%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO025^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:46:18 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 46 ( 17 unt; 0 typ; 2 def)
% Number of atoms : 223 ( 64 equ; 8 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 158 ( 80 ~; 56 |; 11 &; 9 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 21 ( 0 sgn 0 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
vAND: $o > $o > $o ).
thf(func_def_1,type,
vNOT: $o > $o ).
thf(func_def_2,type,
vOR: $o > $o > $o ).
thf(func_def_3,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
sK0: $o ).
thf(func_def_10,type,
sK1: $o ).
thf(f1,conjecture,
( ( ^ [X0: $o,X1: $o] :
~ ( ~ X1
| ~ X0 ) )
= (&) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f2,negated_conjecture,
( ( ^ [X0: $o,X1: $o] :
~ ( ~ X1
| ~ X0 ) )
!= (&) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( ( ^ [X0: $o,X1: $o] :
~ ( ~ X1
| ~ X0 ) )
!= (&) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( (&)
!= ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y0
| ~ Y1 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( (&)
!= ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y0
| ~ Y1 ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( (&)
!= ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y0
| ~ Y1 ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( ( (&) @ sK0 )
!= ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y0
| ~ Y1 )
@ sK0 ) ),
inference(negative_extensionality,[],[f6]) ).
thf(f10,plain,
( ( ^ [Y0: $o] :
~ ( ~ sK0
| ~ Y0 ) )
!= ( (&) @ sK0 ) ),
inference(beta-eta_normalization,[],[f9]) ).
thf(f11,plain,
( ( sK0
& sK1 )
!= ( ^ [Y0: $o] :
~ ( ~ sK0
| ~ Y0 )
@ sK1 ) ),
inference(negative_extensionality,[],[f10]) ).
thf(f12,plain,
( ( ( sK0
& sK1 )
= $true )
| ( ( ^ [Y0: $o] :
~ ( ~ sK0
| ~ Y0 )
@ sK1 )
= $true ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f13,plain,
( ( $false
= ( sK0
& sK1 ) )
| ( $false
= ( ^ [Y0: $o] :
~ ( ~ sK0
| ~ Y0 )
@ sK1 ) ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f14,plain,
( ( $false = sK1 )
| ( $false = sK0 )
| ( $false
= ( ^ [Y0: $o] :
~ ( ~ sK0
| ~ Y0 )
@ sK1 ) ) ),
inference(and_proxy_clausification,[],[f13]) ).
thf(f15,plain,
( ( $false = sK1 )
| ( $false = sK0 )
| ( $false
= ( ~ ( ~ sK0
| ~ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f16,plain,
( ( ( ~ sK0
| ~ sK1 )
= $true )
| ( $false = sK0 )
| ( $false = sK1 ) ),
inference(not_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( ( ~ sK1 ) = $true )
| ( $false = sK0 )
| ( $false = sK1 )
| ( $true = ( ~ sK0 ) ) ),
inference(or_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( $true = ( ~ sK0 ) )
| ( $false = sK1 )
| ( $false = sK1 )
| ( $false = sK0 ) ),
inference(not_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $false = sK0 )
| ( $false = sK0 )
| ( $false = sK1 )
| ( $false = sK1 ) ),
inference(not_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( $false = sK1 )
| ( $false = sK0 ) ),
inference(duplicate_literal_removal,[],[f19]) ).
thf(f21,plain,
( ( ( ^ [Y0: $o] :
~ ( ~ sK0
| ~ Y0 )
@ sK1 )
= $true )
| ( $true = sK1 ) ),
inference(and_proxy_clausification,[],[f12]) ).
thf(f22,plain,
( ( $true = sK0 )
| ( ( ^ [Y0: $o] :
~ ( ~ sK0
| ~ Y0 )
@ sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f12]) ).
thf(f23,plain,
( ( $true = sK0 )
| ( $true
= ( ~ ( ~ sK0
| ~ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( ( $false
= ( ~ sK0
| ~ sK1 ) )
| ( $true = sK0 ) ),
inference(not_proxy_clausification,[],[f23]) ).
thf(f26,plain,
( ( $true = sK0 )
| ( $false = ( ~ sK0 ) ) ),
inference(or_proxy_clausification,[],[f24]) ).
thf(f27,plain,
( ( $true = sK0 )
| ( $true = sK0 ) ),
inference(not_proxy_clausification,[],[f26]) ).
thf(f28,plain,
$true = sK0,
inference(duplicate_literal_removal,[],[f27]) ).
thf(f30,plain,
( ( $true = sK1 )
| ( $true
= ( ~ ( ~ sK0
| ~ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f31,plain,
( ( $false
= ( ~ sK0
| ~ sK1 ) )
| ( $true = sK1 ) ),
inference(not_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( ( $false = ( ~ sK1 ) )
| ( $true = sK1 ) ),
inference(or_proxy_clausification,[],[f31]) ).
thf(f35,plain,
( ( $true = sK1 )
| ( $true = sK1 ) ),
inference(not_proxy_clausification,[],[f32]) ).
thf(f36,plain,
$true = sK1,
inference(duplicate_literal_removal,[],[f35]) ).
thf(f38,definition,
( spl2_1
<=> ( $false = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f40,plain,
( ( $false = sK1 )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f38]) ).
thf(f42,definition,
( spl2_2
<=> ( $false = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f44,plain,
( ( $false = sK0 )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f45,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f20,f42,f38]) ).
thf(f46,plain,
( ( $false = $true )
| ~ spl2_2 ),
inference(forward_demodulation,[],[f44,f28]) ).
thf(f47,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f48,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f47]) ).
thf(f50,plain,
( ( $false = $true )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f40,f36]) ).
thf(f51,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f50]) ).
thf(f52,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f51]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f45]) ).
cnf(s2,plain,
~ spl2_2,
inference(sat_conversion,[],[f48]) ).
cnf(s3,plain,
~ spl2_1,
inference(sat_conversion,[],[f52]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f53,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO025^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n011.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:22:35 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.21 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
% 0.08/0.26 % (289562)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.26 % (289567)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3651984609:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.26 % (289567) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-289562-289567"...
% 0.08/0.26 % (289567)...printing done.
% 0.08/0.26 % (289567)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (289567)------------------------------
% 0.08/0.26 % (289567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (289567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (289567)CaDiCaL version: 2.1.3
% 0.08/0.26 % (289567)Termination reason: Refutation
% 0.08/0.26 % (289567)Time elapsed: 0.001 s
% 0.08/0.26 % (289567)Peak memory usage: 13 MB
% 0.08/0.26 % (289567)Instructions burned: 2 (million)
% 0.08/0.26 % (289562)Success in time 0.032 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------