%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM686^1 : 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 : n006.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 08:18:32 AM UTC 2026
% Result : Theorem 0.24s 0.34s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 22 unt; 0 typ; 3 def)
% Number of atoms : 315 ( 65 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 474 ( 49 ~; 42 |; 0 &; 371 @)
% ( 3 <=>; 9 =>; 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 : 16 ( 13 usr; 9 con; 0-4 aty)
% Number of variables : 105 ( 0 sgn 58 !; 0 ?; 105 :)
% 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,
u: nat ).
thf(func_def_4,type,
some: ( nat > $o ) > $o ).
thf(func_def_5,type,
diffprop: nat > nat > nat > $o ).
thf(func_def_7,type,
pl: nat > nat > nat ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ x @ y @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(f2,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ z @ u @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(f3,axiom,
! [X0: nat,X1: nat,X2: nat] :
( ( some
@ ^ [X3: nat] : ( diffprop @ X1 @ X0 @ X3 ) )
=> ( ( some
@ ^ [X3: nat] : ( diffprop @ X2 @ X1 @ X3 ) )
=> ( some
@ ^ [X3: nat] : ( diffprop @ X2 @ X0 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz15) ).
thf(f4,axiom,
! [X1: nat,X0: nat,X2: nat] :
( ( some
@ ^ [X3: nat] : ( diffprop @ X0 @ X1 @ X3 ) )
=> ( some
@ ^ [X3: nat] : ( diffprop @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X2 ) @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19a) ).
thf(f5,axiom,
! [X1: nat,X0: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).
thf(f6,conjecture,
( some
@ ^ [X0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz21) ).
thf(f7,negated_conjecture,
~ ( some
@ ^ [X0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( some
@ ^ [X3: nat] : ( diffprop @ X1 @ X0 @ X3 ) )
=> ( some
@ ^ [X4: nat] : ( diffprop @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X2 ) @ X4 ) ) ),
inference(rectify,[],[f4]) ).
thf(f9,plain,
! [X0: nat,X2: nat,X1: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X0 @ Y0 ) )
= $true )
=> ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X2 ) @ Y0 ) )
= $true ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ( some
@ ^ [X0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ X0 ) ),
inference(rectify,[],[f7]) ).
thf(f11,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ Y0 ) )
!= $true ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( some
@ ^ [X3: nat] : ( diffprop @ X1 @ X0 @ X3 ) )
=> ( ( some
@ ^ [X4: nat] : ( diffprop @ X2 @ X1 @ X4 ) )
=> ( some
@ ^ [X5: nat] : ( diffprop @ X2 @ X0 @ X5 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
! [X0: nat,X2: nat,X1: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X0 @ Y0 ) )
= $true )
=> ( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) )
= $true )
=> ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X0 @ Y0 ) )
= $true ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( some
@ ^ [X0: nat] : ( diffprop @ x @ y @ X0 ) ),
inference(rectify,[],[f1]) ).
thf(f15,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ x @ y @ Y0 ) )
= $true ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( some
@ ^ [X0: nat] : ( diffprop @ z @ u @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f17,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ z @ u @ Y0 ) )
= $true ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ Y0 ) )
!= $true ),
inference(flattening,[],[f11]) ).
thf(f19,plain,
! [X0: nat,X2: nat,X1: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X0 @ Y0 ) )
= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) )
!= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X0 @ Y0 ) )
!= $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f20,plain,
! [X2: nat,X1: nat,X0: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X0 @ Y0 ) )
!= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X0 @ Y0 ) )
= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) )
!= $true ) ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
! [X2: nat,X1: nat,X0: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X2 ) @ Y0 ) )
= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X0 @ Y0 ) )
!= $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f22,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(rectify,[],[f5]) ).
thf(f23,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X1 @ X0 ) @ ( pl @ X2 @ X0 ) @ Y0 ) )
= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X2 @ Y0 ) )
!= $true ) ),
inference(rectify,[],[f21]) ).
thf(f24,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X2 @ Y0 ) )
!= $true )
| ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) ) )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) )
!= $true ) ),
inference(rectify,[],[f20]) ).
thf(f25,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f26,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ x @ y @ Y0 ) )
= $true ),
inference(cnf_transformation,[],[f15]) ).
thf(f27,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X1 @ X0 ) @ ( pl @ X2 @ X0 ) @ Y0 ) )
= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X2 @ Y0 ) )
!= $true ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f28,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ z @ u @ Y0 ) )
= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f29,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) )
!= $true )
| ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) ) )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X2 @ Y0 ) )
!= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f30,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ Y0 ) )
!= $true ),
inference(cnf_transformation,[],[f18]) ).
thf(f32,plain,
( ( some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f33,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( some @ ( diffprop @ X0 @ X2 ) )
= $true )
| ( ( some @ ( diffprop @ X0 @ X1 ) )
!= $true )
| ( ( some @ ( diffprop @ X1 @ X2 ) )
!= $true ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f34,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( some @ ( diffprop @ ( pl @ X1 @ X0 ) @ ( pl @ X2 @ X0 ) ) )
= $true )
| ( ( some @ ( diffprop @ X1 @ X2 ) )
!= $true ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f35,plain,
( ( some @ ( diffprop @ x @ y ) )
= $true ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f36,plain,
( $true
= ( some @ ( diffprop @ z @ u ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f38,definition,
( spl0_1
<=> ( ( some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f40,plain,
( ( ( some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[],[f38]) ).
thf(f41,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f32,f38]) ).
thf(f43,definition,
( spl0_2
<=> ( ( some @ ( diffprop @ x @ y ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f45,plain,
( ( ( some @ ( diffprop @ x @ y ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f46,plain,
spl0_2,
inference(avatar_split_clause,[],[f35,f43]) ).
thf(f48,definition,
( spl0_3
<=> ( $true
= ( some @ ( diffprop @ z @ u ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f50,plain,
( ( $true
= ( some @ ( diffprop @ z @ u ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f51,plain,
spl0_3,
inference(avatar_split_clause,[],[f36,f48]) ).
thf(f59,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( some @ ( diffprop @ ( pl @ X2 @ X0 ) @ ( pl @ X0 @ X1 ) ) )
= $true )
| ( $true
!= ( some @ ( diffprop @ X2 @ X1 ) ) ) ),
inference(superposition,[],[f34,f25]) ).
thf(f63,plain,
( ! [X0: nat] :
( ( ( some @ ( diffprop @ ( pl @ x @ z ) @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( some @ ( diffprop @ X0 @ ( pl @ y @ u ) ) )
!= $true ) )
| spl0_1 ),
inference(superposition,[],[f40,f33]) ).
thf(f64,plain,
( ! [X0: nat] :
( ( ( some @ ( diffprop @ ( pl @ x @ z ) @ X0 ) )
!= $true )
| ( ( some @ ( diffprop @ X0 @ ( pl @ y @ u ) ) )
!= $true ) )
| spl0_1 ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f72,plain,
( ! [X0: nat] :
( ( ( some @ ( diffprop @ x @ X0 ) )
!= $true )
| ( $true
!= ( some @ ( diffprop @ ( pl @ z @ X0 ) @ ( pl @ y @ u ) ) ) )
| ( $true != $true ) )
| spl0_1 ),
inference(superposition,[],[f64,f59]) ).
thf(f75,plain,
( ! [X0: nat] :
( ( $true
!= ( some @ ( diffprop @ ( pl @ z @ X0 ) @ ( pl @ y @ u ) ) ) )
| ( ( some @ ( diffprop @ x @ X0 ) )
!= $true ) )
| spl0_1 ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f96,plain,
( ( ( some @ ( diffprop @ x @ y ) )
!= $true )
| ( $true
!= ( some @ ( diffprop @ z @ u ) ) )
| ( $true != $true )
| spl0_1 ),
inference(superposition,[],[f75,f59]) ).
thf(f98,plain,
( ( ( some @ ( diffprop @ x @ y ) )
!= $true )
| ( $true
!= ( some @ ( diffprop @ z @ u ) ) )
| spl0_1 ),
inference(trivial_inequality_removal,[],[f96]) ).
thf(f101,plain,
( ( $true
!= ( some @ ( diffprop @ z @ u ) ) )
| spl0_1
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f98,f45]) ).
thf(f111,plain,
( $false
| spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f101,f50]) ).
thf(f112,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f111]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f41]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f46]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f51]) ).
cnf(s7,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f112]) ).
cnf(s8,plain,
spl0_1,
inference(rat,[],[s7,s3,s2]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8]) ).
thf(f113,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM686^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 % Computer : n006.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Sep 29 12:37:39 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.28 Running higher-order theorem proving
% 0.24/0.29 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
% 0.24/0.34 % (654498)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.34 % (654506)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=3086506847: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)
% 0.24/0.34 % (654504)lrs+10_16_si=on:nwc=1.5:random_seed=1429142164:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.34 % (654506) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-654498-654506"...
% 0.24/0.34 % (654506)...printing done.
% 0.24/0.34 % (654509)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.34 % (654509)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
% 0.24/0.34 % (654506)Refutation found. Thanks to Tanya!
% 0.24/0.34 % SZS status Theorem for theBenchmark
% 0.24/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.34 % (654506)------------------------------
% 0.24/0.34 % (654506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.34 % (654506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.34 % (654506)CaDiCaL version: 2.1.3
% 0.24/0.34 % (654506)Termination reason: Refutation
% 0.24/0.34 % (654506)Time elapsed: 0.007 s
% 0.24/0.34 % (654506)Peak memory usage: 13 MB
% 0.24/0.34 % (654506)Instructions burned: 12 (million)
% 0.24/0.34 % (654498)Success in time 0.03 s
% 0.24/0.34 % Vampire exiting
%------------------------------------------------------------------------------