%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO373^5 : 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 : n003.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 08:47:32 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 192 ( 43 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 147 ( 39 ~; 33 |; 6 &; 54 @)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 14 !; 2 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
g: b > $o ).
thf(func_def_1,type,
f: b > $o ).
thf(func_def_5,type,
sK0: ( b > $o ) > $o ).
thf(func_def_6,type,
sK1: b ).
thf(f1,conjecture,
( ! [X0: b] :
( ( f @ X0 )
<=> ( g @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( X1 @ f )
=> ( X1 @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT_SET) ).
thf(f2,negated_conjecture,
~ ( ! [X0: b] :
( ( f @ X0 )
<=> ( g @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( X1 @ f )
=> ( X1 @ g ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: b] :
( ( f @ X0 )
<=> ( g @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( X1 @ f )
=> ( X1 @ g ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( ( X1 @ f )
= $true )
=> ( ( X1 @ g )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X1: ( b > $o ) > $o] :
( ( ( X1 @ f )
= $true )
& ( ( X1 @ g )
!= $true ) )
& ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ? [X0: ( b > $o ) > $o] :
( ( $true
= ( X0 @ f ) )
& ( $true
!= ( X0 @ g ) ) )
& ! [X1: b] :
( ( g @ X1 )
= ( f @ X1 ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( $true
= ( sK0 @ f ) )
& ( $true
!= ( sK0 @ g ) )
& ! [X1: b] :
( ( g @ X1 )
= ( f @ X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
thf(f8,plain,
! [X1: b] :
( ( g @ X1 )
= ( f @ X1 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( $true
!= ( sK0 @ g ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( $true
= ( sK0 @ f ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X1: b] :
( ( ( f @ X1 )
= $false )
| ( $true
= ( g @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f8]) ).
thf(f14,plain,
! [X1: b] :
( ( $true
= ( f @ X1 ) )
| ( ( g @ X1 )
= $false ) ),
inference(iff_proxy_clausification,[],[f8]) ).
thf(f15,plain,
( ( $true != $true )
| ( f != g ) ),
inference(constrained_superposition,[],[f9,f10]) ).
thf(f16,plain,
f != g,
inference(trivial_inequality_removal,[],[f15]) ).
thf(f17,plain,
( ( f @ sK1 )
!= ( g @ sK1 ) ),
inference(negative_extensionality,[],[f16]) ).
thf(f18,plain,
( ( $true
= ( f @ sK1 ) )
| ( $true
= ( g @ sK1 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( g @ sK1 ) )
| ( ( f @ sK1 )
= $false ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f21,definition,
( spl2_1
<=> ( $false
= ( g @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f23,plain,
( ( $false
= ( g @ sK1 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f25,definition,
( spl2_2
<=> ( ( f @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f27,plain,
( ( ( f @ sK1 )
= $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f25]) ).
thf(f28,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f19,f25,f21]) ).
thf(f30,definition,
( spl2_3
<=> ( $true
= ( g @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f32,plain,
( ( $true
= ( g @ sK1 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f34,definition,
( spl2_4
<=> ( $true
= ( f @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f36,plain,
( ( $true
= ( f @ sK1 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f37,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f18,f34,f30]) ).
thf(f38,plain,
( ( $true = $false )
| ( $false
= ( g @ sK1 ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f14,f27]) ).
thf(f42,plain,
( ( $false
= ( g @ sK1 ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f38]) ).
thf(f44,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f42,f25,f21]) ).
thf(f45,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_3 ),
inference(constrained_superposition,[],[f23,f32]) ).
thf(f49,plain,
( $false
| ~ spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f50,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f49]) ).
thf(f52,plain,
( ( $true
= ( g @ sK1 ) )
| ( $true = $false )
| ~ spl2_4 ),
inference(constrained_superposition,[],[f36,f13]) ).
thf(f55,plain,
( ( $true
= ( g @ sK1 ) )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f59,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_4 ),
inference(forward_demodulation,[],[f55,f23]) ).
thf(f60,plain,
( $false
| ~ spl2_1
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f59]) ).
thf(f61,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f60]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f28]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f37]) ).
cnf(s3,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s6,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f50]) ).
cnf(s8,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(sat_conversion,[],[f61]) ).
cnf(s9,plain,
spl2_1,
inference(rat,[],[s1,s3]) ).
cnf(s10,plain,
~ spl2_4,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
~ spl2_3,
inference(rat,[],[s6,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s2,s10,s11]) ).
thf(f62,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO373^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:51:29 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.21/0.29 % (2745927)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (2745937)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3558627494:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (2745937)Refutation not found, incomplete strategy
% 0.21/0.29 % (2745937)------------------------------
% 0.21/0.29 % (2745937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2745937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2745937)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2745937)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (2745937)Time elapsed: 0.001 s
% 0.21/0.29 % (2745937)Peak memory usage: 12 MB
% 0.21/0.29 % (2745937)Instructions burned: 1 (million)
% 0.21/0.29 % (2745937)------------------------------
% 0.21/0.29 % (2745937)------------------------------
% 0.21/0.29 % (2745939)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (2745939)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
% 0.21/0.29 % (2745935)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3158584688:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (2745932)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2623167660:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (2745934)lrs+10_16_si=on:nwc=1.5:random_seed=791129063:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (2745939)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=684397565:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (2745936)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=352328456: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)
% 0.21/0.29 % (2745938)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1221028640:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (2745935)Refutation not found, incomplete strategy
% 0.21/0.29 % (2745935)------------------------------
% 0.21/0.29 % (2745935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2745935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2745935)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2745935)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (2745935)Time elapsed: 0.001 s
% 0.21/0.29 % (2745935)Peak memory usage: 12 MB
% 0.21/0.29 % (2745932)Refutation not found, incomplete strategy
% 0.21/0.29 % (2745932)------------------------------
% 0.21/0.29 % (2745932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2745932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2745932)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2745932)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (2745932)Time elapsed: 0.001 s
% 0.21/0.29 % (2745932)Peak memory usage: 12 MB
% 0.21/0.29 % (2745935)------------------------------
% 0.21/0.29 % (2745935)------------------------------
% 0.21/0.29 % (2745936)Refutation not found, incomplete strategy
% 0.21/0.29 % (2745936)------------------------------
% 0.21/0.29 % (2745936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2745936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2745936)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2745936)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (2745936)Time elapsed: 0.001 s
% 0.21/0.29 % (2745936)Peak memory usage: 12 MB
% 0.21/0.29 % (2745936)Instructions burned: 1 (million)
% 0.21/0.29 % (2745932)------------------------------
% 0.21/0.29 % (2745932)------------------------------
% 0.21/0.29 % (2745934) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2745927-2745934"...
% 0.21/0.29 % (2745936)------------------------------
% 0.21/0.29 % (2745936)------------------------------
% 0.21/0.29 % (2745938) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2745927-2745938"...
% 0.21/0.29 % (2745939)Refutation not found, incomplete strategy
% 0.21/0.29 % (2745939)------------------------------
% 0.21/0.29 % (2745939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2745939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2745939)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2745939)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (2745939)Time elapsed: 0.003 s
% 0.21/0.29 % (2745939)Peak memory usage: 12 MB
% 0.21/0.29 % (2745939)Instructions burned: 4 (million)
% 0.21/0.29 % (2745934)...printing done.
% 0.21/0.29 % (2745938)...printing done.
% 0.21/0.29 % (2745939)------------------------------
% 0.21/0.29 % (2745939)------------------------------
% 0.21/0.29 % (2745947)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4104491430:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.29 % (2745934)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (2745934)------------------------------
% 0.21/0.29 % (2745934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2745934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2745934)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2745934)Termination reason: Refutation
% 0.21/0.29 % (2745934)Time elapsed: 0.003 s
% 0.21/0.29 % (2745934)Peak memory usage: 13 MB
% 0.21/0.29 % (2745934)Instructions burned: 3 (million)
% 0.21/0.29 % (2745927)Success in time 0.036 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------