%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO885^1.033.003 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:48:33 AM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 181 ( 26 equ; 0 cnn)
% Maximal formula atoms : 4 ( 20 avg)
% Number of connectives : 207 ( 21 ~; 14 |; 4 &; 168 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 32 ( 24 ^; 6 !; 2 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
f: $i > $i > $i > $i ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
? [X0: $i > $i > $i > $i] :
( ( ( X0 @ a0 @ a2 @ a1 )
= ( f @ a0 @ a1 @ a2 ) )
& ( ( X0 @ a0 @ a1 @ a2 )
= ( f @ a0 @ a1 @ a2 ) )
& ( ( X0 @ a2 @ a1 @ a0 )
= ( f @ a0 @ a1 @ a2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(f2,negated_conjecture,
~ ? [X0: $i > $i > $i > $i] :
( ( ( X0 @ a0 @ a2 @ a1 )
= ( f @ a0 @ a1 @ a2 ) )
& ( ( X0 @ a0 @ a1 @ a2 )
= ( f @ a0 @ a1 @ a2 ) )
& ( ( X0 @ a2 @ a1 @ a0 )
= ( f @ a0 @ a1 @ a2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
! [X0: $i > $i > $i > $i] :
( ( ( X0 @ a0 @ a1 @ a2 )
!= ( f @ a0 @ a1 @ a2 ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( X0 @ a0 @ a2 @ a1 ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( X0 @ a2 @ a1 @ a0 ) ) ),
inference(ennf_transformation,[],[f2]) ).
thf(f4,plain,
! [X0: $i > $i > $i > $i] :
( ( ( f @ a0 @ a1 @ a2 )
!= ( X0 @ a2 @ a1 @ a0 ) )
| ( ( X0 @ a0 @ a1 @ a2 )
!= ( f @ a0 @ a1 @ a2 ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( X0 @ a0 @ a2 @ a1 ) ) ),
inference(cnf_transformation,[],[f3]) ).
thf(f6,plain,
! [X0: $i > $i > $i > $i,X1: $i > $i > $i > $i] :
( ( ( f @ a0 @ a1 @ a2 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( f @ ( X0 @ Y0 @ Y1 @ Y2 ) @ ( X1 @ Y0 @ Y1 @ Y2 )
@ ( ^ [Y3: $i,Y4: $i,Y5: $i] : a2
@ Y0
@ Y1
@ Y2 ) )
@ a0
@ a1
@ a2 ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( f @ ( X0 @ Y0 @ Y1 @ Y2 ) @ ( X1 @ Y0 @ Y1 @ Y2 )
@ ( ^ [Y3: $i,Y4: $i,Y5: $i] : a2
@ Y0
@ Y1
@ Y2 ) )
@ a0
@ a2
@ a1 ) )
| ( a0
!= ( X0 @ a2 @ a1 @ a0 ) )
| ( a1
!= ( X1 @ a2 @ a1 @ a0 ) ) ),
inference(equality_resolution,[],[f4]) ).
thf(f8,plain,
! [X0: $i > $i > $i > $i,X1: $i > $i > $i > $i] :
( ( ( f @ a0 @ a1 @ a2 )
!= ( f @ ( X0 @ a0 @ a2 @ a1 ) @ ( X1 @ a0 @ a2 @ a1 ) @ a2 ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( f @ ( X0 @ a0 @ a1 @ a2 ) @ ( X1 @ a0 @ a1 @ a2 ) @ a2 ) )
| ( a1
!= ( X1 @ a2 @ a1 @ a0 ) )
| ( a0
!= ( X0 @ a2 @ a1 @ a0 ) ) ),
inference(beta-eta_normalization,[],[f6]) ).
thf(f12,plain,
( ( ( f @ a0 @ a1 @ a2 )
!= ( f
@ ( ^ [Y0: $i,Y1: $i,Y2: $i] : a0
@ a0
@ a1
@ a2 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i] : a1
@ a0
@ a1
@ a2 )
@ a2 ) )
| ( a0
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] : a0
@ a2
@ a1
@ a0 ) )
| ( a1
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] : a1
@ a2
@ a1
@ a0 ) ) ),
inference(equality_resolution,[],[f8]) ).
thf(f14,plain,
( ( a1 != a1 )
| ( a0 != a0 )
| ( ( f @ a0 @ a1 @ a2 )
!= ( f @ a0 @ a1 @ a2 ) ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f15,plain,
$false,
inference(trivial_inequality_removal,[],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO885^1.033.003 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n001.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 17:30:51 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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
% 0.19/0.29 % (1554185)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.29 % (1554195)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3629378648:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.29 % (1554195)Refutation not found, incomplete strategy
% 0.19/0.29 % (1554195)------------------------------
% 0.19/0.29 % (1554195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1554195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1554195)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1554195)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.29 % (1554195)Time elapsed: 0.001 s
% 0.19/0.29 % (1554195)Peak memory usage: 12 MB
% 0.19/0.29 % (1554195)Instructions burned: 1 (million)
% 0.19/0.29 % (1554195)------------------------------
% 0.19/0.29 % (1554195)------------------------------
% 0.19/0.29 % (1554201)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.29 % (1554201)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
% 0.19/0.29 % (1554199)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3406374586:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.29 % (1554196)lrs+10_16_si=on:nwc=1.5:random_seed=3449842544:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.29 % (1554197)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4154015668:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.29 % (1554201)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=3424482958:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.29 % (1554198)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=1255844472: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)
% 0.19/0.29 % (1554200)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=288924658:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.29 % (1554199)Refutation not found, incomplete strategy
% 0.19/0.29 % (1554199)------------------------------
% 0.19/0.29 % (1554199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1554199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1554199)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1554199)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.29 % (1554199)Time elapsed: 0.001 s
% 0.19/0.29 % (1554199)Peak memory usage: 11 MB
% 0.19/0.29 % (1554199)Instructions burned: 1 (million)
% 0.19/0.29 % (1554197)Refutation not found, incomplete strategy
% 0.19/0.29 % (1554197)------------------------------
% 0.19/0.29 % (1554197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1554197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1554197)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1554197)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.29 % (1554197)Time elapsed: 0.001 s
% 0.19/0.29 % (1554197)Peak memory usage: 12 MB
% 0.19/0.29 % (1554197)Instructions burned: 1 (million)
% 0.19/0.29 % (1554201)Refutation not found, incomplete strategy
% 0.19/0.29 % (1554201)------------------------------
% 0.19/0.29 % (1554201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1554201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1554198)Refutation not found, incomplete strategy
% 0.19/0.29 % (1554198)------------------------------
% 0.19/0.29 % (1554198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1554201)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1554201)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.29 % (1554201)Time elapsed: 0.002 s
% 0.19/0.29 % (1554198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1554201)Peak memory usage: 12 MB
% 0.19/0.29 % (1554201)Instructions burned: 1 (million)
% 0.19/0.29 % (1554198)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1554198)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.29 % (1554198)Time elapsed: 0.001 s
% 0.19/0.29 % (1554198)Peak memory usage: 12 MB
% 0.19/0.29 % (1554198)Instructions burned: 1 (million)
% 0.19/0.29 % (1554196) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1554185-1554196"...
% 0.19/0.29 % (1554199)------------------------------
% 0.19/0.29 % (1554199)------------------------------
% 0.19/0.29 % (1554197)------------------------------
% 0.19/0.29 % (1554197)------------------------------
% 0.19/0.29 % (1554200) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1554185-1554200"...
% 0.19/0.29 % (1554201)------------------------------
% 0.19/0.29 % (1554201)------------------------------
% 0.19/0.29 % (1554198)------------------------------
% 0.19/0.29 % (1554198)------------------------------
% 0.19/0.29 % (1554196)...printing done.
% 0.19/0.29 % (1554207)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1090395524:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.29 % (1554200)...printing done.
% 0.19/0.29 % (1554196)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (1554196)------------------------------
% 0.19/0.29 % (1554196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1554196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1554196)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1554196)Termination reason: Refutation
% 0.19/0.29 % (1554196)Time elapsed: 0.003 s
% 0.19/0.29 % (1554196)Peak memory usage: 12 MB
% 0.19/0.29 % (1554196)Instructions burned: 3 (million)
% 0.19/0.29 % (1554185)Success in time 0.042 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------