%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV288^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 08:39:16 AM UTC 2026
% Result : Theorem 0.05s 0.24s
% Output : Refutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 15 unt; 0 typ; 4 def)
% Number of atoms : 157 ( 62 equ; 3 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 207 ( 40 ~; 41 |; 0 &; 89 @)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 16 usr; 10 con; 0-4 aty)
% ( 13 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 57 ( 0 sgn 8 !; 0 ?; 57 :)
% 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_7,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_10,type,
vNOT: $o > $o ).
thf(func_def_11,type,
sK0: a ).
thf(func_def_12,type,
sK1: a ).
thf(func_def_13,type,
sK2: a > $o ).
thf(f1,conjecture,
( ( ^ [X0: a,X1: a] :
! [X2: a > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= ( ^ [X0: a,X1: a] : ( X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cE1_eq__pme) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a,X1: a] :
! [X2: a > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
!= ( ^ [X0: a,X1: a] : ( X0 = X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( ( ^ [X0: a,X1: a] :
! [X2: a > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
!= ( ^ [X3: a,X4: a] : ( X3 = X4 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) )
!= (=) ),
inference(beta-eta_normalization,[],[f6]) ).
thf(f10,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK0 )
!= ( (=) @ sK0 ) ),
inference(negative_extensionality,[],[f9]) ).
thf(f11,plain,
( ( (=) @ sK0 )
!= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK0 )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f10]) ).
thf(f12,plain,
( ( sK0 = sK1 )
!= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK0 )
=> ( Y1 @ Y0 ) ) )
@ sK1 ) ),
inference(negative_extensionality,[],[f11]) ).
thf(f13,plain,
( ( $true
= ( sK0 = sK1 ) )
| ( $true
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK0 )
=> ( Y1 @ Y0 ) ) )
@ sK1 ) ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f14,plain,
( ( $false
= ( sK0 = sK1 ) )
| ( $false
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK0 )
=> ( Y1 @ Y0 ) ) )
@ sK1 ) ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f15,plain,
( ( sK0 != sK1 )
| ( $false
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK0 )
=> ( Y1 @ Y0 ) ) )
@ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( sK0 != sK1 )
| ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
( ( sK0 != sK1 )
| ( $false
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( sK0 != sK1 )
| ( $false
= ( ( sK2 @ sK0 )
=> ( sK2 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
( ( sK0 != sK1 )
| ( $false
= ( sK2 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( sK0 != sK1 )
| ( $true
= ( sK2 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f21,plain,
( ( sK0 = sK1 )
| ( $true
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK0 )
=> ( Y1 @ Y0 ) ) )
@ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f13]) ).
thf(f22,plain,
( ( sK0 = sK1 )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
! [X1: a > $o] :
( ( sK0 = sK1 )
| ( $true
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X1: a > $o] :
( ( sK0 = sK1 )
| ( $true
= ( ( X1 @ sK0 )
=> ( X1 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X1: a > $o] :
( ( sK0 = sK1 )
| ( $false
= ( X1 @ sK0 ) )
| ( $true
= ( X1 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f24]) ).
thf(f27,definition,
( spl3_1
<=> ( $true
= ( sK2 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f29,plain,
( ( $true
= ( sK2 @ sK0 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f31,definition,
( spl3_2
<=> ( sK0 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f32,plain,
( ( sK0 = sK1 )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f34,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f20,f31,f27]) ).
thf(f36,definition,
( spl3_3
<=> ( $false
= ( sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f38,plain,
( ( $false
= ( sK2 @ sK1 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f39,plain,
( spl3_3
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f19,f31,f36]) ).
thf(f41,definition,
( spl3_4
<=> ! [X1: a > $o] :
( ( $false
= ( X1 @ sK0 ) )
| ( $true
= ( X1 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f42,plain,
( ! [X1: a > $o] :
( ( $true
= ( X1 @ sK1 ) )
| ( $false
= ( X1 @ sK0 ) ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f43,plain,
( spl3_4
| spl3_2 ),
inference(avatar_split_clause,[],[f25,f31,f41]) ).
thf(f52,plain,
( ( sK0 = sK1 )
| ~ spl3_4 ),
inference(leibniz_equality_elimination,[],[f42]) ).
thf(f70,plain,
( spl3_2
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f52,f41,f31]) ).
thf(f72,plain,
( ( $false
= ( sK2 @ sK0 ) )
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f38,f32]) ).
thf(f75,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(constrained_superposition,[],[f72,f29]) ).
thf(f82,plain,
( $false
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f83,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f82]) ).
cnf(s1,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f34]) ).
cnf(s2,plain,
( ~ spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
( spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f43]) ).
cnf(s4,plain,
( spl3_2
| ~ spl3_4 ),
inference(sat_conversion,[],[f70]) ).
cnf(s7,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f83]) ).
cnf(s8,plain,
spl3_2,
inference(rat,[],[s3,s4]) ).
cnf(s9,plain,
spl3_3,
inference(rat,[],[s2,s8]) ).
cnf(s10,plain,
spl3_1,
inference(rat,[],[s1,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s7,s8,s10,s9]) ).
thf(f87,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV288^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.05/0.17 % Computer : n019.cluster.edu
% 0.05/0.17 % Model : x86_64 x86_64
% 0.05/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.17 % Memory : 8046.5625MB
% 0.05/0.17 % OS : Linux 6.8.0-71-generic
% 0.05/0.17 % CPULimit : 300
% 0.05/0.17 % WCLimit : 300
% 0.05/0.17 % DateTime : Tue Sep 29 15:31:33 UTC 2026
% 0.05/0.17 % CPUTime :
% 0.05/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.05/0.20 Running first-order model finding
% 0.05/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.24 % (924034)Will run a generic schedule for satisfiability detection.
% 0.05/0.24 % (924040)% WARNING: option uhcvi not known.
% 0.05/0.24 % (924040)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3642388837:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.05/0.24 % (924040)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.05/0.24 % (924040)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.05/0.24 % (924040) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-924034-924040"...
% 0.05/0.24 % (924040)...printing done.
% 0.05/0.24 % (924040)Refutation found. Thanks to Tanya!
% 0.05/0.24 % SZS status Theorem for theBenchmark
% 0.05/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.05/0.24 % (924040)------------------------------
% 0.05/0.24 % (924040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.05/0.24 % (924040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.05/0.24 % (924040)CaDiCaL version: 2.1.3
% 0.05/0.24 % (924040)Termination reason: Refutation
% 0.05/0.24 % (924040)Time elapsed: 0.003 s
% 0.05/0.24 % (924040)Peak memory usage: 13 MB
% 0.05/0.24 % (924040)Instructions burned: 4 (million)
% 0.05/0.24 % (924034)Success in time 0.034 s
% 0.05/0.24 % Vampire exiting
%------------------------------------------------------------------------------