%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO059^4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 08:48:50 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 265 ( 57 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 298 ( 24 ~; 10 |; 0 &; 218 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 34 usr; 4 con; 0-4 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 87 ( 70 ^; 17 !; 0 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
a: $i > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_28,type,
vOR: $o > $o > $o ).
thf(func_def_29,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
vAND: $o > $o > $o ).
thf(func_def_31,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
vIMP: $o > $o > $o ).
thf(func_def_33,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_35,type,
sK1: $i > $i ).
thf(f1,axiom,
! [X0: $i] : ( irel @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f7,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f9,axiom,
( inot
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',inot) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( iatom @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(f23,conjecture,
ivalid @ ( inot @ ( inot @ ( iatom @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f24,negated_conjecture,
~ ( ivalid @ ( inot @ ( inot @ ( iatom @ a ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f25,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f26,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f25]) ).
thf(f29,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f30,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f29]) ).
thf(f36,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f37,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f39,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f47,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f48,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f55,plain,
ivalid @ ( iatom @ a ),
inference(rectify,[],[f22]) ).
thf(f56,plain,
( ( ivalid @ ( iatom @ a ) )
= $true ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
~ ( ivalid @ ( inot @ ( inot @ ( iatom @ a ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f58,plain,
( ( ivalid @ ( inot @ ( inot @ ( iatom @ a ) ) ) )
!= $true ),
inference(fool_elimination,[],[f57]) ).
thf(f59,plain,
( ( ivalid @ ( inot @ ( inot @ ( iatom @ a ) ) ) )
!= $true ),
inference(flattening,[],[f58]) ).
thf(f62,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f26]) ).
thf(f64,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f68,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f69,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f70,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f79,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f83,plain,
( ( ivalid @ ( iatom @ a ) )
= $true ),
inference(cnf_transformation,[],[f56]) ).
thf(f84,plain,
( ( ivalid @ ( inot @ ( inot @ ( iatom @ a ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f59]) ).
thf(f88,plain,
( inot
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f70,f64,f68]) ).
thf(f96,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a ) ) ),
inference(definition_unfolding,[],[f83,f79,f69]) ).
thf(f97,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a ) ) ) ) ),
inference(definition_unfolding,[],[f84,f79,f88,f88,f69]) ).
thf(f98,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
( $false
= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f98]) ).
thf(f100,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f99]) ).
thf(f101,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f100]) ).
thf(f102,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X1: $i] :
( $true
= ( ( irel @ sK0 @ X1 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a @ Y0 ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( a @ ( sK1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f108,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( a @ ( sK1 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f109,plain,
! [X1: $i] :
( ( $true
= ( irel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f110,plain,
( $true
= ( !! @ $i @ a ) ),
inference(beta-eta_normalization,[],[f96]) ).
thf(f111,plain,
! [X1: $i] :
( $true
= ( a @ X1 ) ),
inference(pi_proxy_clausification,[],[f110]) ).
thf(f113,plain,
( ( $true = $false )
| ( $false
= ( a @ ( sK1 @ ( sK1 @ sK0 ) ) ) )
| ( $false
= ( irel @ sK0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f108,f109]) ).
thf(f114,plain,
( ( $false
= ( a @ ( sK1 @ ( sK1 @ sK0 ) ) ) )
| ( $false
= ( irel @ sK0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f113]) ).
thf(f116,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK0 ) ) ),
inference(forward_demodulation,[],[f114,f111]) ).
thf(f117,plain,
( $false
= ( irel @ sK0 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f116]) ).
thf(f120,plain,
$true = $false,
inference(forward_demodulation,[],[f117,f62]) ).
thf(f121,plain,
$false,
inference(trivial_inequality_removal,[],[f120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO059^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n019.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:26:18 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.26 % (1001746)Will run a generic schedule for satisfiability detection.
% 0.19/0.26 % (1001751)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1976216928_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.26 % Exception at run slice level
% 0.19/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.26 % (1001752)% WARNING: option uhcvi not known.
% 0.19/0.26 % (1001755)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3759321437:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.26 % (1001752)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2011345073:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.26 % (1001753)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=219718265:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.26 % (1001754)dis+10_1_sil=32000:sp=arity:random_seed=3534048302:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.26 % (1001755)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.26 % (1001752)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.26 % (1001752)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.26 % (1001755) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1001746-1001755"...
% 0.19/0.26 % (1001752) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1001746-1001752"...
% 0.19/0.26 % (1001754) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1001746-1001754"...
% 0.19/0.26 % (1001753) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1001746-1001753"...
% 0.19/0.26 % (1001759)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1966375821:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.26 % (1001755)...printing done.
% 0.19/0.26 % (1001752)...printing done.
% 0.19/0.26 % Exception at run slice level
% 0.19/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.26 % (1001755)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (1001755)------------------------------
% 0.19/0.27 % (1001755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (1001755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (1001755)CaDiCaL version: 2.1.3
% 0.19/0.27 % (1001755)Termination reason: Refutation
% 0.19/0.27 % (1001755)Time elapsed: 0.005 s
% 0.19/0.27 % (1001755)Peak memory usage: 12 MB
% 0.19/0.27 % (1001755)Instructions burned: 7 (million)
% 0.19/0.27 % (1001746)Success in time 0.044 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------