%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO271^5 : 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 : n017.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 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 23 unt; 0 typ; 6 def)
% Number of atoms : 155 ( 101 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 254 ( 47 ~; 16 |; 6 &; 173 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 6 con; 0-4 aty)
% Number of variables : 78 ( 28 ^; 42 !; 8 ?; 78 :)
% 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_0,type,
cJ: ( b > $o ) > b ).
thf(func_def_4,type,
db0:
!>[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_8,type,
sK0: b > a ).
thf(func_def_9,type,
sK1: b > a ).
thf(func_def_10,type,
sF2: ( b > $o ) > b ).
thf(func_def_11,type,
sF3: ( b > $o ) > $o ).
thf(func_def_12,type,
sF4: b > ( b > $o ) > $o ).
thf(func_def_13,type,
sF5: b ).
thf(func_def_14,type,
sF6: a ).
thf(func_def_15,type,
sF7: a ).
thf(func_def_16,type,
sK8: b ).
thf(f1,conjecture,
( ! [X0: b > $o] :
( ? [X1: b] : ( X0 @ X1 )
=> ( X0 @ ( cJ @ X0 ) ) )
=> ! [X3: b > a,X2: b > a] :
( ( ( X2
@ ( cJ
@ ^ [X1: b] :
( ( X2 @ X1 )
!= ( X3 @ X1 ) ) ) )
= ( X3
@ ( cJ
@ ^ [X1: b] :
( ( X2 @ X1 )
!= ( X3 @ X1 ) ) ) ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5500) ).
thf(f2,negated_conjecture,
~ ( ! [X0: b > $o] :
( ? [X1: b] : ( X0 @ X1 )
=> ( X0 @ ( cJ @ X0 ) ) )
=> ! [X3: b > a,X2: b > a] :
( ( ( X2
@ ( cJ
@ ^ [X1: b] :
( ( X2 @ X1 )
!= ( X3 @ X1 ) ) ) )
= ( X3
@ ( cJ
@ ^ [X1: b] :
( ( X2 @ X1 )
!= ( X3 @ X1 ) ) ) ) )
=> ( X2 = X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: b > $o] :
( ? [X1: b] : ( X0 @ X1 )
=> ( X0 @ ( cJ @ X0 ) ) )
=> ! [X2: b > a,X3: b > a] :
( ( ( X3
@ ( cJ
@ ^ [X4: b] :
( ( X3 @ X4 )
!= ( X2 @ X4 ) ) ) )
= ( X2
@ ( cJ
@ ^ [X5: b] :
( ( X3 @ X5 )
!= ( X2 @ X5 ) ) ) ) )
=> ( X2 = X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: b > $o] :
( ? [X1: b] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( cJ @ X0 ) )
= $true ) )
=> ! [X3: b > a,X2: b > a] :
( ( ( X2
@ ( cJ
@ ^ [Y0: b] :
( ( X3 @ Y0 )
!= ( X2 @ Y0 ) ) ) )
= ( X3
@ ( cJ
@ ^ [Y0: b] :
( ( X3 @ Y0 )
!= ( X2 @ Y0 ) ) ) ) )
=> ( X2 = X3 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X0: b > $o] :
( ( ( X0 @ ( cJ @ X0 ) )
= $true )
| ! [X1: b] :
( ( X0 @ X1 )
!= $true ) )
& ? [X3: b > a,X2: b > a] :
( ( X2 != X3 )
& ( ( X2
@ ( cJ
@ ^ [Y0: b] :
( ( X3 @ Y0 )
!= ( X2 @ Y0 ) ) ) )
= ( X3
@ ( cJ
@ ^ [Y0: b] :
( ( X3 @ Y0 )
!= ( X2 @ Y0 ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X0: b > $o] :
( ( ( X0 @ ( cJ @ X0 ) )
= $true )
| ! [X1: b] :
( ( X0 @ X1 )
!= $true ) )
& ? [X2: b > a,X3: b > a] :
( ( X2 != X3 )
& ( ( X3
@ ( cJ
@ ^ [Y0: b] :
( ( X2 @ Y0 )
!= ( X3 @ Y0 ) ) ) )
= ( X2
@ ( cJ
@ ^ [Y0: b] :
( ( X2 @ Y0 )
!= ( X3 @ Y0 ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X0: b > $o] :
( ( ( X0 @ ( cJ @ X0 ) )
= $true )
| ! [X1: b] :
( ( X0 @ X1 )
!= $true ) )
& ( sK1 != sK0 )
& ( ( sK1
@ ( cJ
@ ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) ) ) )
= ( sK0
@ ( cJ
@ ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f6]) ).
thf(f8,plain,
( ( sK1
@ ( cJ
@ ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) ) ) )
= ( sK0
@ ( cJ
@ ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
sK1 != sK0,
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X0: b > $o,X1: b] :
( ( ( X0 @ ( cJ @ X0 ) )
= $true )
| ( ( X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,definition,
! [X0: b > $o] :
( ( sF2 @ X0 )
= ( cJ @ X0 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f14,plain,
! [X0: b > $o] :
( ( cJ @ X0 )
= ( sF2 @ X0 ) ),
inference(reorient_equations,[],[f13]) ).
thf(f15,definition,
! [X0: b > $o] :
( ( sF3 @ X0 )
= ( X0 @ ( sF2 @ X0 ) ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f16,plain,
! [X0: b > $o] :
( ( X0 @ ( sF2 @ X0 ) )
= ( sF3 @ X0 ) ),
inference(reorient_equations,[],[f15]) ).
thf(f17,definition,
! [X0: b > $o,X1: b] :
( ( sF4 @ X1 @ X0 )
= ( X0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f18,plain,
! [X0: b > $o,X1: b] :
( ( X0 @ X1 )
= ( sF4 @ X1 @ X0 ) ),
inference(reorient_equations,[],[f17]) ).
thf(f19,plain,
! [X0: b > $o,X1: b] :
( ( $true
!= ( sF4 @ X1 @ X0 ) )
| ( $true
= ( sF3 @ X0 ) ) ),
inference(definition_folding,[],[f10,f18,f16,f14]) ).
thf(f20,definition,
( sF5
= ( cJ
@ ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f21,plain,
( ( cJ
@ ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) ) )
= sF5 ),
inference(reorient_equations,[],[f20]) ).
thf(f22,definition,
( sF6
= ( sK1 @ sF5 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f23,definition,
( sF7
= ( sK0 @ sF5 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f24,plain,
sF7 = sF6,
inference(definition_folding,[],[f8,f23,f21,f22,f21]) ).
thf(f25,plain,
! [X0: b > $o] :
( ( ( X0 @ ( sF2 @ X0 ) )
= $true )
| ( $false
= ( sF3 @ X0 ) ) ),
inference(iff_proxy_clausification,[],[f16]) ).
thf(f28,plain,
! [X0: b > $o,X1: b] :
( ( $true
= ( sF4 @ X1 @ X0 ) )
| ( ( X0 @ X1 )
= $false ) ),
inference(iff_proxy_clausification,[],[f18]) ).
thf(f29,plain,
( ( sK0 @ sK8 )
!= ( sK1 @ sK8 ) ),
inference(negative_extensionality,[],[f9]) ).
thf(f43,plain,
( sF7
= ( sK1 @ sF5 ) ),
inference(forward_demodulation,[],[f22,f24]) ).
thf(f57,plain,
! [X0: b,X1: b > $o] :
( ( $true != $true )
| ( $true
= ( sF3 @ X1 ) )
| ( ( X1 @ X0 )
= $false ) ),
inference(constrained_superposition,[],[f19,f28]) ).
thf(f59,plain,
! [X0: b,X1: b > $o] :
( ( $true
= ( sF3 @ X1 ) )
| ( ( X1 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f63,plain,
( ( sF2
@ ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) ) )
= sF5 ),
inference(forward_demodulation,[],[f21,f14]) ).
thf(f65,plain,
( ( $true
= ( ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) )
@ sF5 ) )
| ( ( sF3
@ ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) ) )
= $false ) ),
inference(constrained_superposition,[],[f25,f63]) ).
thf(f66,plain,
( ( ( ( sK0 @ sF5 )
!= ( sK1 @ sF5 ) )
= $true )
| ( ( sF3
@ ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f67,plain,
( ( $false
= ( ( sK0 @ sF5 )
= ( sK1 @ sF5 ) ) )
| ( ( sF3
@ ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( ( ( sK0 @ sF5 )
!= ( sK1 @ sF5 ) )
| ( ( sF3
@ ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) ) )
= $false ) ),
inference(equality_proxy_clausification,[],[f67]) ).
thf(f72,plain,
( ( ( sF3
@ ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) ) )
= $false )
| ( sF7
!= ( sK0 @ sF5 ) ) ),
inference(forward_demodulation,[],[f68,f43]) ).
thf(f74,plain,
( ( sF3
@ ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) ) )
= $false ),
inference(forward_subsumption_resolution,[],[f72,f23]) ).
thf(f75,plain,
! [X0: b] :
( ( ( ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) )
@ X0 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f74,f59]) ).
thf(f78,plain,
! [X0: b] :
( ( ^ [Y0: b] :
( ( sK0 @ Y0 )
!= ( sK1 @ Y0 ) )
@ X0 )
= $false ),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f79,plain,
! [X0: b] :
( $false
= ( ( sK0 @ X0 )
!= ( sK1 @ X0 ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X0: b] :
( ( ( sK0 @ X0 )
= ( sK1 @ X0 ) )
= $true ),
inference(not_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X0: b] :
( ( sK1 @ X0 )
= ( sK0 @ X0 ) ),
inference(equality_proxy_clausification,[],[f80]) ).
thf(f88,plain,
( ( sK0 @ sK8 )
!= ( sK0 @ sK8 ) ),
inference(constrained_superposition,[],[f29,f81]) ).
thf(f90,plain,
$false,
inference(trivial_inequality_removal,[],[f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO271^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:37:37 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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 % (572643)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (572654)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 % (572654)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 % (572648)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2693264684:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (572650)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=337875146:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (572649)lrs+10_16_si=on:nwc=1.5:random_seed=4276625553:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (572653)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2178716939:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (572652)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3796199640:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (572651)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=2333722687: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 % (572654)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=558297415:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (572650)Refutation not found, incomplete strategy
% 0.21/0.29 % (572650)------------------------------
% 0.21/0.29 % (572650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (572650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (572650)CaDiCaL version: 2.1.3
% 0.21/0.29 % (572650)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (572650)Time elapsed: 0.002 s
% 0.21/0.29 % (572650)Peak memory usage: 12 MB
% 0.21/0.29 % (572650)Instructions burned: 1 (million)
% 0.21/0.29 % (572650)------------------------------
% 0.21/0.29 % (572650)------------------------------
% 0.21/0.29 % (572648)Refutation not found, incomplete strategy
% 0.21/0.29 % (572648)------------------------------
% 0.21/0.29 % (572648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (572648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (572648)CaDiCaL version: 2.1.3
% 0.21/0.29 % (572648)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (572648)Time elapsed: 0.003 s
% 0.21/0.29 % (572648)Peak memory usage: 12 MB
% 0.21/0.29 % (572648)Instructions burned: 3 (million)
% 0.21/0.29 % (572652)Refutation not found, incomplete strategy
% 0.21/0.29 % (572652)------------------------------
% 0.21/0.29 % (572652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (572652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (572652)CaDiCaL version: 2.1.3
% 0.21/0.29 % (572652)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (572652)Time elapsed: 0.003 s
% 0.21/0.29 % (572652)Peak memory usage: 12 MB
% 0.21/0.29 % (572652)Instructions burned: 4 (million)
% 0.21/0.29 % (572651)Refutation not found, incomplete strategy
% 0.21/0.29 % (572651)------------------------------
% 0.21/0.29 % (572651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (572651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (572651)CaDiCaL version: 2.1.3
% 0.21/0.29 % (572651)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (572651)Time elapsed: 0.003 s
% 0.21/0.29 % (572651)Peak memory usage: 12 MB
% 0.21/0.29 % (572651)Instructions burned: 3 (million)
% 0.21/0.29 % (572648)------------------------------
% 0.21/0.29 % (572648)------------------------------
% 0.21/0.29 % (572652)------------------------------
% 0.21/0.29 % (572652)------------------------------
% 0.21/0.29 % (572651)------------------------------
% 0.21/0.29 % (572651)------------------------------
% 0.21/0.29 % (572654) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-572643-572654"...
% 0.21/0.30 % (572654)...printing done.
% 0.21/0.30 % (572654)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (572654)------------------------------
% 0.21/0.30 % (572654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (572654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (572654)CaDiCaL version: 2.1.3
% 0.21/0.30 % (572654)Termination reason: Refutation
% 0.21/0.30 % (572654)Time elapsed: 0.005 s
% 0.21/0.30 % (572654)Peak memory usage: 12 MB
% 0.21/0.30 % (572654)Instructions burned: 7 (million)
% 0.21/0.30 % (572643)Success in time 0.044 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------