%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ104^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:20:54 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 2
% Syntax : Number of formulae : 49 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 294 ( 75 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 331 ( 8 ~; 27 |; 16 &; 224 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 5 con; 0-4 aty)
% ( 20 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 50 ( 30 ^; 19 !; 1 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
cCKB6_NUM: $i > $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIMP: $o > $o > $o ).
thf(func_def_6,type,
vAND: $o > $o > $o ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
sK1: $i > $o ).
thf(func_def_15,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_16,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ( X1 @ c1 )
& ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) ) )
=> ( X1 @ X0 ) ) )
= cCKB6_NUM ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB6_NUM_def) ).
thf(f2,conjecture,
! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ ( s @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB6_L4000) ).
thf(f3,negated_conjecture,
~ ! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ ( s @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ( X1 @ c1 )
& ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) ) )
=> ( X1 @ X0 ) ) )
= cCKB6_NUM ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( cCKB6_NUM
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) )
& ( Y1 @ c1 ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ ( s @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X0: $i] :
( ( ( cCKB6_NUM @ X0 )
= $true )
=> ( ( cCKB6_NUM @ ( s @ ( s @ X0 ) ) )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $i] :
( ( ( cCKB6_NUM @ X0 )
= $true )
& ( ( cCKB6_NUM @ ( s @ ( s @ X0 ) ) )
!= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( $true
= ( cCKB6_NUM @ sK0 ) )
& ( $true
!= ( cCKB6_NUM @ ( s @ ( s @ sK0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f8]) ).
thf(f10,plain,
( cCKB6_NUM
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) )
& ( Y1 @ c1 ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
( $true
!= ( cCKB6_NUM @ ( s @ ( s @ sK0 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( $true
= ( cCKB6_NUM @ sK0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) )
& ( Y1 @ c1 ) )
=> ( Y1 @ Y0 ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f12,f10]) ).
thf(f16,plain,
( $true
!= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) )
& ( Y1 @ c1 ) )
=> ( Y1 @ Y0 ) ) )
@ ( s @ ( s @ sK0 ) ) ) ),
inference(definition_unfolding,[],[f11,f10]) ).
thf(f17,plain,
( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ ( s @ ( s @ sK0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
( ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ ( s @ ( s @ sK0 ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK1 @ ( s @ Y0 ) ) ) )
& ( sK1 @ c1 ) )
=> ( sK1 @ ( s @ ( s @ sK0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
( ( sK1 @ ( s @ ( s @ sK0 ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK1 @ ( s @ Y0 ) ) ) )
& ( sK1 @ c1 ) )
= $true ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f22,plain,
( $true
= ( sK1 @ c1 ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK1 @ ( s @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK1 @ ( s @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( ( sK1 @ X1 )
=> ( sK1 @ ( s @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ ( s @ X1 ) ) )
| ( ( sK1 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f28,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X1: $i > $o] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) )
& ( X1 @ c1 ) )
=> ( X1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ sK0 ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) )
& ( X1 @ c1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) )
= $false )
| ( $true
= ( X1 @ sK0 ) )
| ( ( X1 @ c1 )
= $false ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X1: $i > $o] :
( ( ( X1 @ c1 )
= $false )
| ( $true
= ( X1 @ sK0 ) )
| ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) )
@ ( sK2 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ sK0 ) )
| ( ( ( X1 @ ( sK2 @ X1 ) )
=> ( X1 @ ( s @ ( sK2 @ X1 ) ) ) )
= $false )
| ( ( X1 @ c1 )
= $false ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
! [X1: $i > $o] :
( ( ( X1 @ ( s @ ( sK2 @ X1 ) ) )
= $false )
| ( ( X1 @ c1 )
= $false )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f33]) ).
thf(f35,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ ( sK2 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 ) )
| ( ( X1 @ c1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f33]) ).
thf(f36,plain,
( ( ( sK1 @ ( s @ sK0 ) )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f26,f20]) ).
thf(f38,plain,
( ( sK1 @ ( s @ sK0 ) )
= $false ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f40,plain,
( ( $true = $false )
| ( ( sK1 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f38,f26]) ).
thf(f42,plain,
( ( sK1 @ sK0 )
= $false ),
inference(trivial_inequality_removal,[],[f40]) ).
thf(f76,plain,
( ( $true = $false )
| ( ( sK1 @ ( sK2 @ sK1 ) )
= $false )
| ( $true
= ( sK1 @ sK0 ) )
| ( ( sK1 @ c1 )
= $false ) ),
inference(constrained_superposition,[],[f26,f34]) ).
thf(f83,plain,
( ( $true
= ( sK1 @ sK0 ) )
| ( ( sK1 @ c1 )
= $false )
| ( ( sK1 @ ( sK2 @ sK1 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f76]) ).
thf(f94,plain,
( ( $true = $false )
| ( ( sK1 @ c1 )
= $false )
| ( ( sK1 @ ( sK2 @ sK1 ) )
= $false ) ),
inference(forward_demodulation,[],[f83,f42]) ).
thf(f95,plain,
( ( ( sK1 @ ( sK2 @ sK1 ) )
= $false )
| ( ( sK1 @ c1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f108,plain,
( ( ( sK1 @ ( sK2 @ sK1 ) )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f95,f22]) ).
thf(f109,plain,
( ( sK1 @ ( sK2 @ sK1 ) )
= $false ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f119,plain,
( ( $true = $false )
| ( ( sK1 @ c1 )
= $false )
| ( $true
= ( sK1 @ sK0 ) ) ),
inference(constrained_superposition,[],[f35,f109]) ).
thf(f120,plain,
( ( $true
= ( sK1 @ sK0 ) )
| ( ( sK1 @ c1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f119]) ).
thf(f122,plain,
( ( $true = $false )
| ( ( sK1 @ c1 )
= $false ) ),
inference(forward_demodulation,[],[f120,f42]) ).
thf(f123,plain,
( ( sK1 @ c1 )
= $false ),
inference(trivial_inequality_removal,[],[f122]) ).
thf(f126,plain,
$true = $false,
inference(forward_demodulation,[],[f123,f22]) ).
thf(f127,plain,
$false,
inference(trivial_inequality_removal,[],[f126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ104^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:24:08 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.27 % (1267255)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (1267271)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2358306663:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.27 % (1267272)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.27 % (1267272)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
% 0.20/0.27 % (1267266)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2424391143:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (1267267)lrs+10_16_si=on:nwc=1.5:random_seed=1295873758:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.27 % (1267269)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=2351659508: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)
% 0.20/0.27 % (1267268)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3011351811:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.27 % (1267270)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=117986339:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.27 % (1267272)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=3620549725:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.27 % (1267268)Refutation not found, incomplete strategy
% 0.20/0.27 % (1267268)------------------------------
% 0.20/0.27 % (1267268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1267268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1267268)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1267268)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.27 % (1267268)Time elapsed: 0.001 s
% 0.20/0.27 % (1267268)Peak memory usage: 12 MB
% 0.20/0.27 % (1267268)Instructions burned: 1 (million)
% 0.20/0.27 % (1267268)------------------------------
% 0.20/0.27 % (1267268)------------------------------
% 0.20/0.27 % (1267266) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1267255-1267266"...
% 0.20/0.27 % (1267272) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1267255-1267272"...
% 0.20/0.27 % (1267266)...printing done.
% 0.20/0.27 % (1267266)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (1267266)------------------------------
% 0.20/0.27 % (1267266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1267266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1267266)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1267266)Termination reason: Refutation
% 0.20/0.27 % (1267266)Time elapsed: 0.005 s
% 0.20/0.27 % (1267266)Peak memory usage: 12 MB
% 0.20/0.27 % (1267266)Instructions burned: 7 (million)
% 0.20/0.27 % (1267255)Success in time 0.028 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------