%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM672^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:18:29 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 123 ( 35 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 195 ( 16 ~; 10 |; 0 &; 160 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% 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,
less: nat > nat > $o ).
thf(func_def_5,type,
pl: nat > nat > nat ).
thf(func_def_6,type,
more: nat > nat > $o ).
thf(f1,axiom,
less @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
! [X0: nat,X1: nat] :
( ( more @ X0 @ X1 )
=> ( less @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz11) ).
thf(f3,axiom,
! [X1: nat,X2: nat,X0: nat] :
( ( more @ X0 @ X1 )
=> ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a) ).
thf(f4,axiom,
! [X1: nat,X0: nat] :
( ( less @ X0 @ X1 )
=> ( more @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz12) ).
thf(f5,conjecture,
less @ ( pl @ x @ z ) @ ( pl @ y @ z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19c) ).
thf(f6,negated_conjecture,
~ ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( more @ X2 @ X0 )
=> ( more @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f8,plain,
! [X1: nat,X0: nat,X2: nat] :
( ( ( more @ X2 @ X0 )
= $true )
=> ( $true
= ( more @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: nat,X1: nat] :
( ( more @ X0 @ X1 )
=> ( less @ X1 @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
! [X1: nat,X0: nat] :
( ( ( more @ X0 @ X1 )
= $true )
=> ( ( less @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( ( less @ X1 @ X0 )
=> ( more @ X0 @ X1 ) ),
inference(rectify,[],[f4]) ).
thf(f12,plain,
! [X1: nat,X0: nat] :
( ( ( less @ X1 @ X0 )
= $true )
=> ( ( more @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
less @ x @ y,
inference(rectify,[],[f1]) ).
thf(f14,plain,
( ( less @ x @ y )
= $true ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
~ ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
!= $true ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
!= $true ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
!= $true )
| ( ( less @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f19,plain,
! [X0: nat,X1: nat] :
( ( ( less @ X1 @ X0 )
!= $true )
| ( ( more @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f20,plain,
! [X0: nat,X2: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) ) )
| ( ( more @ X2 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f21,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
= ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X2 ) ) )
| ( ( more @ X1 @ X0 )
!= $true ) ),
inference(rectify,[],[f20]) ).
thf(f22,plain,
( ( less @ x @ y )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f23,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
!= $true )
| ( ( less @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f24,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( more @ X1 @ X0 )
!= $true )
| ( $true
= ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X2 ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f25,plain,
! [X0: nat,X1: nat] :
( ( ( less @ X1 @ X0 )
!= $true )
| ( ( more @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
!= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f29,plain,
( ( ( more @ y @ x )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f25,f22]) ).
thf(f30,plain,
( ( more @ y @ x )
= $true ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f33,plain,
! [X0: nat] :
( ( $true
= ( more @ ( pl @ y @ X0 ) @ ( pl @ x @ X0 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f24,f30]) ).
thf(f34,plain,
! [X0: nat] :
( $true
= ( more @ ( pl @ y @ X0 ) @ ( pl @ x @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f36,plain,
! [X0: nat] :
( ( $true
= ( less @ ( pl @ x @ X0 ) @ ( pl @ y @ X0 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f23,f34]) ).
thf(f38,plain,
! [X0: nat] :
( $true
= ( less @ ( pl @ x @ X0 ) @ ( pl @ y @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f39,plain,
$true != $true,
inference(constrained_superposition,[],[f26,f38]) ).
thf(f41,plain,
$false,
inference(trivial_inequality_removal,[],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM672^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n016.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 12:40:19 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.29 % (285362)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (285373)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (285373)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
% 0.21/0.29 % (285367)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4266184926:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (285368)lrs+10_16_si=on:nwc=1.5:random_seed=1480545226:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (285369)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4178669980:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (285372)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=192566541:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (285371)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1016107131:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (285373)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=2759477095:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (285370)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=2545582098: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)
% 0.21/0.29 % (285369) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-285362-285369"...
% 0.21/0.29 % (285367) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-285362-285367"...
% 0.21/0.29 % (285371) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-285362-285371"...
% 0.21/0.29 % (285368) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-285362-285368"...
% 0.21/0.29 % (285370) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-285362-285370"...
% 0.21/0.29 % (285367)...printing done.
% 0.21/0.29 % (285369)...printing done.
% 0.21/0.29 % (285371)...printing done.
% 0.21/0.29 % (285368)...printing done.
% 0.21/0.29 % (285372) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-285362-285372"...
% 0.21/0.29 % (285373) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-285362-285373"...
% 0.21/0.29 % (285369)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (285369)------------------------------
% 0.21/0.29 % (285369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (285369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (285369)CaDiCaL version: 2.1.3
% 0.21/0.29 % (285369)Termination reason: Refutation
% 0.21/0.29 % (285369)Time elapsed: 0.003 s
% 0.21/0.29 % (285369)Peak memory usage: 12 MB
% 0.21/0.29 % (285369)Instructions burned: 3 (million)
% 0.21/0.29 % (285362)Success in time 0.036 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------