%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV447^1 : TPTP v9.3.1. Released v3.7.0.
% 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 08:40:01 AM UTC 2026
% Result : Theorem 0.06s 0.17s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 18 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 117 ( 8 ~; 0 |; 0 &; 109 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 33 ( 8 ^; 24 !; 1 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cons: $i > $i > $i ).
thf(func_def_2,type,
map: ( $i > $i ) > $i > $i ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
! [X0: $i > $i] :
( ( map @ X0 @ nil )
= nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(f2,axiom,
! [X2: $i,X1: $i,X0: $i > $i] :
( ( map @ X0 @ ( cons @ X1 @ X2 ) )
= ( cons @ ( X0 @ X1 ) @ ( map @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(f3,conjecture,
! [X0: $i] :
( ( map
@ ^ [X1: $i] : X1
@ ( cons @ X0 @ nil ) )
= ( cons @ X0 @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test) ).
thf(f4,negated_conjecture,
~ ! [X0: $i] :
( ( map
@ ^ [X1: $i] : X1
@ ( cons @ X0 @ nil ) )
= ( cons @ X0 @ nil ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ! [X0: $i] :
( ( map
@ ^ [X1: $i] : X1
@ ( cons @ X0 @ nil ) )
= ( cons @ X0 @ nil ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $i] :
( ( cons @ X0 @ nil )
= ( map
@ ^ [Y0: $i] : Y0
@ ( cons @ X0 @ nil ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i > $i] :
( nil
= ( map @ X0 @ nil ) ),
inference(fool_elimination,[],[f1]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i > $i] :
( ( map @ X2 @ ( cons @ X1 @ X0 ) )
= ( cons @ ( X2 @ X1 ) @ ( map @ X2 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
! [X2: $i > $i,X0: $i,X1: $i] :
( ( map @ X2 @ ( cons @ X1 @ X0 ) )
= ( cons @ ( X2 @ X1 ) @ ( map @ X2 @ X0 ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
? [X0: $i] :
( ( cons @ X0 @ nil )
!= ( map
@ ^ [Y0: $i] : Y0
@ ( cons @ X0 @ nil ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f11,plain,
( ( map
@ ^ [Y0: $i] : Y0
@ ( cons @ sK0 @ nil ) )
!= ( cons @ sK0 @ nil ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f10]) ).
thf(f12,plain,
! [X0: $i > $i,X1: $i,X2: $i] :
( ( map @ X0 @ ( cons @ X2 @ X1 ) )
= ( cons @ ( X0 @ X2 ) @ ( map @ X0 @ X1 ) ) ),
inference(rectify,[],[f9]) ).
thf(f13,plain,
( ( map
@ ^ [Y0: $i] : Y0
@ ( cons @ sK0 @ nil ) )
!= ( cons @ sK0 @ nil ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f14,plain,
! [X0: $i > $i] :
( nil
= ( map @ X0 @ nil ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f15,plain,
! [X2: $i,X0: $i > $i,X1: $i] :
( ( map @ X0 @ ( cons @ X2 @ X1 ) )
= ( cons @ ( X0 @ X2 ) @ ( map @ X0 @ X1 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
! [X0: $i > $i,X1: $i] :
( ( map @ X0 @ ( cons @ X1 @ nil ) )
= ( cons @ ( X0 @ X1 ) @ nil ) ),
inference(constrained_superposition,[],[f15,f14]) ).
thf(f19,plain,
( ( cons
@ ( ^ [Y0: $i] : Y0
@ sK0 )
@ nil )
!= ( cons @ sK0 @ nil ) ),
inference(constrained_superposition,[],[f13,f16]) ).
thf(f22,plain,
( ( cons @ sK0 @ nil )
!= ( cons @ sK0 @ nil ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f23,plain,
$false,
inference(trivial_inequality_removal,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV447^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 16:04:19 UTC 2026
% 0.06/0.11 % CPUTime :
% 0.06/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.13 Running higher-order theorem proving
% 0.06/0.14 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
% 0.06/0.17 % (295005)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.06/0.17 % (295016)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.06/0.17 % (295016)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
% 0.06/0.17 % (295010)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2975942224:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.06/0.17 % (295011)lrs+10_16_si=on:nwc=1.5:random_seed=2333212482:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.06/0.17 % (295012)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1602176590:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.06/0.17 % (295014)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=175101105:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.06/0.17 % (295015)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=873113964:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.06/0.17 % (295014) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-295005-295014"...
% 0.06/0.17 % (295016)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=614148743:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.06/0.17 % (295010) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-295005-295010"...
% 0.06/0.17 % (295012) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-295005-295012"...
% 0.06/0.17 % (295011) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-295005-295011"...
% 0.06/0.17 % (295014)...printing done.
% 0.06/0.17 % (295010)...printing done.
% 0.06/0.17 % (295012)...printing done.
% 0.06/0.17 % (295012)Refutation found. Thanks to Tanya!
% 0.06/0.17 % SZS status Theorem for theBenchmark
% 0.06/0.17 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.17 % (295012)------------------------------
% 0.06/0.17 % (295012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.17 % (295012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.17 % (295012)CaDiCaL version: 2.1.3
% 0.06/0.17 % (295012)Termination reason: Refutation
% 0.06/0.17 % (295012)Time elapsed: 0.001 s
% 0.06/0.17 % (295012)Peak memory usage: 12 MB
% 0.06/0.17 % (295012)Instructions burned: 2 (million)
% 0.06/0.17 % (295005)Success in time 0.024 s
% 0.06/0.17 % Vampire exiting
%------------------------------------------------------------------------------