%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO265^5 : 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 : n018.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 08:47:19 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 12 unt; 0 typ; 4 def)
% Number of atoms : 181 ( 110 equ; 1 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 163 ( 47 ~; 47 |; 18 &; 36 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 49 ( 0 sgn 9 !; 3 ?; 49 :)
% 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] :
( ( X1 = x )
& ( X2 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5210) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a,X1: a] : ( X0 = X1 )
@ x )
!= ( ^ [X2: a] :
? [X1: a] :
( ( X1 = x )
& ( X2 = X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( ( ^ [X0: a,X1: a] : ( X0 = X1 )
@ x )
!= ( ^ [X2: a] :
? [X3: a] :
( ( x = X3 )
& ( X2 = X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( Y0 = Y1 )
& ( x = Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ x ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( Y0 = Y1 )
& ( x = Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ x ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( Y0 = Y1 )
& ( x = Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ x ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( Y0 = Y1 )
& ( x = Y1 ) ) ) )
!= ( (=) @ x ) ),
inference(beta-eta_normalization,[],[f6]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( Y0 = Y1 )
& ( x = Y1 ) ) )
@ sK0 )
!= ( x = sK0 ) ),
inference(negative_extensionality,[],[f9]) ).
thf(f11,plain,
( ( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( Y0 = Y1 )
& ( x = Y1 ) ) )
@ sK0 )
= $true )
| ( $true
= ( x = sK0 ) ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f12,plain,
( ( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( Y0 = Y1 )
& ( x = Y1 ) ) )
@ sK0 )
= $false )
| ( $false
= ( x = sK0 ) ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f13,plain,
( ( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( Y0 = Y1 )
& ( x = Y1 ) ) )
@ sK0 )
= $false )
| ( x != sK0 ) ),
inference(equality_proxy_clausification,[],[f12]) ).
thf(f14,plain,
( ( ( ?? @ a
@ ^ [Y0: a] :
( ( sK0 = Y0 )
& ( x = Y0 ) ) )
= $false )
| ( x != sK0 ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
! [X1: a] :
( ( x != sK0 )
| ( ( ^ [Y0: a] :
( ( sK0 = Y0 )
& ( x = Y0 ) )
@ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f14]) ).
thf(f16,plain,
! [X1: a] :
( ( x != sK0 )
| ( ( ( sK0 = X1 )
& ( x = X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
! [X1: a] :
( ( ( x = X1 )
= $false )
| ( x != sK0 )
| ( ( sK0 = X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f16]) ).
thf(f18,plain,
! [X1: a] :
( ( x != sK0 )
| ( x != X1 )
| ( ( sK0 = X1 )
= $false ) ),
inference(equality_proxy_clausification,[],[f17]) ).
thf(f19,plain,
! [X1: a] :
( ( sK0 != X1 )
| ( x != sK0 )
| ( x != X1 ) ),
inference(equality_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( Y0 = Y1 )
& ( x = Y1 ) ) )
@ sK0 )
= $true )
| ( x = sK0 ) ),
inference(equality_proxy_clausification,[],[f11]) ).
thf(f21,plain,
( ( x = sK0 )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ( sK0 = Y0 )
& ( x = Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
( ( x = sK0 )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 = Y0 )
& ( x = Y0 ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( x = sK0 )
| ( ( ( sK0 = sK1 )
& ( x = sK1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( ( x = sK0 )
| ( $true
= ( x = sK1 ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( x = sK0 )
| ( $true
= ( sK0 = sK1 ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f26,plain,
( ( x = sK0 )
| ( sK0 = sK1 ) ),
inference(equality_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( x = sK0 )
| ( x = sK1 ) ),
inference(equality_proxy_clausification,[],[f24]) ).
thf(f29,definition,
( spl2_1
<=> ( x = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f30,plain,
( ( x = sK0 )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f33,definition,
( spl2_2
<=> ! [X1: a] :
( ( sK0 != X1 )
| ( x != X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f34,plain,
( ! [X1: a] :
( ( x != X1 )
| ( sK0 != X1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f35,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f19,f33,f29]) ).
thf(f37,definition,
( spl2_3
<=> ( sK0 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f39,plain,
( ( sK0 = sK1 )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
( spl2_3
| spl2_1 ),
inference(avatar_split_clause,[],[f26,f29,f37]) ).
thf(f42,definition,
( spl2_4
<=> ( x = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f44,plain,
( ( x = sK1 )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f45,plain,
( spl2_4
| spl2_1 ),
inference(avatar_split_clause,[],[f27,f29,f42]) ).
thf(f46,plain,
( ( x = sK0 )
| ~ spl2_3
| ~ spl2_4 ),
inference(forward_demodulation,[],[f44,f39]) ).
thf(f49,plain,
( spl2_1
| ~ spl2_3
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f46,f42,f37,f29]) ).
thf(f50,plain,
( ! [X1: a] :
( ( x != X1 )
| ( x != X1 ) )
| ~ spl2_1
| ~ spl2_2 ),
inference(forward_demodulation,[],[f34,f30]) ).
thf(f51,plain,
( ! [X1: a] : ( x != X1 )
| ~ spl2_1
| ~ spl2_2 ),
inference(duplicate_literal_removal,[],[f50]) ).
thf(f53,plain,
( $false
| ~ spl2_1
| ~ spl2_2 ),
inference(equality_resolution,[],[f51]) ).
thf(f56,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[],[f53]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f35]) ).
cnf(s2,plain,
( spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f40]) ).
cnf(s3,plain,
( spl2_1
| spl2_4 ),
inference(sat_conversion,[],[f45]) ).
cnf(s5,plain,
( spl2_1
| ~ spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f49]) ).
cnf(s7,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s8,plain,
spl2_1,
inference(rat,[],[s5,s2,s3]) ).
cnf(s9,plain,
~ spl2_2,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9,s8]) ).
thf(f57,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO265^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:44:26 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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 % (322611)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (322622)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (322622)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.28 % (322622)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2995816662:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (322622) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-322611-322622"...
% 0.21/0.28 % (322622)...printing done.
% 0.21/0.28 % (322617)lrs+10_16_si=on:nwc=1.5:random_seed=1224950398:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (322618)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2449635871:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (322622)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 % (322622)------------------------------
% 0.21/0.28 % (322622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (322622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (322622)CaDiCaL version: 2.1.3
% 0.21/0.28 % (322622)Termination reason: Refutation
% 0.21/0.28 % (322622)Time elapsed: 0.002 s
% 0.21/0.28 % (322622)Peak memory usage: 13 MB
% 0.21/0.28 % (322622)Instructions burned: 3 (million)
% 0.21/0.28 % (322611)Success in time 0.041 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------