%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO547^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:48:23 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 103 ( 39 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 151 ( 39 ~; 8 |; 2 &; 94 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 3 con; 0-4 aty)
% Number of variables : 64 ( 31 ^; 23 !; 10 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
epscomp: ( $i > $o ) > $i ).
thf(func_def_5,type,
vNOT: $o > $o ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
sK0: $i > $o ).
thf(func_def_11,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_13,type,
sK3: $i > $i ).
thf(func_def_14,type,
sK4: $i > $i ).
thf(func_def_15,type,
sK5: $i > $i > $i ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceax) ).
thf(f2,axiom,
( ( ^ [X0: $i > $o] :
( eps
@ ^ [X1: $i] :
~ ( X0 @ X1 ) ) )
= epscomp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epscompd) ).
thf(f3,conjecture,
! [X0: $i > $o] :
( ? [X1: $i] :
~ ( X0 @ X1 )
=> ~ ( X0 @ ( epscomp @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choicecomp) ).
thf(f4,negated_conjecture,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
~ ( X0 @ X1 )
=> ~ ( X0 @ ( epscomp @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( ( ^ [X0: $i > $o] :
( eps
@ ^ [X1: $i] :
~ ( X0 @ X1 ) ) )
= epscomp ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( epscomp
= ( ^ [Y0: $i > $o] :
( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
~ ( X0 @ X1 )
=> ~ ( X0 @ ( epscomp @ X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
!= $true )
=> ( ( X0 @ ( epscomp @ X0 ) )
!= $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
!= $true )
=> ( ( X0 @ ( epscomp @ X0 ) )
!= $true ) ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
! [X0: $i > $o] :
( ( ( X0 @ ( eps @ X0 ) )
= $true )
| ! [X1: $i] :
( ( X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f13,plain,
? [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
!= $true )
& ( ( X0 @ ( epscomp @ X0 ) )
= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f14,plain,
( ( $true
!= ( sK0 @ sK1 ) )
& ( $true
= ( sK0 @ ( epscomp @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f13]) ).
thf(f15,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
( epscomp
= ( ^ [Y0: $i > $o] :
( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
( $true
= ( sK0 @ ( epscomp @ sK0 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f18,plain,
( $true
!= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
( $true
= ( sK0
@ ( ^ [Y0: $i > $o] :
( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f17,f16]) ).
thf(f22,plain,
( $true
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f26,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
!= ( ^ [Y0: $i] :
~ ( X2 @ Y0 )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
~ ( X2 @ Y0 )
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) ) ),
inference(primitive_instantiation,[],[f15]) ).
thf(f37,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
!= ( ~ ( X2 @ X1 ) ) )
| ( $true
= ( ~ ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f38,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( X2 @ X1 ) )
| ( $true
= ( ~ ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( X2 @ X1 ) )
| ( $false
= ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f38]) ).
thf(f110,plain,
( ( $false
= ( ^ [Y0: $i] :
( sK0
@ ( ^ [Y1: $i] : sK1
@ Y0 ) )
@ ( eps
@ ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( sK0
@ ( ^ [Y2: $i] : sK1
@ Y1 ) )
@ Y0 ) ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f18,f39]) ).
thf(f115,plain,
! [X0: $i] :
( ( $true
= ( ^ [Y0: $i] :
( sK0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ X0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f22,f39]) ).
thf(f132,plain,
! [X0: $i] :
( $true
= ( ^ [Y0: $i] :
( sK0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ X0 ) ),
inference(trivial_inequality_removal,[],[f115]) ).
thf(f133,plain,
! [X0: $i] :
( $true
= ( sK0 @ X0 ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f171,plain,
( $false
= ( ^ [Y0: $i] :
( sK0
@ ( ^ [Y1: $i] : sK1
@ Y0 ) )
@ ( eps
@ ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( sK0
@ ( ^ [Y2: $i] : sK1
@ Y1 ) )
@ Y0 ) ) ) ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f172,plain,
( ( sK0 @ sK1 )
= $false ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f194,plain,
$true = $false,
inference(forward_demodulation,[],[f172,f133]) ).
thf(f195,plain,
$false,
inference(trivial_inequality_removal,[],[f194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO547^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n019.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 17:14:48 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.28 % (1098945)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (1098952)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=720879655:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.28 % (1098951)lrs+10_16_si=on:nwc=1.5:random_seed=645313720:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.28 % (1098950)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=292258868:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.28 % (1098952)Refutation not found, incomplete strategy
% 0.19/0.28 % (1098952)------------------------------
% 0.19/0.28 % (1098952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (1098952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (1098952)CaDiCaL version: 2.1.3
% 0.19/0.28 % (1098952)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.28 % (1098952)Time elapsed: 0.002 s
% 0.19/0.28 % (1098952)Peak memory usage: 11 MB
% 0.19/0.28 % (1098952)Instructions burned: 1 (million)
% 0.19/0.28 % (1098952)------------------------------
% 0.19/0.28 % (1098952)------------------------------
% 0.19/0.28 % (1098950)Refutation not found, incomplete strategy
% 0.19/0.28 % (1098950)------------------------------
% 0.19/0.28 % (1098950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (1098950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (1098950)CaDiCaL version: 2.1.3
% 0.19/0.28 % (1098950)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.28 % (1098950)Time elapsed: 0.003 s
% 0.19/0.28 % (1098950)Peak memory usage: 12 MB
% 0.19/0.28 % (1098950)Instructions burned: 4 (million)
% 0.19/0.28 % (1098950)------------------------------
% 0.19/0.28 % (1098950)------------------------------
% 0.19/0.28 % (1098956)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.28 % (1098956)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
% 0.19/0.28 % (1098951) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1098945-1098951"...
% 0.19/0.28 % (1098951)...printing done.
% 0.19/0.28 % (1098956)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=3810413656:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.28 % (1098951)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (1098951)------------------------------
% 0.19/0.28 % (1098951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (1098951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (1098951)CaDiCaL version: 2.1.3
% 0.19/0.28 % (1098951)Termination reason: Refutation
% 0.19/0.28 % (1098951)Time elapsed: 0.007 s
% 0.19/0.28 % (1098951)Peak memory usage: 12 MB
% 0.19/0.28 % (1098951)Instructions burned: 13 (million)
% 0.19/0.28 % (1098945)Success in time 0.048 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------