%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO217^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:47:13 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 14 unt; 0 typ; 6 def)
% Number of atoms : 180 ( 41 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 183 ( 44 ~; 46 |; 2 &; 78 @)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 26 !; 2 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
sK0: b > a > $o ).
thf(func_def_2,type,
sK1: b > a > $o ).
thf(func_def_6,type,
sK3: b ).
thf(func_def_7,type,
sK4: a ).
thf(f1,conjecture,
! [X1: b > a > $o,X0: b > a > $o] :
( ! [X2: b,X3: a] :
( ( X0 @ X2 @ X3 )
<=> ( X1 @ X2 @ X3 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM174) ).
thf(f2,negated_conjecture,
~ ! [X1: b > a > $o,X0: b > a > $o] :
( ! [X2: b,X3: a] :
( ( X0 @ X2 @ X3 )
<=> ( X1 @ X2 @ X3 ) )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: b > a > $o,X1: b > a > $o] :
( ! [X2: b,X3: a] :
( ( X1 @ X2 @ X3 )
<=> ( X0 @ X2 @ X3 ) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X1: b > a > $o,X0: b > a > $o] :
( ! [X2: b,X3: a] :
( ( X0 @ X2 @ X3 )
= ( X1 @ X2 @ X3 ) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: b > a > $o,X1: b > a > $o] :
( ( X0 != X1 )
& ! [X2: b,X3: a] :
( ( X0 @ X2 @ X3 )
= ( X1 @ X2 @ X3 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( sK0 != sK1 )
& ! [X2: b,X3: a] :
( ( sK0 @ X2 @ X3 )
= ( sK1 @ X2 @ X3 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).
thf(f7,plain,
! [X2: b,X3: a] :
( ( sK0 @ X2 @ X3 )
= ( sK1 @ X2 @ X3 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
! [X2: b,X3: a] :
( ( $true
= ( sK0 @ X2 @ X3 ) )
| ( ( sK1 @ X2 @ X3 )
= $false ) ),
inference(iff_proxy_clausification,[],[f7]) ).
thf(f11,plain,
! [X2: b,X3: a] :
( ( $true
= ( sK1 @ X2 @ X3 ) )
| ( ( sK0 @ X2 @ X3 )
= $false ) ),
inference(iff_proxy_clausification,[],[f7]) ).
thf(f13,definition,
( spl2_1
<=> ( sK0 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f15,plain,
( ( sK0 != sK1 )
| spl2_1 ),
inference(avatar_component_clause,[],[f13]) ).
thf(f16,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f8,f13]) ).
thf(f17,plain,
( ( ( sK1 @ sK3 )
!= ( sK0 @ sK3 ) )
| spl2_1 ),
inference(negative_extensionality,[],[f15]) ).
thf(f19,definition,
( spl2_2
<=> ( ( sK1 @ sK3 )
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f21,plain,
( ( ( sK1 @ sK3 )
!= ( sK0 @ sK3 ) )
| spl2_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f22,plain,
( ~ spl2_2
| spl2_1 ),
inference(avatar_split_clause,[],[f17,f13,f19]) ).
thf(f23,plain,
( ( ( sK0 @ sK3 @ sK4 )
!= ( sK1 @ sK3 @ sK4 ) )
| spl2_2 ),
inference(negative_extensionality,[],[f21]) ).
thf(f24,plain,
( ( $true
= ( sK1 @ sK3 @ sK4 ) )
| ( $true
= ( sK0 @ sK3 @ sK4 ) )
| spl2_2 ),
inference(xor_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( $false
= ( sK1 @ sK3 @ sK4 ) )
| ( ( sK0 @ sK3 @ sK4 )
= $false )
| spl2_2 ),
inference(xor_proxy_clausification,[],[f23]) ).
thf(f27,definition,
( spl2_3
<=> ( ( sK0 @ sK3 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f29,plain,
( ( ( sK0 @ sK3 @ sK4 )
= $false )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f31,definition,
( spl2_4
<=> ( $false
= ( sK1 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f33,plain,
( ( $false
= ( sK1 @ sK3 @ sK4 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f34,plain,
( spl2_3
| spl2_4
| spl2_2 ),
inference(avatar_split_clause,[],[f25,f19,f31,f27]) ).
thf(f36,definition,
( spl2_5
<=> ( $true
= ( sK1 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
thf(f38,plain,
( ( $true
= ( sK1 @ sK3 @ sK4 ) )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f40,definition,
( spl2_6
<=> ( $true
= ( sK0 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
thf(f42,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,plain,
( spl2_5
| spl2_6
| spl2_2 ),
inference(avatar_split_clause,[],[f24,f19,f40,f36]) ).
thf(f44,plain,
( ( $true = $false )
| ( ( sK0 @ sK3 @ sK4 )
= $false )
| ~ spl2_4 ),
inference(superposition,[],[f33,f11]) ).
thf(f46,plain,
( ( ( sK0 @ sK3 @ sK4 )
= $false )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f44]) ).
thf(f48,plain,
( spl2_3
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f46,f31,f27]) ).
thf(f50,plain,
( ( $false
= ( sK1 @ sK3 @ sK4 ) )
| ( $true = $false )
| ~ spl2_3 ),
inference(superposition,[],[f10,f29]) ).
thf(f52,plain,
( ( $false
= ( sK1 @ sK3 @ sK4 ) )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f50]) ).
thf(f53,plain,
( ( $true = $false )
| ~ spl2_4
| ~ spl2_5 ),
inference(forward_demodulation,[],[f38,f33]) ).
thf(f54,plain,
( $false
| ~ spl2_4
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f55,plain,
( ~ spl2_4
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f54]) ).
thf(f57,plain,
( spl2_4
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f52,f27,f31]) ).
thf(f58,plain,
( ( $true = $false )
| ~ spl2_3
| ~ spl2_6 ),
inference(forward_demodulation,[],[f42,f29]) ).
thf(f59,plain,
( $false
| ~ spl2_3
| ~ spl2_6 ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f60,plain,
( ~ spl2_3
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f59]) ).
cnf(s1,plain,
~ spl2_1,
inference(sat_conversion,[],[f16]) ).
cnf(s2,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s3,plain,
( spl2_2
| spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f34]) ).
cnf(s4,plain,
( spl2_2
| spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f43]) ).
cnf(s5,plain,
( spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f48]) ).
cnf(s7,plain,
( ~ spl2_4
| ~ spl2_5 ),
inference(sat_conversion,[],[f55]) ).
cnf(s9,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f57]) ).
cnf(s10,plain,
( ~ spl2_3
| ~ spl2_6 ),
inference(sat_conversion,[],[f60]) ).
cnf(s12,plain,
~ spl2_2,
inference(rat,[],[s2,s1]) ).
cnf(s13,plain,
spl2_3,
inference(rat,[],[s3,s5,s12]) ).
cnf(s14,plain,
~ spl2_6,
inference(rat,[],[s10,s13]) ).
cnf(s15,plain,
spl2_4,
inference(rat,[],[s9,s13]) ).
cnf(s16,plain,
spl2_5,
inference(rat,[],[s4,s12,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s7,s16,s15]) ).
thf(f61,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO217^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n011.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:39:46 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.26 % (317609)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.26 % (317617)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=573129120:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.26 % (317617) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-317609-317617"...
% 0.20/0.26 % (317617)...printing done.
% 0.20/0.26 % (317617)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (317617)------------------------------
% 0.20/0.27 % (317617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (317617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (317617)CaDiCaL version: 2.1.3
% 0.20/0.27 % (317617)Termination reason: Refutation
% 0.20/0.27 % (317617)Time elapsed: 0.002 s
% 0.20/0.27 % (317617)Peak memory usage: 13 MB
% 0.20/0.27 % (317617)Instructions burned: 3 (million)
% 0.20/0.27 % (317609)Success in time 0.027 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------