%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET632^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:23:25 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 150 ( 60 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 160 ( 38 ~; 20 |; 24 &; 66 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 59 ( 11 ^; 35 !; 13 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: a > $o ).
thf(func_def_7,type,
sK3: a ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ~ ? [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) )
=> ( ( ^ [X3: a] : $false )
= X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_114_pme) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ~ ? [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) )
=> ( ( ^ [X3: a] : $false )
= X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X2 @ X3 )
=> ( X0 @ X3 ) )
& ~ ? [X4: a] :
( ( X0 @ X4 )
& ( X1 @ X4 ) )
& ! [X5: a] :
( ( X2 @ X5 )
=> ( X1 @ X5 ) ) )
=> ( ( ^ [X6: a] : $false )
= X2 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X5: a] :
( ( ( X2 @ X5 )
= $true )
=> ( ( X1 @ X5 )
= $true ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( X0 @ X3 )
= $true ) )
& ~ ? [X4: a] :
( ( $true
= ( X1 @ X4 ) )
& ( $true
= ( X0 @ X4 ) ) ) )
=> ( ( ^ [Y0: a] : $false )
= X2 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X2 )
& ! [X5: a] :
( ( ( X1 @ X5 )
= $true )
| ( ( X2 @ X5 )
!= $true ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
!= ( X1 @ X4 ) )
| ( $true
!= ( X0 @ X4 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X4: a] :
( ( $true
!= ( X1 @ X4 ) )
| ( $true
!= ( X0 @ X4 ) ) )
& ! [X5: a] :
( ( ( X1 @ X5 )
= $true )
| ( ( X2 @ X5 )
!= $true ) )
& ( ( ^ [Y0: a] : $false )
!= X2 )
& ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( $true
= ( X1 @ X4 ) )
| ( $true
!= ( X2 @ X4 ) ) )
& ( ( ^ [Y0: a] : $false )
!= X2 )
& ! [X5: a] :
( ( ( X2 @ X5 )
!= $true )
| ( ( X0 @ X5 )
= $true ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( $true
!= ( sK0 @ X3 ) ) )
& ! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( $true
!= ( sK2 @ X4 ) ) )
& ( ( ^ [Y0: a] : $false )
!= sK2 )
& ! [X5: a] :
( ( ( sK2 @ X5 )
!= $true )
| ( ( sK0 @ X5 )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f7]) ).
thf(f9,plain,
! [X5: a] :
( ( ( sK2 @ X5 )
!= $true )
| ( ( sK0 @ X5 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( ^ [Y0: a] : $false )
!= sK2 ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X4: a] :
( ( $true
!= ( sK2 @ X4 ) )
| ( $true
= ( sK1 @ X4 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( ( sK2 @ sK3 )
!= ( ^ [Y0: a] : $false
@ sK3 ) ),
inference(negative_extensionality,[],[f10]) ).
thf(f16,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( $true
= ( ^ [Y0: a] : $false
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f15]) ).
thf(f19,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( $true = $false ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f20,plain,
( ( sK2 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[],[f19]) ).
thf(f21,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f9,f20]) ).
thf(f22,plain,
( ( sK0 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[],[f21]) ).
thf(f23,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f11,f20]) ).
thf(f24,plain,
( ( sK1 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f25,plain,
( ( $true != $true )
| ( ( sK1 @ sK3 )
!= $true ) ),
inference(constrained_superposition,[],[f12,f22]) ).
thf(f26,plain,
( ( sK1 @ sK3 )
!= $true ),
inference(trivial_inequality_removal,[],[f25]) ).
thf(f27,plain,
$false,
inference(forward_subsumption_resolution,[],[f26,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET632^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n015.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:43:33 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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 % (3541071)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (3541085)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2346822826:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (3541085)Refutation not found, incomplete strategy
% 0.21/0.29 % (3541085)------------------------------
% 0.21/0.29 % (3541085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3541085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3541085)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3541085)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (3541085)Time elapsed: 0.001 s
% 0.21/0.29 % (3541085)Peak memory usage: 12 MB
% 0.21/0.29 % (3541085)------------------------------
% 0.21/0.29 % (3541085)------------------------------
% 0.21/0.29 % (3541089)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 % (3541089)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 % (3541084)lrs+10_16_si=on:nwc=1.5:random_seed=3066878657:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (3541087)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=905527456:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (3541083)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3467675002:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (3541086)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=2226800218: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 % (3541089)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=2218982168:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (3541088)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=912994649:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (3541084) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3541071-3541084"...
% 0.21/0.29 % (3541087) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3541071-3541087"...
% 0.21/0.29 % (3541083) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3541071-3541083"...
% 0.21/0.29 % (3541086) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3541071-3541086"...
% 0.21/0.29 % (3541088) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3541071-3541088"...
% 0.21/0.29 % (3541089) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3541071-3541089"...
% 0.21/0.29 % (3541084)...printing done.
% 0.21/0.29 % (3541087)...printing done.
% 0.21/0.29 % (3541083)...printing done.
% 0.21/0.29 % (3541086)...printing done.
% 0.21/0.29 % (3541084)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 % (3541084)------------------------------
% 0.21/0.29 % (3541084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3541084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3541084)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3541084)Termination reason: Refutation
% 0.21/0.29 % (3541084)Time elapsed: 0.002 s
% 0.21/0.29 % (3541084)Peak memory usage: 12 MB
% 0.21/0.29 % (3541084)Instructions burned: 2 (million)
% 0.21/0.29 % (3541071)Success in time 0.042 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------