%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO262^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:47:18 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 18 unt; 0 typ; 5 def)
% Number of atoms : 118 ( 31 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 238 ( 36 ~; 3 |; 7 &; 192 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 2 con; 0-4 aty)
% Number of variables : 60 ( 28 ^; 32 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cP: $i > $i > $o ).
thf(func_def_1,type,
cE: ( $i > $o ) > $i ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(func_def_8,type,
sF0: $i > $i ).
thf(func_def_9,type,
sF1: $i > $o ).
thf(func_def_10,type,
sF2: ( $i > $i ) > $i ).
thf(func_def_11,type,
sF3: ( $i > $i ) > $i ).
thf(func_def_12,type,
sF4: ( $i > $i ) > $o ).
thf(f1,conjecture,
~ ( ! [X2: $i > $i] :
~ ( cP
@ ( cE
@ ^ [X0: $i] :
~ ( cP @ X0 @ ( X2 @ X0 ) ) )
@ ( X2
@ ( cE
@ ^ [X0: $i] :
~ ( cP @ X0 @ ( X2 @ X0 ) ) ) ) )
& ! [X0: $i] :
( cP @ X0
@ ( cE
@ ^ [X1: $i] : ( cP @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM19SK1) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X2: $i > $i] :
~ ( cP
@ ( cE
@ ^ [X0: $i] :
~ ( cP @ X0 @ ( X2 @ X0 ) ) )
@ ( X2
@ ( cE
@ ^ [X0: $i] :
~ ( cP @ X0 @ ( X2 @ X0 ) ) ) ) )
& ! [X0: $i] :
( cP @ X0
@ ( cE
@ ^ [X1: $i] : ( cP @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ~ ( ! [X0: $i > $i] :
~ ( cP
@ ( cE
@ ^ [X1: $i] :
~ ( cP @ X1 @ ( X0 @ X1 ) ) )
@ ( X0
@ ( cE
@ ^ [X2: $i] :
~ ( cP @ X2 @ ( X0 @ X2 ) ) ) ) )
& ! [X3: $i] :
( cP @ X3
@ ( cE
@ ^ [X4: $i] : ( cP @ X3 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i > $i] :
( $true
!= ( cP
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X0 @ Y0 ) ) )
@ ( X0
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X0 @ Y0 ) ) ) ) ) )
& ! [X3: $i] :
( $true
= ( cP @ X3
@ ( cE
@ ^ [Y0: $i] : ( cP @ X3 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ~ ( ! [X0: $i > $i] :
( $true
!= ( cP
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X0 @ Y0 ) ) )
@ ( X0
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X0 @ Y0 ) ) ) ) ) )
& ! [X1: $i] :
( $true
= ( cP @ X1
@ ( cE
@ ^ [Y0: $i] : ( cP @ X1 @ Y0 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
( ! [X1: $i] :
( $true
= ( cP @ X1
@ ( cE
@ ^ [Y0: $i] : ( cP @ X1 @ Y0 ) ) ) )
& ! [X0: $i > $i] :
( $true
!= ( cP
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X0 @ Y0 ) ) )
@ ( X0
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X0 @ Y0 ) ) ) ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i] :
( $true
= ( cP @ X0
@ ( cE
@ ^ [Y0: $i] : ( cP @ X0 @ Y0 ) ) ) )
& ! [X1: $i > $i] :
( $true
!= ( cP
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X1 @ Y0 ) ) )
@ ( X1
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X1 @ Y0 ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
! [X1: $i > $i] :
( $true
!= ( cP
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X1 @ Y0 ) ) )
@ ( X1
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X0: $i] :
( $true
= ( cP @ X0
@ ( cE
@ ^ [Y0: $i] : ( cP @ X0 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,definition,
! [X0: $i] :
( ( sF0 @ X0 )
= ( cE
@ ^ [Y0: $i] : ( cP @ X0 @ Y0 ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f13,plain,
! [X0: $i] :
( ( cE
@ ^ [Y0: $i] : ( cP @ X0 @ Y0 ) )
= ( sF0 @ X0 ) ),
inference(reorient_equations,[],[f12]) ).
thf(f14,definition,
! [X0: $i] :
( ( sF1 @ X0 )
= ( cP @ X0 @ ( sF0 @ X0 ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f15,plain,
! [X0: $i] :
( ( cP @ X0 @ ( sF0 @ X0 ) )
= ( sF1 @ X0 ) ),
inference(reorient_equations,[],[f14]) ).
thf(f16,plain,
! [X0: $i] :
( $true
= ( sF1 @ X0 ) ),
inference(definition_folding,[],[f9,f15,f13]) ).
thf(f17,definition,
! [X1: $i > $i] :
( ( sF2 @ X1 )
= ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X1 @ Y0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f18,plain,
! [X1: $i > $i] :
( ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X1 @ Y0 ) ) )
= ( sF2 @ X1 ) ),
inference(reorient_equations,[],[f17]) ).
thf(f19,definition,
! [X1: $i > $i] :
( ( sF3 @ X1 )
= ( X1 @ ( sF2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f20,definition,
! [X1: $i > $i] :
( ( sF4 @ X1 )
= ( cP @ ( sF2 @ X1 ) @ ( sF3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f21,plain,
! [X1: $i > $i] :
( ( cP @ ( sF2 @ X1 ) @ ( sF3 @ X1 ) )
= ( sF4 @ X1 ) ),
inference(reorient_equations,[],[f20]) ).
thf(f22,plain,
! [X1: $i > $i] :
( $true
!= ( sF4 @ X1 ) ),
inference(definition_folding,[],[f8,f21,f19,f18,f18]) ).
thf(f24,plain,
! [X1: $i > $i] :
( ( $true
= ( sF4 @ X1 ) )
| ( ( cP @ ( sF2 @ X1 ) @ ( sF3 @ X1 ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f21]) ).
thf(f25,plain,
! [X0: $i] :
( ( $true
= ( cP @ X0 @ ( sF0 @ X0 ) ) )
| ( $false
= ( sF1 @ X0 ) ) ),
inference(iff_proxy_clausification,[],[f15]) ).
thf(f40,plain,
! [X0: $i] :
( ( $true
= ( cP @ X0 @ ( sF0 @ X0 ) ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f25,f16]) ).
thf(f41,plain,
! [X0: $i] :
( $true
= ( cP @ X0 @ ( sF0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f40]) ).
thf(f42,plain,
( $true
= ( cP @ ( sF2 @ sF0 ) @ ( sF3 @ sF0 ) ) ),
inference(constrained_superposition,[],[f41,f19]) ).
thf(f43,plain,
! [X1: $i > $i] :
( ( cP @ ( sF2 @ X1 ) @ ( sF3 @ X1 ) )
= $false ),
inference(forward_subsumption_resolution,[],[f24,f22]) ).
thf(f46,plain,
$true = $false,
inference(constrained_superposition,[],[f42,f43]) ).
thf(f47,plain,
$false,
inference(trivial_inequality_removal,[],[f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO262^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n013.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 16:41:22 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.21/0.30 % (2355334)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (2355339)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2038839284:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (2355339)Refutation not found, incomplete strategy
% 0.21/0.30 % (2355339)------------------------------
% 0.21/0.30 % (2355339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2355339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2355339)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2355339)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (2355339)Time elapsed: 0.001 s
% 0.21/0.30 % (2355339)Peak memory usage: 12 MB
% 0.21/0.30 % (2355339)Instructions burned: 1 (million)
% 0.21/0.30 % (2355339)------------------------------
% 0.21/0.30 % (2355339)------------------------------
% 0.21/0.30 % (2355345)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (2355345)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
% 0.21/0.30 % (2355340)lrs+10_16_si=on:nwc=1.5:random_seed=320400098:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (2355341)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3604507101:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (2355345)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=3357798602:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (2355342)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=1146265450: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)
% 0.21/0.30 % (2355343)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1951820794:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (2355344)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=890939896:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (2355341)Refutation not found, incomplete strategy
% 0.21/0.30 % (2355341)------------------------------
% 0.21/0.30 % (2355341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2355341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2355341)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2355341)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (2355341)Time elapsed: 0.001 s
% 0.21/0.30 % (2355341)Peak memory usage: 12 MB
% 0.21/0.30 % (2355341)Instructions burned: 1 (million)
% 0.21/0.30 % (2355343)Refutation not found, incomplete strategy
% 0.21/0.30 % (2355343)------------------------------
% 0.21/0.30 % (2355343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2355343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2355343)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2355343)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (2355343)Time elapsed: 0.001 s
% 0.21/0.30 % (2355343)Peak memory usage: 11 MB
% 0.21/0.30 % (2355343)Instructions burned: 1 (million)
% 0.21/0.30 % (2355342)Refutation not found, incomplete strategy
% 0.21/0.30 % (2355342)------------------------------
% 0.21/0.30 % (2355342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2355342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2355342)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2355342)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (2355342)Time elapsed: 0.001 s
% 0.21/0.30 % (2355342)Peak memory usage: 12 MB
% 0.21/0.30 % (2355342)Instructions burned: 1 (million)
% 0.21/0.30 % (2355341)------------------------------
% 0.21/0.30 % (2355341)------------------------------
% 0.21/0.30 % (2355343)------------------------------
% 0.21/0.30 % (2355343)------------------------------
% 0.21/0.30 % (2355342)------------------------------
% 0.21/0.30 % (2355342)------------------------------
% 0.21/0.30 % (2355345) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2355334-2355345"...
% 0.21/0.30 % (2355347)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3953231251:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.30 % (2355345)...printing done.
% 0.21/0.30 % (2355347)Instruction limit reached!
% 0.21/0.30 % (2355347)------------------------------
% 0.21/0.30 % (2355347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2355347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2355347)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2355347)Termination reason: Instruction limit
% 0.21/0.30 % (2355347)Termination phase: Saturation
% 0.21/0.30 % (2355347)Time elapsed: 0.001 s
% 0.21/0.30 % (2355347)Peak memory usage: 12 MB
% 0.21/0.30 % (2355347)Instructions burned: 2 (million)
% 0.21/0.30 % (2355345)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (2355345)------------------------------
% 0.21/0.30 % (2355345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2355345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2355345)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2355345)Termination reason: Refutation
% 0.21/0.30 % (2355345)Time elapsed: 0.003 s
% 0.21/0.30 % (2355345)Peak memory usage: 12 MB
% 0.21/0.30 % (2355345)Instructions burned: 4 (million)
% 0.21/0.30 % (2355334)Success in time 0.038 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------