%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM681^1 : 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 : n001.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 08:18:31 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 16 unt; 0 typ; 4 def)
% Number of atoms : 281 ( 95 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 408 ( 91 ~; 51 |; 4 &; 224 @)
% ( 4 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 67 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: nat ).
thf(func_def_1,type,
y: nat ).
thf(func_def_2,type,
z: nat ).
thf(func_def_3,type,
pl: nat > nat > nat ).
thf(func_def_5,type,
less: nat > nat > $o ).
thf(func_def_6,type,
more: nat > nat > $o ).
thf(f1,axiom,
( ( pl @ x @ z )
= ( pl @ y @ z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i) ).
thf(f3,axiom,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ~ ( more @ X0 @ X1 ) )
=> ~ ~ ( ( ( more @ X0 @ X1 )
=> ~ ( less @ X0 @ X1 ) )
=> ~ ( ( less @ X0 @ X1 )
=> ( X0 != X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10b) ).
thf(f4,axiom,
! [X2: nat,X1: nat,X0: nat] :
( ( less @ X0 @ X1 )
=> ( less @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19c) ).
thf(f5,axiom,
! [X1: nat,X0: nat] :
( ( X0 != X1 )
=> ( ~ ( more @ X0 @ X1 )
=> ( less @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10a) ).
thf(f6,axiom,
! [X0: nat,X2: nat,X1: nat] :
( ( more @ X0 @ X1 )
=> ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19a) ).
thf(f7,conjecture,
x = y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz20b) ).
thf(f8,negated_conjecture,
x != y,
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( less @ X2 @ X1 )
=> ( less @ ( pl @ X2 @ X0 ) @ ( pl @ X1 @ X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
= ( less @ X2 @ X1 ) )
=> ( $true
= ( less @ ( pl @ X2 @ X0 ) @ ( pl @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ( more @ X1 @ X0 )
=> ( less @ X1 @ X0 ) ) ),
inference(rectify,[],[f5]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( $true
!= ( more @ X1 @ X0 ) )
=> ( $true
= ( less @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ~ ( more @ X0 @ X1 ) )
=> ~ ~ ( ( ( more @ X0 @ X1 )
=> ~ ( less @ X0 @ X1 ) )
=> ~ ( ( less @ X0 @ X1 )
=> ( X0 != X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ( ( more @ X0 @ X1 )
!= $true ) )
=> ~ ~ ( ( ( ( more @ X0 @ X1 )
= $true )
=> ( ( less @ X0 @ X1 )
!= $true ) )
=> ~ ( ( ( less @ X0 @ X1 )
= $true )
=> ( X0 != X1 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( more @ X0 @ X2 )
=> ( more @ ( pl @ X0 @ X1 ) @ ( pl @ X2 @ X1 ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
! [X1: nat,X0: nat,X2: nat] :
( ( $true
= ( more @ X0 @ X2 ) )
=> ( $true
= ( more @ ( pl @ X0 @ X1 ) @ ( pl @ X2 @ X1 ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f19,plain,
! [X1: nat,X0: nat] :
( ( X0 != X1 )
=> ( ( $true
!= ( more @ X1 @ X0 ) )
=> ( $true
= ( less @ X1 @ X0 ) ) ) ),
inference(flattening,[],[f12]) ).
thf(f20,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ( ( more @ X0 @ X1 )
!= $true ) )
=> ( ( ( ( more @ X0 @ X1 )
= $true )
=> ( ( less @ X0 @ X1 )
!= $true ) )
=> ~ ( ( ( less @ X0 @ X1 )
= $true )
=> ( X0 != X1 ) ) ) ),
inference(flattening,[],[f14]) ).
thf(f21,plain,
x != y,
inference(flattening,[],[f8]) ).
thf(f23,plain,
! [X1: nat,X0: nat] :
( ( $true
= ( less @ X1 @ X0 ) )
| ( $true
= ( more @ X1 @ X0 ) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f24,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( more @ X1 @ X0 ) )
| ( $true
= ( less @ X1 @ X0 ) )
| ( X0 = X1 ) ),
inference(flattening,[],[f23]) ).
thf(f25,plain,
! [X0: nat,X1: nat] :
( ( ( X0 != X1 )
| ( ( less @ X0 @ X1 )
!= $true ) )
& ( ( ( less @ X0 @ X1 )
!= $true )
| ( ( more @ X0 @ X1 )
!= $true ) )
& ( ( ( more @ X0 @ X1 )
!= $true )
| ( X0 != X1 ) ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f26,plain,
! [X0: nat,X1: nat] :
( ( ( ( more @ X0 @ X1 )
!= $true )
| ( X0 != X1 ) )
& ( ( X0 != X1 )
| ( ( less @ X0 @ X1 )
!= $true ) )
& ( ( ( less @ X0 @ X1 )
!= $true )
| ( ( more @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f25]) ).
thf(f28,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
= ( less @ ( pl @ X2 @ X0 ) @ ( pl @ X1 @ X0 ) ) )
| ( $true
!= ( less @ X2 @ X1 ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f29,plain,
! [X1: nat,X0: nat,X2: nat] :
( ( $true
!= ( more @ X0 @ X2 ) )
| ( $true
= ( more @ ( pl @ X0 @ X1 ) @ ( pl @ X2 @ X1 ) ) ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f30,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( more @ X1 @ X2 )
!= $true )
| ( $true
= ( more @ ( pl @ X1 @ X0 ) @ ( pl @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f32,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
= ( less @ ( pl @ X2 @ X0 ) @ ( pl @ X1 @ X0 ) ) )
| ( $true
!= ( less @ X2 @ X1 ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f33,plain,
( ( pl @ x @ z )
= ( pl @ y @ z ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f35,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( ( less @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f36,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
!= $true )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f37,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X1 @ X0 ) @ ( pl @ X2 @ X0 ) ) )
| ( ( more @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f38,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( more @ X1 @ X0 ) )
| ( $true
= ( less @ X1 @ X0 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f39,plain,
x != y,
inference(cnf_transformation,[],[f21]) ).
thf(f42,plain,
! [X1: nat] :
( $true
!= ( more @ X1 @ X1 ) ),
inference(equality_resolution,[],[f36]) ).
thf(f43,plain,
! [X1: nat] :
( $true
!= ( less @ X1 @ X1 ) ),
inference(equality_resolution,[],[f35]) ).
thf(f45,definition,
( spl0_1
<=> ( ( pl @ x @ z )
= ( pl @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f47,plain,
( ( ( pl @ x @ z )
= ( pl @ y @ z ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f48,plain,
spl0_1,
inference(avatar_split_clause,[],[f33,f45]) ).
thf(f50,definition,
( spl0_2
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f52,plain,
( ( x != y )
| spl0_2 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f53,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f39,f50]) ).
thf(f55,plain,
( ! [X0: nat] :
( ( ( less @ ( pl @ y @ z ) @ ( pl @ X0 @ z ) )
= $true )
| ( $true
!= ( less @ x @ X0 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f32,f47]) ).
thf(f57,plain,
( ! [X0: nat] :
( ( $true
= ( more @ ( pl @ y @ z ) @ ( pl @ X0 @ z ) ) )
| ( ( more @ x @ X0 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[],[f37,f47]) ).
thf(f87,plain,
( ( $true != $true )
| ( ( less @ x @ y )
!= $true )
| ~ spl0_1 ),
inference(superposition,[],[f43,f55]) ).
thf(f88,plain,
( ( ( less @ x @ y )
!= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f92,definition,
( spl0_4
<=> ( ( less @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f94,plain,
( ( ( less @ x @ y )
!= $true )
| spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f95,plain,
( ~ spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f88,f45,f92]) ).
thf(f109,plain,
( ( ( more @ x @ y )
!= $true )
| ( $true != $true )
| ~ spl0_1 ),
inference(superposition,[],[f42,f57]) ).
thf(f110,plain,
( ( ( more @ x @ y )
!= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f113,definition,
( spl0_6
<=> ( ( more @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
thf(f115,plain,
( ( ( more @ x @ y )
!= $true )
| spl0_6 ),
inference(avatar_component_clause,[],[f113]) ).
thf(f116,plain,
( ~ spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f110,f45,f113]) ).
thf(f117,plain,
( ( $true != $true )
| ( x = y )
| ( ( less @ x @ y )
= $true )
| spl0_6 ),
inference(superposition,[],[f115,f38]) ).
thf(f118,plain,
( ( ( less @ x @ y )
= $true )
| ( x = y )
| spl0_6 ),
inference(trivial_inequality_removal,[],[f117]) ).
thf(f119,plain,
( ( x = y )
| spl0_4
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f118,f94]) ).
thf(f120,plain,
( $false
| spl0_2
| spl0_4
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f119,f52]) ).
thf(f121,plain,
( spl0_2
| spl0_4
| spl0_6 ),
inference(avatar_contradiction_clause,[],[f120]) ).
cnf(s1,plain,
spl0_1,
inference(sat_conversion,[],[f48]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f95]) ).
cnf(s7,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(sat_conversion,[],[f116]) ).
cnf(s8,plain,
( spl0_2
| spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f121]) ).
cnf(s9,plain,
~ spl0_6,
inference(rat,[],[s7,s1]) ).
cnf(s11,plain,
~ spl0_4,
inference(rat,[],[s4,s1]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s8,s2,s9,s11]) ).
thf(f122,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM681^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n001.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 12:43:35 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.23 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 % (1179637)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (1179645)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=715173718: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 % (1179645) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1179637-1179645"...
% 0.20/0.27 % (1179645)...printing done.
% 0.20/0.27 % (1179645)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 % (1179645)------------------------------
% 0.20/0.27 % (1179645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1179645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1179645)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1179645)Termination reason: Refutation
% 0.20/0.27 % (1179645)Time elapsed: 0.004 s
% 0.20/0.27 % (1179645)Peak memory usage: 13 MB
% 0.20/0.27 % (1179645)Instructions burned: 9 (million)
% 0.20/0.27 % (1179637)Success in time 0.029 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------