%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO265^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:49:38 AM UTC 2026
% Result : Theorem 0.26s 0.35s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 12 unt; 0 typ; 4 def)
% Number of atoms : 171 ( 107 equ; 1 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 148 ( 39 ~; 40 |; 18 &; 36 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 14 usr; 11 con; 0-4 aty)
% ( 0 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 47 ( 0 sgn 7 !; 3 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: a ).
thf(func_def_2,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vAND: $o > $o > $o ).
thf(func_def_10,type,
sK0: a ).
thf(func_def_11,type,
sK1: a ).
thf(f1,conjecture,
( ( ^ [X0: a,X1: a] : ( X0 = X1 )
@ x )
= ( ^ [X2: a] :
? [X1: a] :
( ( X2 = X1 )
& ( X1 = x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5210) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a,X1: a] : ( X0 = X1 )
@ x )
!= ( ^ [X2: a] :
? [X1: a] :
( ( X2 = X1 )
& ( X1 = x ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( ( ^ [X0: a,X1: a] : ( X0 = X1 )
@ x )
!= ( ^ [X2: a] :
? [X3: a] :
( ( X2 = X3 )
& ( x = X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ x )
!= ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( x = Y1 )
& ( Y0 = Y1 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ x )
!= ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( x = Y1 )
& ( Y0 = Y1 ) ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ x )
!= ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( x = Y1 )
& ( Y0 = Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( ( (=) @ x )
!= ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( x = Y1 )
& ( Y0 = Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f6]) ).
thf(f10,plain,
( ( x = sK0 )
!= ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( x = Y1 )
& ( Y0 = Y1 ) ) )
@ sK0 ) ),
inference(negative_extensionality,[],[f9]) ).
thf(f11,plain,
( ( $true
= ( x = sK0 ) )
| ( $true
= ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( x = Y1 )
& ( Y0 = Y1 ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f12,plain,
( ( $false
= ( x = sK0 ) )
| ( $false
= ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( x = Y1 )
& ( Y0 = Y1 ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f13,plain,
( ( x != sK0 )
| ( $false
= ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( x = Y1 )
& ( Y0 = Y1 ) ) )
@ sK0 ) ) ),
inference(equality_proxy_clausification,[],[f12]) ).
thf(f14,plain,
( ( x != sK0 )
| ( $false
= ( ?? @ a
@ ^ [Y0: a] :
( ( x = Y0 )
& ( sK0 = Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
! [X1: a] :
( ( x != sK0 )
| ( $false
= ( ^ [Y0: a] :
( ( x = Y0 )
& ( sK0 = Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f14]) ).
thf(f16,plain,
! [X1: a] :
( ( x != sK0 )
| ( $false
= ( ( x = X1 )
& ( sK0 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
! [X1: a] :
( ( x != sK0 )
| ( $false
= ( sK0 = X1 ) )
| ( $false
= ( x = X1 ) ) ),
inference(and_proxy_clausification,[],[f16]) ).
thf(f18,plain,
! [X1: a] :
( ( x != sK0 )
| ( sK0 != X1 )
| ( $false
= ( x = X1 ) ) ),
inference(equality_proxy_clausification,[],[f17]) ).
thf(f19,plain,
! [X1: a] :
( ( x != sK0 )
| ( sK0 != X1 )
| ( x != X1 ) ),
inference(equality_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( x = sK0 )
| ( $true
= ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( x = Y1 )
& ( Y0 = Y1 ) ) )
@ sK0 ) ) ),
inference(equality_proxy_clausification,[],[f11]) ).
thf(f21,plain,
( ( x = sK0 )
| ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ( x = Y0 )
& ( sK0 = Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
( ( x = sK0 )
| ( $true
= ( ^ [Y0: a] :
( ( x = Y0 )
& ( sK0 = Y0 ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( x = sK0 )
| ( $true
= ( ( x = sK1 )
& ( sK0 = sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( ( x = sK0 )
| ( $true
= ( sK0 = sK1 ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( x = sK0 )
| ( $true
= ( x = sK1 ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f26,plain,
( ( x = sK0 )
| ( x = sK1 ) ),
inference(equality_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( x = sK0 )
| ( sK0 = sK1 ) ),
inference(equality_proxy_clausification,[],[f24]) ).
thf(f29,definition,
( spl2_1
<=> ! [X1: a] :
( ( sK0 != X1 )
| ( x != X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f30,plain,
( ! [X1: a] :
( ( sK0 != X1 )
| ( x != X1 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f32,definition,
( spl2_2
<=> ( x = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f35,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f19,f32,f29]) ).
thf(f37,definition,
( spl2_3
<=> ( x = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f39,plain,
( ( x = sK1 )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
( spl2_3
| spl2_2 ),
inference(avatar_split_clause,[],[f26,f32,f37]) ).
thf(f42,definition,
( spl2_4
<=> ( sK0 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f44,plain,
( ( sK0 = sK1 )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f45,plain,
( spl2_4
| spl2_2 ),
inference(avatar_split_clause,[],[f27,f32,f42]) ).
thf(f47,plain,
( ( x = sK0 )
| ~ spl2_3
| ~ spl2_4 ),
inference(constrained_superposition,[],[f39,f44]) ).
thf(f48,plain,
( spl2_2
| ~ spl2_3
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f47,f42,f37,f32]) ).
thf(f50,plain,
( ( x != sK0 )
| ~ spl2_1 ),
inference(equality_resolution,[],[f30]) ).
thf(f52,plain,
( ~ spl2_2
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f50,f29,f32]) ).
cnf(s1,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f35]) ).
cnf(s2,plain,
( spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f40]) ).
cnf(s3,plain,
( spl2_2
| spl2_4 ),
inference(sat_conversion,[],[f45]) ).
cnf(s4,plain,
( spl2_2
| ~ spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f48]) ).
cnf(s6,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f52]) ).
cnf(s7,plain,
spl2_2,
inference(rat,[],[s4,s2,s3]) ).
cnf(s8,plain,
~ spl2_1,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s7,s8]) ).
thf(f53,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO265^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.26 % Computer : n011.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 16:42:17 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.31 Running first-order model finding
% 0.26/0.31 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.35 % (324699)Will run a generic schedule for satisfiability detection.
% 0.26/0.35 % (324710)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3414437812:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.26/0.35 % (324705)% WARNING: option uhcvi not known.
% 0.26/0.35 % (324710) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-324699-324710"...
% 0.26/0.35 % (324710)...printing done.
% 0.26/0.35 % (324705)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1950680819:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.26/0.35 % (324705)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.26/0.35 % (324705)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.26/0.35 % (324705) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-324699-324705"...
% 0.26/0.35 % (324710)Refutation found. Thanks to Tanya!
% 0.26/0.35 % SZS status Theorem for theBenchmark
% 0.26/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.35 % (324710)------------------------------
% 0.26/0.35 % (324710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.35 % (324710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.35 % (324710)CaDiCaL version: 2.1.3
% 0.26/0.35 % (324710)Termination reason: Refutation
% 0.26/0.35 % (324710)Time elapsed: 0.003 s
% 0.26/0.35 % (324710)Peak memory usage: 12 MB
% 0.26/0.35 % (324710)Instructions burned: 3 (million)
% 0.26/0.35 % (324699)Success in time 0.028 s
% 0.26/0.35 % Vampire exiting
%------------------------------------------------------------------------------