%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO303^5 : 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 : 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 08:47:24 AM UTC 2026
% Result : Theorem 0.08s 0.21s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 151 ( 35 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 117 ( 27 ~; 17 |; 16 &; 52 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cS: $i > $o ).
thf(func_def_3,type,
cT: $i > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(func_def_9,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ! [X0: $i > $o] :
( ! [X1: $i] : ( X0 @ X1 )
| ~ ( X0 @ c0 ) )
=> ( ~ ( ( cT @ c0 )
& ( cS @ c0 ) )
| ( ( cT @ a )
& ( cS @ b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cMIN_QUAN_BUG) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i > $o] :
( ! [X1: $i] : ( X0 @ X1 )
| ~ ( X0 @ c0 ) )
=> ( ~ ( ( cT @ c0 )
& ( cS @ c0 ) )
| ( ( cT @ a )
& ( cS @ b ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i > $o] :
( ! [X1: $i] : ( X0 @ X1 )
| ~ ( X0 @ c0 ) )
=> ( ~ ( ( cT @ c0 )
& ( cS @ c0 ) )
| ( ( cT @ a )
& ( cS @ b ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
= $true )
| ( ( X0 @ c0 )
!= $true ) )
=> ( ( ( ( cT @ a )
= $true )
& ( ( cS @ b )
= $true ) )
| ~ ( ( ( cT @ c0 )
= $true )
& ( ( cS @ c0 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ! [X0: $i > $o] :
( ( ( X0 @ c0 )
!= $true )
| ! [X1: $i] :
( ( X0 @ X1 )
= $true ) )
=> ( ( ( ( cT @ a )
= $true )
& ( ( cS @ b )
= $true ) )
| ~ ( ( ( cT @ c0 )
= $true )
& ( ( cS @ c0 )
= $true ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ( ( cT @ a )
!= $true )
| ( ( cS @ b )
!= $true ) )
& ( ( cT @ c0 )
= $true )
& ( ( cS @ c0 )
= $true )
& ! [X0: $i > $o] :
( ( ( X0 @ c0 )
!= $true )
| ! [X1: $i] :
( ( X0 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ( cS @ c0 )
= $true )
& ( ( cT @ c0 )
= $true )
& ! [X0: $i > $o] :
( ( ( X0 @ c0 )
!= $true )
| ! [X1: $i] :
( ( X0 @ X1 )
= $true ) )
& ( ( ( cT @ a )
!= $true )
| ( ( cS @ b )
!= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( ( cS @ b )
!= $true )
| ( ( cT @ a )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ c0 )
!= $true )
| ( ( X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( cT @ c0 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( cS @ c0 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X0: $i] : ( c0 = X0 ),
inference(leibniz_equality_elimination,[],[f9]) ).
thf(f33,plain,
( ( ( cS @ c0 )
!= $true )
| ( ( cT @ a )
!= $true ) ),
inference(superposition,[],[f8,f13]) ).
thf(f34,plain,
( ( cT @ a )
!= $true ),
inference(forward_subsumption_resolution,[],[f33,f11]) ).
thf(f35,plain,
( ( cT @ c0 )
!= $true ),
inference(forward_demodulation,[],[f34,f13]) ).
thf(f36,plain,
$false,
inference(forward_subsumption_resolution,[],[f35,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO303^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.14 % Computer : n012.cluster.edu
% 0.08/0.14 % Model : x86_64 x86_64
% 0.08/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.14 % Memory : 8046.5625MB
% 0.08/0.14 % OS : Linux 6.8.0-71-generic
% 0.08/0.14 % CPULimit : 300
% 0.08/0.14 % WCLimit : 300
% 0.08/0.15 % DateTime : Tue Sep 29 16:44:04 UTC 2026
% 0.08/0.15 % CPUTime :
% 0.08/0.15 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 Running higher-order theorem proving
% 0.08/0.18 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
% 0.08/0.21 % (358117)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.21 % (358128)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.21 % (358128)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
% 0.08/0.21 % (358122)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3054049860:s2a=on:i=87:rtra=on:ntd=on_3000 on theBenchmark for (3000ds/87Mi)
% 0.08/0.21 % (358123)lrs+10_16_si=on:nwc=1.5:random_seed=1151155992:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_3000 on theBenchmark for (3000ds/18Mi)
% 0.08/0.21 % (358124)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1071962267:i=3:rtra=on:inj=on:ntd=on_3000 on theBenchmark for (3000ds/3Mi)
% 0.08/0.21 % (358125)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=3259051910: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_3000 on theBenchmark for (3000ds/634Mi)
% 0.08/0.21 % (358126)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2546781538:i=24:av=off:rtra=on_3000 on theBenchmark for (3000ds/24Mi)
% 0.08/0.21 % (358128)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=2070695829:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_3000 on theBenchmark for (3000ds/157Mi)
% 0.08/0.21 % (358127)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=492823691:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_3000 on theBenchmark for (3000ds/75Mi)
% 0.08/0.21 % (358126) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-358117-358126"...
% 0.08/0.21 % (358122) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-358117-358122"...
% 0.08/0.21 % (358124) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-358117-358124"...
% 0.08/0.21 % (358127) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-358117-358127"...
% 0.08/0.21 % (358123) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-358117-358123"...
% 0.08/0.21 % (358125) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-358117-358125"...
% 0.08/0.21 % (358126)...printing done.
% 0.08/0.21 % (358122)...printing done.
% 0.08/0.21 % (358124)...printing done.
% 0.08/0.21 % (358127)...printing done.
% 0.08/0.21 % (358123)...printing done.
% 0.08/0.21 % (358125)...printing done.
% 0.08/0.21 % (358128) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-358117-358128"...
% 0.08/0.21 % (358126)Refutation found. Thanks to Tanya!
% 0.08/0.21 % SZS status Theorem for theBenchmark
% 0.08/0.21 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.21 % (358126)------------------------------
% 0.08/0.21 % (358126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.21 % (358126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.21 % (358126)CaDiCaL version: 2.1.3
% 0.08/0.21 % (358126)Termination reason: Refutation
% 0.08/0.21 % (358126)Time elapsed: 0.002 s
% 0.08/0.21 % (358126)Peak memory usage: 12 MB
% 0.08/0.21 % (358126)Instructions burned: 2 (million)
% 0.08/0.21 % (358117)Success in time 0.023 s
% 0.08/0.21 % Vampire exiting
%------------------------------------------------------------------------------