%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO300^5 : 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 : n006.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 08:47:23 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 13 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 64 ( 11 ~; 3 |; 2 &; 44 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 75 ( 75 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 41 ( 18 ^; 18 !; 5 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
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_5,type,
sK0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o ).
thf(f1,conjecture,
! [X0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
? [X1: ( $i > $i ) > $i] :
( ! [X2: ( $i > $i ) > $i] : ( X0 @ X2 @ X2 )
=> ( X0
@ ^ [X3: $i > $i] :
( X3
@ ( X1
@ ^ [X4: $i] : X4 ) )
@ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cUNIFTHM1) ).
thf(f2,negated_conjecture,
~ ! [X0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
? [X1: ( $i > $i ) > $i] :
( ! [X2: ( $i > $i ) > $i] : ( X0 @ X2 @ X2 )
=> ( X0
@ ^ [X3: $i > $i] :
( X3
@ ( X1
@ ^ [X4: $i] : X4 ) )
@ X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
? [X1: ( $i > $i ) > $i] :
( ! [X2: ( $i > $i ) > $i] : ( X0 @ X2 @ X2 )
=> ( X0
@ ^ [X3: $i > $i] :
( X3
@ ( X1
@ ^ [X4: $i] : X4 ) )
@ X1 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
? [X1: ( $i > $i ) > $i] :
( ! [X2: ( $i > $i ) > $i] :
( ( X0 @ X2 @ X2 )
= $true )
=> ( $true
= ( X0
@ ^ [Y0: $i > $i] :
( Y0
@ ( X1
@ ^ [Y1: $i] : Y1 ) )
@ X1 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
! [X1: ( $i > $i ) > $i] :
( ( $true
!= ( X0
@ ^ [Y0: $i > $i] :
( Y0
@ ( X1
@ ^ [Y1: $i] : Y1 ) )
@ X1 ) )
& ! [X2: ( $i > $i ) > $i] :
( ( X0 @ X2 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
! [X1: ( $i > $i ) > $i] :
( ( $true
!= ( sK0
@ ^ [Y0: $i > $i] :
( Y0
@ ( X1
@ ^ [Y1: $i] : Y1 ) )
@ X1 ) )
& ! [X2: ( $i > $i ) > $i] :
( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f5]) ).
thf(f7,plain,
! [X2: ( $i > $i ) > $i] :
( $true
= ( sK0 @ X2 @ X2 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
! [X1: ( $i > $i ) > $i] :
( $true
!= ( sK0
@ ^ [Y0: $i > $i] :
( Y0
@ ( X1
@ ^ [Y1: $i] : Y1 ) )
@ X1 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
! [X0: ( $i > $i ) > $i,X1: ( $i > $i ) > $i] :
( ( X0 != X1 )
| ( $true != $true )
| ( ( ^ [Y0: $i > $i] :
( X0
@ ^ [Y1: $i] : Y1 ) )
!= X1 ) ),
inference(constrained_superposition,[],[f8,f7]) ).
thf(f12,plain,
! [X0: ( $i > $i ) > $i,X1: ( $i > $i ) > $i] :
( ( X0 != X1 )
| ( ( ^ [Y0: $i > $i] :
( X0
@ ^ [Y1: $i] : Y1 ) )
!= X1 ) ),
inference(trivial_inequality_removal,[],[f11]) ).
thf(f13,plain,
$false,
inference(flex-flex_simplification,[],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO300^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n006.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 16:44:10 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
% 0.08/0.24 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
% 0.21/0.30 % (995449)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (995457)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=7846069:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (995457)Refutation not found, incomplete strategy
% 0.21/0.30 % (995457)------------------------------
% 0.21/0.30 % (995457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (995457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (995457)CaDiCaL version: 2.1.3
% 0.21/0.30 % (995457)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (995457)Time elapsed: 0.001 s
% 0.21/0.30 % (995457)Peak memory usage: 12 MB
% 0.21/0.30 % (995457)------------------------------
% 0.21/0.30 % (995457)------------------------------
% 0.21/0.30 % (995463)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 % (995463)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 % (995458)lrs+10_16_si=on:nwc=1.5:random_seed=3360932695:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (995462)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3512488766:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (995459)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2632691399:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (995463)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=803634801:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (995460)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=743056898: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 % (995461)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3873096489:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (995458)Refutation not found, incomplete strategy
% 0.21/0.30 % (995458)------------------------------
% 0.21/0.30 % (995458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (995458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (995458)CaDiCaL version: 2.1.3
% 0.21/0.30 % (995458)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (995458)Time elapsed: 0.001 s
% 0.21/0.30 % (995458)Peak memory usage: 12 MB
% 0.21/0.30 % (995459)Refutation not found, incomplete strategy
% 0.21/0.30 % (995459)------------------------------
% 0.21/0.30 % (995459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (995459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (995459)CaDiCaL version: 2.1.3
% 0.21/0.30 % (995459)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (995459)Time elapsed: 0.001 s
% 0.21/0.30 % (995459)Peak memory usage: 12 MB
% 0.21/0.30 % (995461)Refutation not found, incomplete strategy
% 0.21/0.30 % (995461)------------------------------
% 0.21/0.30 % (995461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (995461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (995461)CaDiCaL version: 2.1.3
% 0.21/0.30 % (995461)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (995461)Time elapsed: 0.001 s
% 0.21/0.30 % (995461)Peak memory usage: 12 MB
% 0.21/0.30 % (995462)Refutation not found, incomplete strategy
% 0.21/0.30 % (995462)------------------------------
% 0.21/0.30 % (995462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (995462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (995462)CaDiCaL version: 2.1.3
% 0.21/0.30 % (995462)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (995462)Time elapsed: 0.001 s
% 0.21/0.30 % (995462)Peak memory usage: 12 MB
% 0.21/0.30 % (995462)Instructions burned: 1 (million)
% 0.21/0.30 % (995460)Refutation not found, incomplete strategy
% 0.21/0.30 % (995460)------------------------------
% 0.21/0.30 % (995460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (995460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (995460)CaDiCaL version: 2.1.3
% 0.21/0.30 % (995460)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (995460)Time elapsed: 0.001 s
% 0.21/0.30 % (995460)Peak memory usage: 12 MB
% 0.21/0.30 % (995458)------------------------------
% 0.21/0.30 % (995458)------------------------------
% 0.21/0.30 % (995460)Instructions burned: 1 (million)
% 0.21/0.30 % (995459)------------------------------
% 0.21/0.30 % (995459)------------------------------
% 0.21/0.30 % (995463)Refutation not found, incomplete strategy
% 0.21/0.30 % (995463)------------------------------
% 0.21/0.30 % (995463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (995463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (995463)CaDiCaL version: 2.1.3
% 0.21/0.30 % (995463)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (995463)Time elapsed: 0.002 s
% 0.21/0.30 % (995463)Peak memory usage: 12 MB
% 0.21/0.30 % (995463)Instructions burned: 2 (million)
% 0.21/0.30 % (995461)------------------------------
% 0.21/0.30 % (995461)------------------------------
% 0.21/0.30 % (995462)------------------------------
% 0.21/0.30 % (995462)------------------------------
% 0.21/0.30 % (995460)------------------------------
% 0.21/0.30 % (995460)------------------------------
% 0.21/0.30 % (995463)------------------------------
% 0.21/0.30 % (995463)------------------------------
% 0.21/0.30 % (995465)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3668478513:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.30 % (995465) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-995449-995465"...
% 0.21/0.30 % (995465)...printing done.
% 0.21/0.30 % (995465)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 % (995465)------------------------------
% 0.21/0.30 % (995465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (995465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (995465)CaDiCaL version: 2.1.3
% 0.21/0.30 % (995465)Termination reason: Refutation
% 0.21/0.30 % (995465)Time elapsed: 0.001 s
% 0.21/0.30 % (995465)Peak memory usage: 12 MB
% 0.21/0.30 % (995465)Instructions burned: 1 (million)
% 0.21/0.30 % (995449)Success in time 0.048 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------