%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO364^5 : 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 08:47:31 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 45 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 214 ( 25 ~; 11 |; 16 &; 146 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 55 ( 0 ^; 52 !; 3 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
j: a > a ).
thf(func_def_1,type,
g: ( a > a ) > a > a ).
thf(func_def_2,type,
h: a > a ).
thf(func_def_3,type,
f: ( a > a ) > a > a ).
thf(func_def_7,type,
sK0: ( a > a ) > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(func_def_9,type,
sK1: a ).
thf(func_def_10,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK2: a ).
thf(f1,conjecture,
( ( ! [X3: a,X2: a > $o] :
( ( X2 @ ( h @ X3 ) )
=> ( X2 @ ( j @ X3 ) ) )
& ! [X0: a > a,X2: a > $o,X1: a] :
( ( X2 @ ( f @ X0 @ X1 ) )
=> ( X2 @ ( g @ X0 @ X1 ) ) ) )
=> ! [X2: ( a > a ) > $o] :
( ( X2 @ ( f @ h ) )
=> ( X2 @ ( g @ j ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEDEC_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: a,X2: a > $o] :
( ( X2 @ ( h @ X3 ) )
=> ( X2 @ ( j @ X3 ) ) )
& ! [X0: a > a,X2: a > $o,X1: a] :
( ( X2 @ ( f @ X0 @ X1 ) )
=> ( X2 @ ( g @ X0 @ X1 ) ) ) )
=> ! [X2: ( a > a ) > $o] :
( ( X2 @ ( f @ h ) )
=> ( X2 @ ( g @ j ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: a,X1: a > $o] :
( ( X1 @ ( h @ X0 ) )
=> ( X1 @ ( j @ X0 ) ) )
& ! [X2: a > a,X3: a > $o,X4: a] :
( ( X3 @ ( f @ X2 @ X4 ) )
=> ( X3 @ ( g @ X2 @ X4 ) ) ) )
=> ! [X5: ( a > a ) > $o] :
( ( X5 @ ( f @ h ) )
=> ( X5 @ ( g @ j ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X1: a > $o,X0: a] :
( ( $true
= ( X1 @ ( h @ X0 ) ) )
=> ( $true
= ( X1 @ ( j @ X0 ) ) ) )
& ! [X4: a,X3: a > $o,X2: a > a] :
( ( ( X3 @ ( f @ X2 @ X4 ) )
= $true )
=> ( ( X3 @ ( g @ X2 @ X4 ) )
= $true ) ) )
=> ! [X5: ( a > a ) > $o] :
( ( ( X5 @ ( f @ h ) )
= $true )
=> ( ( X5 @ ( g @ j ) )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X5: ( a > a ) > $o] :
( ( ( X5 @ ( g @ j ) )
!= $true )
& ( ( X5 @ ( f @ h ) )
= $true ) )
& ! [X1: a > $o,X0: a] :
( ( $true
!= ( X1 @ ( h @ X0 ) ) )
| ( $true
= ( X1 @ ( j @ X0 ) ) ) )
& ! [X4: a,X3: a > $o,X2: a > a] :
( ( ( X3 @ ( g @ X2 @ X4 ) )
= $true )
| ( ( X3 @ ( f @ X2 @ X4 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ? [X5: ( a > a ) > $o] :
( ( ( X5 @ ( g @ j ) )
!= $true )
& ( ( X5 @ ( f @ h ) )
= $true ) )
& ! [X4: a,X3: a > $o,X2: a > a] :
( ( ( X3 @ ( g @ X2 @ X4 ) )
= $true )
| ( ( X3 @ ( f @ X2 @ X4 ) )
!= $true ) )
& ! [X1: a > $o,X0: a] :
( ( $true
!= ( X1 @ ( h @ X0 ) ) )
| ( $true
= ( X1 @ ( j @ X0 ) ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ? [X0: ( a > a ) > $o] :
( ( $true
!= ( X0 @ ( g @ j ) ) )
& ( $true
= ( X0 @ ( f @ h ) ) ) )
& ! [X1: a,X2: a > $o,X3: a > a] :
( ( $true
= ( X2 @ ( g @ X3 @ X1 ) ) )
| ( $true
!= ( X2 @ ( f @ X3 @ X1 ) ) ) )
& ! [X4: a > $o,X5: a] :
( ( $true
!= ( X4 @ ( h @ X5 ) ) )
| ( ( X4 @ ( j @ X5 ) )
= $true ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( $true
!= ( sK0 @ ( g @ j ) ) )
& ( $true
= ( sK0 @ ( f @ h ) ) )
& ! [X1: a,X2: a > $o,X3: a > a] :
( ( $true
= ( X2 @ ( g @ X3 @ X1 ) ) )
| ( $true
!= ( X2 @ ( f @ X3 @ X1 ) ) ) )
& ! [X4: a > $o,X5: a] :
( ( $true
!= ( X4 @ ( h @ X5 ) ) )
| ( ( X4 @ ( j @ X5 ) )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f7]) ).
thf(f9,plain,
! [X4: a > $o,X5: a] :
( ( $true
!= ( X4 @ ( h @ X5 ) ) )
| ( ( X4 @ ( j @ X5 ) )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X2: a > $o,X3: a > a,X1: a] :
( ( $true
!= ( X2 @ ( f @ X3 @ X1 ) ) )
| ( $true
= ( X2 @ ( g @ X3 @ X1 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( $true
= ( sK0 @ ( f @ h ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( $true
!= ( sK0 @ ( g @ j ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( ( $true != $true )
| ( ( f @ h )
!= ( g @ j ) ) ),
inference(constrained_superposition,[],[f12,f11]) ).
thf(f16,plain,
( ( f @ h )
!= ( g @ j ) ),
inference(trivial_inequality_removal,[],[f15]) ).
thf(f17,plain,
( ( g @ j @ sK1 )
!= ( f @ h @ sK1 ) ),
inference(negative_extensionality,[],[f16]) ).
thf(f18,plain,
! [X0: a] :
( ( h @ X0 )
= ( j @ X0 ) ),
inference(leibniz_equality_elimination,[],[f9]) ).
thf(f35,plain,
! [X0: a > a,X1: a] :
( ( f @ X0 @ X1 )
= ( g @ X0 @ X1 ) ),
inference(leibniz_equality_elimination,[],[f10]) ).
thf(f53,plain,
( ( f @ j @ sK1 )
!= ( f @ h @ sK1 ) ),
inference(constrained_superposition,[],[f17,f35]) ).
thf(f54,plain,
h != j,
inference(equality_resolution,[],[f53]) ).
thf(f55,plain,
( ( h @ sK2 )
!= ( j @ sK2 ) ),
inference(negative_extensionality,[],[f54]) ).
thf(f56,plain,
$false,
inference(forward_subsumption_resolution,[],[f55,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO364^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n003.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:50:59 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.25 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
% 0.22/0.30 % (2744533)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (2744542)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3778697859:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (2744542)Refutation not found, incomplete strategy
% 0.22/0.30 % (2744542)------------------------------
% 0.22/0.30 % (2744542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2744542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2744542)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2744542)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.30 % (2744542)Time elapsed: 0.001 s
% 0.22/0.30 % (2744542)Peak memory usage: 12 MB
% 0.22/0.30 % (2744542)Instructions burned: 3 (million)
% 0.22/0.30 % (2744542)------------------------------
% 0.22/0.30 % (2744542)------------------------------
% 0.22/0.30 % (2744544)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (2744544)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
% 0.22/0.30 % (2744540)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1310030344:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (2744538)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=244572161:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (2744539)lrs+10_16_si=on:nwc=1.5:random_seed=199321420:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (2744544)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=3689088287:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (2744541)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=2585532232: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)
% 0.22/0.30 % (2744543)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2750014384:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (2744540)Refutation not found, incomplete strategy
% 0.22/0.30 % (2744540)------------------------------
% 0.22/0.30 % (2744540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2744540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2744538)Refutation not found, incomplete strategy
% 0.22/0.30 % (2744538)------------------------------
% 0.22/0.30 % (2744538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2744540)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2744540)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.30 % (2744540)Time elapsed: 0.002 s
% 0.22/0.30 % (2744540)Peak memory usage: 12 MB
% 0.22/0.30 % (2744538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2744538)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2744540)Instructions burned: 2 (million)
% 0.22/0.30 % (2744538)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.30 % (2744538)Time elapsed: 0.002 s
% 0.22/0.30 % (2744538)Peak memory usage: 12 MB
% 0.22/0.30 % (2744538)Instructions burned: 2 (million)
% 0.22/0.30 % (2744540)------------------------------
% 0.22/0.30 % (2744540)------------------------------
% 0.22/0.30 % (2744538)------------------------------
% 0.22/0.30 % (2744538)------------------------------
% 0.22/0.30 % (2744541)Refutation not found, incomplete strategy
% 0.22/0.30 % (2744541)------------------------------
% 0.22/0.30 % (2744541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2744541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2744541)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2744541)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.30 % (2744541)Time elapsed: 0.002 s
% 0.22/0.30 % (2744541)Peak memory usage: 12 MB
% 0.22/0.30 % (2744541)Instructions burned: 2 (million)
% 0.22/0.30 % (2744539) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2744533-2744539"...
% 0.22/0.30 % (2744541)------------------------------
% 0.22/0.30 % (2744541)------------------------------
% 0.22/0.30 % (2744543) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2744533-2744543"...
% 0.22/0.30 % (2744546)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4161749596:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.30 % (2744539)...printing done.
% 0.22/0.30 % (2744539)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (2744539)------------------------------
% 0.22/0.30 % (2744539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2744539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2744539)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2744539)Termination reason: Refutation
% 0.22/0.30 % (2744539)Time elapsed: 0.004 s
% 0.22/0.30 % (2744539)Peak memory usage: 12 MB
% 0.22/0.30 % (2744539)Instructions burned: 5 (million)
% 0.22/0.30 % (2744533)Success in time 0.043 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------