sK1 = sK2 ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
! [X1: a > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( sK1 = sK2 )
| ( $false
= ( X1 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f31,definition,
( spl4_1
<=> ( sK1 = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f32,plain,
( ( sK1 = sK2 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f33,plain,
( ( sK1 != sK2 )
| spl4_1 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f35,definition,
( spl4_2
<=> ( $true
= ( sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f37,plain,
( ( $true
= ( sK3 @ sK1 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f38,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f24,f35,f31]) ).
thf(f40,definition,
( spl4_3
<=> ( $false
= ( sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f42,plain,
( ( $false
= ( sK3 @ sK2 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,plain,
( spl4_3
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f23,f31,f40]) ).
thf(f45,definition,
( spl4_4
<=> ! [X1: a > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( $false
= ( X1 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f46,plain,
( ! [X1: a > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( $false
= ( X1 @ sK1 ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f47,plain,
( spl4_4
| spl4_1 ),
inference(avatar_split_clause,[],[f29,f31,f45]) ).
thf(f49,plain,
( ( sK1 = sK2 )
| ~ spl4_4 ),
inference(leibniz_equality_elimination,[],[f46]) ).
thf(f68,plain,
( $false
| spl4_1
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f49,f33]) ).
thf(f69,plain,
( spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f68]) ).
thf(f70,plain,
( ( ( sK3 @ sK1 )
= $false )
| ~ spl4_1
| ~ spl4_3 ),
inference(constrained_superposition,[],[f42,f32]) ).
thf(f71,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(constrained_superposition,[],[f70,f37]) ).
thf(f75,plain,
( $false
| ~ spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f76,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f75]) ).
cnf(s1,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f38]) ).
cnf(s2,plain,
( ~ spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
( spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f47]) ).
cnf(s5,plain,
( spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f69]) ).
cnf(s7,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f76]) ).
cnf(s8,plain,
spl4_1,
inference(rat,[],[s3,s5]) ).
cnf(s9,plain,
spl4_3,
inference(rat,[],[s2,s8]) ).
cnf(s10,plain,
spl4_2,
inference(rat,[],[s1,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s7,s8,s9,s10]) ).
thf(f77,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO304^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n020.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 16:45:20 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 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
% 0.21/0.28 % (1291740)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (1291746)lrs+10_16_si=on:nwc=1.5:random_seed=3054856955:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (1291746) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1291740-1291746"...
% 0.21/0.28 % (1291746)...printing done.
% 0.21/0.28 % (1291746)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (1291746)------------------------------
% 0.21/0.28 % (1291746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1291746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1291746)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1291746)Termination reason: Refutation
% 0.21/0.28 % (1291746)Time elapsed: 0.002 s
% 0.21/0.28 % (1291746)Peak memory usage: 13 MB
% 0.21/0.28 % (1291746)Instructions burned: 5 (million)
% 0.21/0.28 % (1291740)Success in time 0.039 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------