%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO223^5 : 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 : n007.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 08:47:14 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 1
% Syntax : Number of formulae : 36 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 454 ( 125 equ; 0 cnn)
% Maximal formula atoms : 10 ( 12 avg)
% Number of connectives : 317 ( 42 ~; 58 |; 30 &; 176 @)
% ( 1 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 67 ( 4 ^; 51 !; 12 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cLIKE: $i > $i > $o ).
thf(func_def_2,type,
cUNIQUE: $i > $o ).
thf(func_def_9,type,
vNOT: $o > $o ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,conjecture,
( ( ! [X0: $i] :
( ( cUNIQUE @ X0 )
=> ! [X1: $i] : ( X0 = X1 ) )
& ( cUNIQUE @ cS ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) )
& ( ( X2 @ cJ )
= ( ? [X0: $i] :
( ( cUNIQUE @ X0 )
& ( cLIKE @ cJ @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cLING2) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( cUNIQUE @ X0 )
=> ! [X1: $i] : ( X0 = X1 ) )
& ( cUNIQUE @ cS ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) )
& ( ( X2 @ cJ )
= ( ? [X0: $i] :
( ( cUNIQUE @ X0 )
& ( cLIKE @ cJ @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i] :
( ( cUNIQUE @ X0 )
=> ! [X1: $i] : ( X0 = X1 ) )
& ( cUNIQUE @ cS ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) )
& ( ( X2 @ cJ )
= ( ? [X3: $i] :
( ( cUNIQUE @ X3 )
& ( cLIKE @ cJ @ X3 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ( cUNIQUE @ cS )
= $true )
& ! [X0: $i] :
( ( ( cUNIQUE @ X0 )
= $true )
=> ! [X1: $i] : ( X0 = X1 ) ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) )
& ( ( ( X2 @ cJ )
= $true )
<=> ? [X3: $i] :
( ( $true
= ( cLIKE @ cJ @ X3 ) )
& ( $true
= ( cUNIQUE @ X3 ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X2: $i > $o] :
( ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( ( X2 @ cJ )
= $true )
<~> ? [X3: $i] :
( ( $true
= ( cLIKE @ cJ @ X3 ) )
& ( $true
= ( cUNIQUE @ X3 ) ) ) ) )
& ( ( cUNIQUE @ cS )
= $true )
& ! [X0: $i] :
( ( ( cUNIQUE @ X0 )
!= $true )
| ! [X1: $i] : ( X0 = X1 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( cUNIQUE @ cS )
= $true )
& ! [X0: $i] :
( ( ( cUNIQUE @ X0 )
!= $true )
| ! [X1: $i] : ( X0 = X1 ) )
& ! [X2: $i > $o] :
( ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( ( X2 @ cJ )
= $true )
<~> ? [X3: $i] :
( ( $true
= ( cLIKE @ cJ @ X3 ) )
& ( $true
= ( cUNIQUE @ X3 ) ) ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( ( cUNIQUE @ cS )
= $true )
& ! [X0: $i] :
( ( ( cUNIQUE @ X0 )
!= $true )
| ! [X1: $i] : ( X0 = X1 ) )
& ! [X2: $i > $o] :
( ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( ! [X3: $i] :
( ( $true
!= ( cLIKE @ cJ @ X3 ) )
| ( $true
!= ( cUNIQUE @ X3 ) ) )
| ( ( X2 @ cJ )
!= $true ) )
& ( ? [X3: $i] :
( ( $true
= ( cLIKE @ cJ @ X3 ) )
& ( $true
= ( cUNIQUE @ X3 ) ) )
| ( ( X2 @ cJ )
= $true ) ) ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f8,plain,
( ( ( cUNIQUE @ cS )
= $true )
& ! [X0: $i] :
( ( ( cUNIQUE @ X0 )
!= $true )
| ! [X1: $i] : ( X0 = X1 ) )
& ! [X2: $i > $o] :
( ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( ! [X3: $i] :
( ( $true
!= ( cLIKE @ cJ @ X3 ) )
| ( $true
!= ( cUNIQUE @ X3 ) ) )
| ( ( X2 @ cJ )
!= $true ) )
& ( ? [X4: $i] :
( ( $true
= ( cLIKE @ cJ @ X4 ) )
& ( $true
= ( cUNIQUE @ X4 ) ) )
| ( ( X2 @ cJ )
= $true ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ( cUNIQUE @ cS )
= $true )
& ! [X0: $i] :
( ( ( cUNIQUE @ X0 )
!= $true )
| ! [X1: $i] : ( X0 = X1 ) )
& ! [X2: $i > $o] :
( ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( ! [X3: $i] :
( ( $true
!= ( cLIKE @ cJ @ X3 ) )
| ( $true
!= ( cUNIQUE @ X3 ) ) )
| ( ( X2 @ cJ )
!= $true ) )
& ( ( ( $true
= ( cLIKE @ cJ @ sK0 ) )
& ( $true
= ( cUNIQUE @ sK0 ) ) )
| ( ( X2 @ cJ )
= $true ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X4,sK0)],[f8]) ).
thf(f11,plain,
! [X2: $i > $o] :
( ( ( X2 @ cJ )
= $true )
| ( $true
= ( cLIKE @ cJ @ sK0 ) )
| ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
! [X2: $i > $o,X3: $i] :
( ( ( X2 @ cJ )
!= $true )
| ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( $true
!= ( cUNIQUE @ X3 ) )
| ( $true
!= ( cLIKE @ cJ @ X3 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ( ( cUNIQUE @ X0 )
!= $true )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
( ( cUNIQUE @ cS )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
! [X2: $i > $o,X3: $i] :
( ( ( X2 @ cJ )
!= $true )
| ( ( X2 @ cP )
= $false )
| ( $true
!= ( cLIKE @ cJ @ X3 ) )
| ( ( cLIKE @ cP @ cS )
= $false )
| ( $true
!= ( cUNIQUE @ X3 ) ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f20,plain,
! [X2: $i > $o] :
( ( ( cLIKE @ cP @ cS )
= $true )
| ( ( X2 @ cJ )
= $true )
| ( ( X2 @ cP )
= $true )
| ( $true
= ( cLIKE @ cJ @ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f22,plain,
! [X0: $i] :
( ( cS = X0 )
| ( $true != $true ) ),
inference(superposition,[],[f13,f14]) ).
thf(f23,plain,
! [X0: $i] : ( cS = X0 ),
inference(trivial_inequality_removal,[],[f22]) ).
thf(f24,plain,
! [X0: $i,X1: $i] : ( X0 = X1 ),
inference(superposition,[],[f23,f23]) ).
thf(f25,plain,
! [X0: $i] :
( ( cUNIQUE @ X0 )
= $true ),
inference(superposition,[],[f14,f23]) ).
thf(f32,plain,
! [X2: $i > $o] :
( ( ( cLIKE @ cJ @ cS )
= $true )
| ( ( X2 @ cJ )
= $true )
| ( ( cLIKE @ cP @ cS )
= $true )
| ( ( X2 @ cP )
= $true ) ),
inference(forward_demodulation,[],[f20,f23]) ).
thf(f35,plain,
( ( ( cLIKE @ cP @ cS )
= $true )
| ( ( cLIKE @ cJ @ cS )
= $true )
| ( $true
= ( ^ [Y0: $i] : $false
@ cP ) )
| ( $true
= ( ^ [Y0: $i] : $false
@ cJ ) ) ),
inference(primitive_instantiation,[],[f32]) ).
thf(f49,plain,
( ( ( cLIKE @ cJ @ cS )
= $true )
| ( $true = $false )
| ( ( cLIKE @ cP @ cS )
= $true )
| ( $true = $false ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f50,plain,
( ( $true = $false )
| ( ( cLIKE @ cP @ cS )
= $true )
| ( ( cLIKE @ cJ @ cS )
= $true ) ),
inference(duplicate_literal_removal,[],[f49]) ).
thf(f51,plain,
( ( ( cLIKE @ cJ @ cS )
= $true )
| ( ( cLIKE @ cP @ cS )
= $true ) ),
inference(trivial_inequality_removal,[],[f50]) ).
thf(f55,plain,
! [X0: $i] :
( ( ( cLIKE @ X0 @ cS )
= $true )
| ( ( cLIKE @ cP @ cS )
= $true ) ),
inference(superposition,[],[f51,f24]) ).
thf(f85,plain,
( ( ( cLIKE @ cP @ cS )
= $true )
| ( $true != $true ) ),
inference(equality_factoring,[],[f55]) ).
thf(f86,plain,
( ( cLIKE @ cP @ cS )
= $true ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f88,plain,
! [X0: $i] :
( $true
= ( cLIKE @ cP @ X0 ) ),
inference(superposition,[],[f86,f23]) ).
thf(f93,plain,
! [X0: $i,X1: $i] :
( $true
= ( cLIKE @ X0 @ X1 ) ),
inference(superposition,[],[f88,f24]) ).
thf(f98,plain,
! [X2: $i > $o,X3: $i] :
( ( $true
!= ( cLIKE @ cJ @ X3 ) )
| ( ( X2 @ cJ )
!= $true )
| ( ( cLIKE @ cP @ cS )
= $false )
| ( ( X2 @ cP )
= $false ) ),
inference(forward_subsumption_resolution,[],[f19,f25]) ).
thf(f99,plain,
! [X2: $i > $o,X3: $i] :
( ( $true = $false )
| ( $true
!= ( cLIKE @ cJ @ X3 ) )
| ( ( X2 @ cP )
= $false )
| ( ( X2 @ cJ )
!= $true ) ),
inference(forward_demodulation,[],[f98,f86]) ).
thf(f100,plain,
! [X2: $i > $o,X3: $i] :
( ( $true
!= ( cLIKE @ cJ @ X3 ) )
| ( ( X2 @ cP )
= $false )
| ( ( X2 @ cJ )
!= $true ) ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f101,plain,
! [X2: $i > $o] :
( ( ( X2 @ cJ )
!= $true )
| ( ( X2 @ cP )
= $false ) ),
inference(forward_subsumption_resolution,[],[f100,f93]) ).
thf(f105,plain,
( ( $true
!= ( ^ [Y0: $i] : $true
@ cJ ) )
| ( ( ^ [Y0: $i] : $true
@ cP )
= $false ) ),
inference(imitation,[],[f101]) ).
thf(f122,plain,
( ( $true != $true )
| ( $true = $false ) ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f123,plain,
$false,
inference(trivial_inequality_removal,[],[f122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO223^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n007.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:38:11 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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 % (3615038)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (3615045)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=78509399:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (3615047)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4214882755:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (3615043)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2878488693:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (3615049)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 % (3615049)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 % (3615045)Instruction limit reached!
% 0.21/0.29 % (3615045)------------------------------
% 0.21/0.29 % (3615045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3615045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3615045)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3615045)Termination reason: Instruction limit
% 0.21/0.30 % (3615045)Termination phase: Saturation
% 0.21/0.30 % (3615045)Time elapsed: 0.003 s
% 0.21/0.30 % (3615045)Peak memory usage: 12 MB
% 0.21/0.30 % (3615045)Instructions burned: 4 (million)
% 0.21/0.30 % (3615048)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3693032240:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (3615047) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3615038-3615047"...
% 0.21/0.30 % (3615043) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3615038-3615043"...
% 0.21/0.30 % (3615049)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=3054579779:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (3615046)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=2761775292: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 % (3615047)...printing done.
% 0.21/0.30 % (3615043)...printing done.
% 0.21/0.30 % (3615047)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 % (3615047)------------------------------
% 0.21/0.30 % (3615047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3615047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3615047)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3615047)Termination reason: Refutation
% 0.21/0.30 % (3615047)Time elapsed: 0.006 s
% 0.21/0.30 % (3615047)Peak memory usage: 12 MB
% 0.21/0.30 % (3615047)Instructions burned: 10 (million)
% 0.21/0.30 % (3615038)Success in time 0.042 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------