%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM691^1 : 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 : 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 08:18:34 AM UTC 2026
% Result : Theorem 0.09s 0.17s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of formulae : 57 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 282 ( 120 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 474 ( 75 ~; 39 |; 7 &; 316 @)
% ( 0 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 74 ( 0 ^; 74 !; 0 ?; 74 :)
% 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,
more: nat > nat > $o ).
thf(func_def_6,type,
pl: nat > nat > nat ).
thf(f1,axiom,
( ~ ( more @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(f2,axiom,
( ~ ( more @ z @ u )
=> ( z = u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(f4,axiom,
! [X3: nat,X1: nat,X0: nat,X2: nat] :
( ( ~ ( more @ X0 @ X1 )
=> ( X0 = X1 ) )
=> ( ( more @ X2 @ X3 )
=> ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz22a) ).
thf(f5,axiom,
! [X1: nat,X0: nat,X2: nat,X3: nat] :
( ( more @ X0 @ X1 )
=> ( ( ~ ( more @ X2 @ X3 )
=> ( X2 = X3 ) )
=> ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz22b) ).
thf(f6,conjecture,
( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz23) ).
thf(f7,negated_conjecture,
~ ( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
~ ( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
~ ( ( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ~ ( more @ X2 @ X1 )
=> ( X1 = X2 ) )
=> ( ( more @ X3 @ X0 )
=> ( more @ ( pl @ X2 @ X3 ) @ ( pl @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f13,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( ( more @ X2 @ X1 )
!= $true )
=> ( X1 = X2 ) )
=> ( ( ( more @ X3 @ X0 )
= $true )
=> ( $true
= ( more @ ( pl @ X2 @ X3 ) @ ( pl @ X1 @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( more @ X1 @ X0 )
=> ( ( ~ ( more @ X2 @ X3 )
=> ( X2 = X3 ) )
=> ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f15,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( more @ X1 @ X0 )
= $true )
=> ( ( ( ( more @ X2 @ X3 )
!= $true )
=> ( X2 = X3 ) )
=> ( ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) )
= $true ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f18,plain,
( ~ ( more @ z @ u )
=> ( z = u ) ),
inference(rectify,[],[f2]) ).
thf(f19,plain,
( ( ( more @ z @ u )
!= $true )
=> ( z = u ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
~ ( ( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
inference(flattening,[],[f9]) ).
thf(f21,plain,
( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[],[f11]) ).
thf(f22,plain,
! [X2: nat,X0: nat,X1: nat,X3: nat] :
( ( ( ( more @ X2 @ X1 )
!= $true )
=> ( X1 = X2 ) )
=> ( ( ( more @ X3 @ X0 )
= $true )
=> ( $true
= ( more @ ( pl @ X2 @ X3 ) @ ( pl @ X1 @ X0 ) ) ) ) ),
inference(flattening,[],[f13]) ).
thf(f23,plain,
! [X2: nat,X0: nat,X3: nat,X1: nat] :
( ( ( more @ X1 @ X0 )
= $true )
=> ( ( ( ( more @ X2 @ X3 )
!= $true )
=> ( X2 = X3 ) )
=> ( ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) )
= $true ) ) ),
inference(flattening,[],[f15]) ).
thf(f25,plain,
( ( ( more @ z @ u )
!= $true )
=> ( z = u ) ),
inference(flattening,[],[f19]) ).
thf(f26,plain,
( ( ( more @ x @ y )
= $true )
| ( x = y ) ),
inference(ennf_transformation,[],[f21]) ).
thf(f27,plain,
! [X2: nat,X0: nat,X3: nat,X1: nat] :
( ( ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) )
= $true )
| ( ( ( more @ X2 @ X3 )
!= $true )
& ( X2 != X3 ) )
| ( ( more @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f23]) ).
thf(f28,plain,
! [X0: nat,X3: nat,X2: nat,X1: nat] :
( ( ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) )
= $true )
| ( ( ( more @ X2 @ X3 )
!= $true )
& ( X2 != X3 ) )
| ( ( more @ X1 @ X0 )
!= $true ) ),
inference(flattening,[],[f27]) ).
thf(f29,plain,
( ( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true )
& ( ( pl @ x @ z )
!= ( pl @ y @ u ) ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f30,plain,
! [X2: nat,X0: nat,X1: nat,X3: nat] :
( ( $true
= ( more @ ( pl @ X2 @ X3 ) @ ( pl @ X1 @ X0 ) ) )
| ( ( more @ X3 @ X0 )
!= $true )
| ( ( ( more @ X2 @ X1 )
!= $true )
& ( X1 != X2 ) ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f31,plain,
! [X0: nat,X1: nat,X3: nat,X2: nat] :
( ( ( more @ X3 @ X0 )
!= $true )
| ( ( ( more @ X2 @ X1 )
!= $true )
& ( X1 != X2 ) )
| ( $true
= ( more @ ( pl @ X2 @ X3 ) @ ( pl @ X1 @ X0 ) ) ) ),
inference(flattening,[],[f30]) ).
thf(f33,plain,
( ( ( more @ z @ u )
= $true )
| ( z = u ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f34,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( more @ X2 @ X0 )
!= $true )
| ( ( ( more @ X3 @ X1 )
!= $true )
& ( X1 != X3 ) )
| ( ( more @ ( pl @ X3 @ X2 ) @ ( pl @ X1 @ X0 ) )
= $true ) ),
inference(rectify,[],[f31]) ).
thf(f35,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
= ( more @ ( pl @ X3 @ X2 ) @ ( pl @ X0 @ X1 ) ) )
| ( ( ( more @ X2 @ X1 )
!= $true )
& ( X1 != X2 ) )
| ( ( more @ X3 @ X0 )
!= $true ) ),
inference(rectify,[],[f28]) ).
thf(f36,plain,
( ( ( more @ x @ y )
= $true )
| ( x = y ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f37,plain,
( ( pl @ x @ z )
!= ( pl @ y @ u ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f38,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true ),
inference(cnf_transformation,[],[f29]) ).
thf(f40,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( ( more @ X2 @ X0 )
!= $true )
| ( X1 != X3 )
| ( ( more @ ( pl @ X3 @ X2 ) @ ( pl @ X1 @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f41,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( ( more @ ( pl @ X3 @ X2 ) @ ( pl @ X1 @ X0 ) )
= $true )
| ( ( more @ X3 @ X1 )
!= $true )
| ( ( more @ X2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f42,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X3 @ X2 ) @ ( pl @ X0 @ X1 ) ) )
| ( X1 != X2 )
| ( ( more @ X3 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f44,plain,
( ( ( more @ z @ u )
= $true )
| ( z = u ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f47,plain,
! [X2: nat,X3: nat,X0: nat] :
( ( ( more @ ( pl @ X3 @ X2 ) @ ( pl @ X3 @ X0 ) )
= $true )
| ( ( more @ X2 @ X0 )
!= $true ) ),
inference(equality_resolution,[],[f40]) ).
thf(f48,plain,
! [X2: nat,X3: nat,X0: nat] :
( ( ( more @ ( pl @ X3 @ X2 ) @ ( pl @ X0 @ X2 ) )
= $true )
| ( ( more @ X3 @ X0 )
!= $true ) ),
inference(equality_resolution,[],[f42]) ).
thf(f49,plain,
( ( $true != $true )
| ( ( more @ x @ y )
!= $true )
| ( ( more @ z @ u )
!= $true ) ),
inference(superposition,[],[f38,f41]) ).
thf(f50,plain,
( ( ( more @ z @ u )
!= $true )
| ( ( more @ x @ y )
!= $true ) ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f51,plain,
( ( ( more @ x @ y )
!= $true )
| ( $true != $true )
| ( z = u ) ),
inference(superposition,[],[f50,f44]) ).
thf(f52,plain,
( ( ( more @ x @ y )
!= $true )
| ( z = u ) ),
inference(trivial_inequality_removal,[],[f51]) ).
thf(f53,plain,
( ( z = u )
| ( $true != $true )
| ( x = y ) ),
inference(superposition,[],[f52,f36]) ).
thf(f54,plain,
( ( x = y )
| ( z = u ) ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f56,plain,
( ( ( more @ ( pl @ x @ z ) @ ( pl @ x @ u ) )
!= $true )
| ( z = u ) ),
inference(superposition,[],[f38,f54]) ).
thf(f59,plain,
( ( ( more @ z @ u )
!= $true )
| ( z = u )
| ( $true != $true ) ),
inference(superposition,[],[f56,f47]) ).
thf(f62,plain,
( ( ( more @ z @ u )
!= $true )
| ( z = u ) ),
inference(trivial_inequality_removal,[],[f59]) ).
thf(f63,plain,
z = u,
inference(forward_subsumption_resolution,[],[f62,f44]) ).
thf(f65,plain,
( $true
!= ( more @ ( pl @ x @ u ) @ ( pl @ y @ u ) ) ),
inference(superposition,[],[f38,f63]) ).
thf(f70,plain,
( ( $true != $true )
| ( ( more @ x @ y )
!= $true ) ),
inference(superposition,[],[f65,f48]) ).
thf(f73,plain,
( ( more @ x @ y )
!= $true ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f75,plain,
( ( x = y )
| ( $true != $true ) ),
inference(superposition,[],[f73,f36]) ).
thf(f76,plain,
x = y,
inference(trivial_inequality_removal,[],[f75]) ).
thf(f77,plain,
( ( pl @ x @ z )
!= ( pl @ x @ u ) ),
inference(superposition,[],[f37,f76]) ).
thf(f83,plain,
( ( pl @ x @ u )
!= ( pl @ x @ u ) ),
inference(forward_demodulation,[],[f77,f63]) ).
thf(f84,plain,
$false,
inference(trivial_inequality_removal,[],[f83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM691^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/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 12:39:04 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.13 Running higher-order theorem proving
% 0.09/0.13 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
% 0.09/0.17 % (45862)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.17 % (45881)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.17 % (45881)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
% 0.09/0.17 % (45876)lrs+10_16_si=on:nwc=1.5:random_seed=4034501869:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.17 % (45877)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=931342523:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.09/0.17 % (45875)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=69304819:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.09/0.17 % (45881)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=887149198:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.09/0.17 % (45878)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=590442399: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)
% 0.09/0.17 % (45879)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2014744293:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.09/0.17 % (45880)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2758838219:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.09/0.17 % (45877)Instruction limit reached!
% 0.09/0.17 % (45877)------------------------------
% 0.09/0.17 % (45877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.17 % (45877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.17 % (45877)CaDiCaL version: 2.1.3
% 0.09/0.17 % (45877)Termination reason: Instruction limit
% 0.09/0.17 % (45877)Termination phase: Saturation
% 0.09/0.17 % (45877)Time elapsed: 0.002 s
% 0.09/0.17 % (45877)Peak memory usage: 12 MB
% 0.09/0.17 % (45877)Instructions burned: 5 (million)
% 0.09/0.17 % (45879) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-45862-45879"...
% 0.09/0.17 % (45879)...printing done.
% 0.09/0.17 % (45878) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-45862-45878"...
% 0.09/0.17 % (45879)Refutation found. Thanks to Tanya!
% 0.09/0.17 % SZS status Theorem for theBenchmark
% 0.09/0.17 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.17 % (45879)------------------------------
% 0.09/0.17 % (45879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.17 % (45879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.17 % (45879)CaDiCaL version: 2.1.3
% 0.09/0.17 % (45879)Termination reason: Refutation
% 0.09/0.17 % (45879)Time elapsed: 0.002 s
% 0.09/0.17 % (45879)Peak memory usage: 12 MB
% 0.09/0.17 % (45879)Instructions burned: 7 (million)
% 0.09/0.17 % (45862)Success in time 0.032 s
% 0.09/0.17 % Vampire exiting
%------------------------------------------------------------------------------