%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO241^5 : 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 : n012.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 08:47:16 AM UTC 2026
% Result : Theorem 0.09s 0.19s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 1
% Syntax : Number of formulae : 25 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 138 ( 77 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 261 ( 42 ~; 17 |; 27 &; 154 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 3 con; 0-4 aty)
% ( 0 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 75 ( 25 ^; 38 !; 12 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
vAND: $o > $o > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_6,type,
vNOT: $o > $o ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_11,type,
sK1: $i > $o ).
thf(func_def_12,type,
sK2: $i > $i > $o ).
thf(func_def_13,type,
sK3: $i > $o ).
thf(func_def_14,type,
sK4: $i > $o ).
thf(f1,conjecture,
! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ? [X3: $i > $o] :
( ~ ( X3 @ ( X0 @ X3 ) )
& ( ( X0 @ X3 )
= ( X0
@ ^ [X4: $i] :
? [X5: $i > $o] :
( ~ ( X5 @ ( X0 @ X5 ) )
& ( X4
= ( X0 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM143_EXPAND) ).
thf(f2,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ? [X3: $i > $o] :
( ~ ( X3 @ ( X0 @ X3 ) )
& ( ( X0 @ X3 )
= ( X0
@ ^ [X4: $i] :
? [X5: $i > $o] :
( ~ ( X5 @ ( X0 @ X5 ) )
& ( X4
= ( X0 @ X5 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ? [X3: $i > $o] :
( ~ ( X3 @ ( X0 @ X3 ) )
& ( ( X0 @ X3 )
= ( X0
@ ^ [X4: $i] :
? [X5: $i > $o] :
( ~ ( X5 @ ( X0 @ X5 ) )
& ( X4
= ( X0 @ X5 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ? [X3: $i > $o] :
( ( ( X3 @ ( X0 @ X3 ) )
!= $true )
& ( ( X0 @ X3 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ? [X3: $i > $o] :
( ( ( X0 @ X3 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) )
& ( ( X3 @ ( X0 @ X3 ) )
!= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X0: ( $i > $o ) > $i] :
( ? [X3: $i > $o] :
( ( ( X0 @ X3 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) )
& ( ( X3 @ ( X0 @ X3 ) )
!= $true ) )
& ! [X2: $i > $o,X1: $i > $o] :
( ( X1 = X2 )
| ( ( X0 @ X1 )
!= ( X0 @ X2 ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: ( $i > $o ) > $i] :
( ? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) )
& ( $true
!= ( X1 @ ( X0 @ X1 ) ) ) )
& ! [X2: $i > $o,X3: $i > $o] :
( ( X2 = X3 )
| ( ( X0 @ X2 )
!= ( X0 @ X3 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) )
= ( sK0 @ sK1 ) )
& ( ( sK1 @ ( sK0 @ sK1 ) )
!= $true )
& ! [X2: $i > $o,X3: $i > $o] :
( ( X2 = X3 )
| ( ( sK0 @ X3 )
!= ( sK0 @ X2 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f7]) ).
thf(f9,plain,
! [X2: $i > $o,X3: $i > $o] :
( ( ( sK0 @ X3 )
!= ( sK0 @ X2 ) )
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( sK1 @ ( sK0 @ sK1 ) )
!= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) )
= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X0: $i > $o] :
( ( ( sK0 @ X0 )
!= ( sK0 @ sK1 ) )
| ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) )
= X0 ) ),
inference(superposition,[],[f9,f11]) ).
thf(f16,plain,
( sK1
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) ) ),
inference(equality_resolution,[],[f14]) ).
thf(f17,plain,
! [X1: $i] :
( ( sK1 @ X1 )
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) )
@ X1 ) ),
inference(argument_congruence,[],[f16]) ).
thf(f18,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) )
@ X1 ) )
| ( ( sK1 @ X1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f17]) ).
thf(f27,plain,
! [X1: $i] :
( ( $false
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( sK0 @ Y0 )
= X1 )
& ~ ( Y0 @ ( sK0 @ Y0 ) ) ) ) )
| ( ( sK1 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f28,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i > $o] :
( ( ( sK0 @ Y0 )
= X1 )
& ~ ( Y0 @ ( sK0 @ Y0 ) ) )
@ X2 )
= $false )
| ( ( sK1 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( ( ( sK0 @ X2 )
= X1 )
& ~ ( X2 @ ( sK0 @ X2 ) ) ) )
| ( ( sK1 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( X2 @ ( sK0 @ X2 ) ) )
= $false )
| ( $false
= ( ( sK0 @ X2 )
= X1 ) )
| ( ( sK1 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( ( sK0 @ X2 )
= X1 ) )
| ( ( sK1 @ X1 )
= $true )
| ( ( X2 @ ( sK0 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X2: $i > $o,X1: $i] :
( ( ( sK0 @ X2 )
!= X1 )
| ( ( X2 @ ( sK0 @ X2 ) )
= $true )
| ( ( sK1 @ X1 )
= $true ) ),
inference(equality_proxy_clausification,[],[f31]) ).
thf(f45,plain,
! [X0: $i > $o] :
( ( ( sK1 @ ( sK0 @ X0 ) )
= $true )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(equality_resolution,[],[f32]) ).
thf(f60,plain,
( ( ( sK1 @ ( sK0 @ sK1 ) )
= $true )
| ( $true != $true ) ),
inference(equality_factoring,[],[f45]) ).
thf(f61,plain,
( ( sK1 @ ( sK0 @ sK1 ) )
= $true ),
inference(trivial_inequality_removal,[],[f60]) ).
thf(f75,plain,
$false,
inference(forward_subsumption_resolution,[],[f61,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO241^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.12 % Computer : n012.cluster.edu
% 0.00/0.12 % Model : x86_64 x86_64
% 0.00/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.12 % Memory : 8046.5625MB
% 0.00/0.12 % OS : Linux 6.8.0-71-generic
% 0.00/0.12 % CPULimit : 300
% 0.00/0.12 % WCLimit : 300
% 0.00/0.12 % DateTime : Tue Sep 29 16:40:34 UTC 2026
% 0.00/0.12 % CPUTime :
% 0.00/0.12 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.14 Running higher-order theorem proving
% 0.09/0.15 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
% 0.09/0.19 % (346155)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.19 % (346167)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.19 % (346167)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
% 0.09/0.19 % (346166)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2431769625:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_3000 on theBenchmark for (3000ds/75Mi)
% 0.09/0.19 % (346164)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=1783175933: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_3000 on theBenchmark for (3000ds/634Mi)
% 0.09/0.19 % (346161)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3245368082:s2a=on:i=87:rtra=on:ntd=on_3000 on theBenchmark for (3000ds/87Mi)
% 0.09/0.19 % (346162)lrs+10_16_si=on:nwc=1.5:random_seed=3776181473:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_3000 on theBenchmark for (3000ds/18Mi)
% 0.09/0.19 % (346165)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3103861036:i=24:av=off:rtra=on_3000 on theBenchmark for (3000ds/24Mi)
% 0.09/0.19 % (346163)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=669268549:i=3:rtra=on:inj=on:ntd=on_3000 on theBenchmark for (3000ds/3Mi)
% 0.09/0.19 % (346167)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=3007634672:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_3000 on theBenchmark for (3000ds/157Mi)
% 0.09/0.19 % (346163)Refutation not found, incomplete strategy
% 0.09/0.19 % (346163)------------------------------
% 0.09/0.19 % (346163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.19 % (346163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.19 % (346163)CaDiCaL version: 2.1.3
% 0.09/0.19 % (346163)Termination reason: Refutation not found, incomplete strategy
% 0.09/0.19 % (346163)Time elapsed: 0.010 s
% 0.09/0.19 % (346163)Peak memory usage: 12 MB
% 0.09/0.19 % (346163)Instructions burned: 2 (million)
% 0.09/0.19 % (346163)------------------------------
% 0.09/0.19 % (346163)------------------------------
% 0.09/0.19 % (346165) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-346155-346165"...
% 0.09/0.19 % (346161) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-346155-346161"...
% 0.09/0.19 % (346166) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-346155-346166"...
% 0.09/0.19 % (346167) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-346155-346167"...
% 0.09/0.19 % (346165)...printing done.
% 0.09/0.19 % (346165)Refutation found. Thanks to Tanya!
% 0.09/0.19 % SZS status Theorem for theBenchmark
% 0.09/0.19 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.19 % (346165)------------------------------
% 0.09/0.19 % (346165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.19 % (346165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.19 % (346165)CaDiCaL version: 2.1.3
% 0.09/0.19 % (346165)Termination reason: Refutation
% 0.09/0.19 % (346165)Time elapsed: 0.012 s
% 0.09/0.19 % (346165)Peak memory usage: 12 MB
% 0.09/0.19 % (346165)Instructions burned: 6 (million)
% 0.09/0.19 % (346155)Success in time 0.034 s
% 0.09/0.19 % Vampire exiting
%------------------------------------------------------------------------------