%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV059^5 : 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 : n018.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 08:37:34 AM UTC 2026
% Result : Theorem 0.12s 0.27s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 198 ( 61 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 345 ( 42 ~; 31 |; 27 &; 233 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 66 ( 0 sgn 50 !; 3 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cG: b > b ).
thf(func_def_1,type,
cA: b > a ).
thf(func_def_2,type,
c_less_: a > a > $o ).
thf(func_def_3,type,
cF: b > b ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
sK0: b ).
thf(f1,conjecture,
( ( ! [X3: b] : ( c_less_ @ ( cA @ X3 ) @ ( cA @ ( cF @ X3 ) ) )
& ( cG
= ( ^ [X4: b] : ( cF @ ( cF @ X4 ) ) ) )
& ! [X0: a,X1: a,X2: a] :
( ( ( c_less_ @ X1 @ X2 )
& ( c_less_ @ X0 @ X1 ) )
=> ( c_less_ @ X0 @ X2 ) ) )
=> ! [X5: b] : ( c_less_ @ ( cA @ X5 ) @ ( cA @ ( cG @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM89A_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: b] : ( c_less_ @ ( cA @ X3 ) @ ( cA @ ( cF @ X3 ) ) )
& ( cG
= ( ^ [X4: b] : ( cF @ ( cF @ X4 ) ) ) )
& ! [X0: a,X1: a,X2: a] :
( ( ( c_less_ @ X1 @ X2 )
& ( c_less_ @ X0 @ X1 ) )
=> ( c_less_ @ X0 @ X2 ) ) )
=> ! [X5: b] : ( c_less_ @ ( cA @ X5 ) @ ( cA @ ( cG @ X5 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: b] : ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
& ( cG
= ( ^ [X1: b] : ( cF @ ( cF @ X1 ) ) ) )
& ! [X2: a,X3: a,X4: a] :
( ( ( c_less_ @ X3 @ X4 )
& ( c_less_ @ X2 @ X3 ) )
=> ( c_less_ @ X2 @ X4 ) ) )
=> ! [X5: b] : ( c_less_ @ ( cA @ X5 ) @ ( cA @ ( cG @ X5 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: b] :
( $true
= ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) ) )
& ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X2: a,X3: a,X4: a] :
( ( ( ( c_less_ @ X3 @ X4 )
= $true )
& ( $true
= ( c_less_ @ X2 @ X3 ) ) )
=> ( $true
= ( c_less_ @ X2 @ X4 ) ) ) )
=> ! [X5: b] :
( ( c_less_ @ ( cA @ X5 ) @ ( cA @ ( cG @ X5 ) ) )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ( ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X0: b] :
( $true
= ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) ) )
& ! [X2: a,X3: a,X1: a] :
( ( ( $true
= ( c_less_ @ X2 @ X3 ) )
& ( ( c_less_ @ X1 @ X2 )
= $true ) )
=> ( $true
= ( c_less_ @ X1 @ X3 ) ) ) )
=> ! [X4: b] :
( ( c_less_ @ ( cA @ X4 ) @ ( cA @ ( cG @ X4 ) ) )
= $true ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
( ? [X4: b] :
( ( c_less_ @ ( cA @ X4 ) @ ( cA @ ( cG @ X4 ) ) )
!= $true )
& ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X0: b] :
( $true
= ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) ) )
& ! [X2: a,X3: a,X1: a] :
( ( $true
= ( c_less_ @ X1 @ X3 ) )
| ( $true
!= ( c_less_ @ X2 @ X3 ) )
| ( ( c_less_ @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X2: a,X3: a,X1: a] :
( ( $true
= ( c_less_ @ X1 @ X3 ) )
| ( $true
!= ( c_less_ @ X2 @ X3 ) )
| ( ( c_less_ @ X1 @ X2 )
!= $true ) )
& ! [X0: b] :
( $true
= ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) ) )
& ? [X4: b] :
( ( c_less_ @ ( cA @ X4 ) @ ( cA @ ( cG @ X4 ) ) )
!= $true ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X0: a,X1: a,X2: a] :
( ( ( c_less_ @ X2 @ X1 )
= $true )
| ( ( c_less_ @ X0 @ X1 )
!= $true )
| ( $true
!= ( c_less_ @ X2 @ X0 ) ) )
& ! [X3: b] :
( ( c_less_ @ ( cA @ X3 ) @ ( cA @ ( cF @ X3 ) ) )
= $true )
& ? [X4: b] :
( ( c_less_ @ ( cA @ X4 ) @ ( cA @ ( cG @ X4 ) ) )
!= $true ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X0: a,X1: a,X2: a] :
( ( ( c_less_ @ X2 @ X1 )
= $true )
| ( ( c_less_ @ X0 @ X1 )
!= $true )
| ( $true
!= ( c_less_ @ X2 @ X0 ) ) )
& ! [X3: b] :
( ( c_less_ @ ( cA @ X3 ) @ ( cA @ ( cF @ X3 ) ) )
= $true )
& ( $true
!= ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cG @ sK0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X4,sK0)],[f8]) ).
thf(f10,plain,
( $true
!= ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cG @ sK0 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
! [X3: b] :
( ( c_less_ @ ( cA @ X3 ) @ ( cA @ ( cF @ X3 ) ) )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
! [X2: a,X0: a,X1: a] :
( ( ( c_less_ @ X2 @ X1 )
= $true )
| ( ( c_less_ @ X0 @ X1 )
!= $true )
| ( $true
!= ( c_less_ @ X2 @ X0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,definition,
( spl1_1
<=> ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f18,plain,
( ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f19,plain,
spl1_1,
inference(avatar_split_clause,[],[f13,f16]) ).
thf(f21,definition,
( spl1_2
<=> ( $true
= ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cG @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f23,plain,
( ( $true
!= ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cG @ sK0 ) ) ) )
| spl1_2 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f24,plain,
~ spl1_2,
inference(avatar_split_clause,[],[f10,f21]) ).
thf(f25,plain,
( ! [X0: a] :
( ( ( c_less_ @ ( cA @ sK0 ) @ X0 )
!= $true )
| ( $true != $true )
| ( ( c_less_ @ X0 @ ( cA @ ( cG @ sK0 ) ) )
!= $true ) )
| spl1_2 ),
inference(superposition,[],[f23,f12]) ).
thf(f26,plain,
( ! [X0: a] :
( ( ( c_less_ @ X0 @ ( cA @ ( cG @ sK0 ) ) )
!= $true )
| ( ( c_less_ @ ( cA @ sK0 ) @ X0 )
!= $true ) )
| spl1_2 ),
inference(trivial_inequality_removal,[],[f25]) ).
thf(f29,plain,
( ! [X1: b] :
( ( cG @ X1 )
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) )
@ X1 ) )
| ~ spl1_1 ),
inference(argument_congruence,[],[f18]) ).
thf(f30,plain,
( ! [X1: b] :
( ( cG @ X1 )
= ( cF @ ( cF @ X1 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f31,plain,
( ! [X0: a] :
( ( ( c_less_ @ X0 @ ( cA @ ( cF @ ( cF @ sK0 ) ) ) )
!= $true )
| ( ( c_less_ @ ( cA @ sK0 ) @ X0 )
!= $true ) )
| ~ spl1_1
| spl1_2 ),
inference(superposition,[],[f26,f30]) ).
thf(f40,plain,
( ( $true != $true )
| ( ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cF @ sK0 ) ) )
!= $true )
| ~ spl1_1
| spl1_2 ),
inference(superposition,[],[f31,f11]) ).
thf(f43,plain,
( ( ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cF @ sK0 ) ) )
!= $true )
| ~ spl1_1
| spl1_2 ),
inference(trivial_inequality_removal,[],[f40]) ).
thf(f44,plain,
( $false
| ~ spl1_1
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f43,f11]) ).
thf(f45,plain,
( ~ spl1_1
| spl1_2 ),
inference(avatar_contradiction_clause,[],[f44]) ).
cnf(s1,plain,
spl1_1,
inference(sat_conversion,[],[f19]) ).
cnf(s2,plain,
~ spl1_2,
inference(sat_conversion,[],[f24]) ).
cnf(s4,plain,
( ~ spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f45]) ).
cnf(s5,plain,
~ spl1_1,
inference(rat,[],[s4,s2]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5]) ).
thf(f46,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV059^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.17 % Computer : n018.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Sep 29 15:07:56 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.21 Running higher-order theorem proving
% 0.12/0.21 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
% 0.12/0.27 % (198599)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.12/0.27 % (198607)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=2050643679: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)
% 0.12/0.27 % (198607) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-198599-198607"...
% 0.12/0.27 % (198607)...printing done.
% 0.12/0.27 % (198607)Refutation found. Thanks to Tanya!
% 0.12/0.27 % SZS status Theorem for theBenchmark
% 0.12/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.27 % (198607)------------------------------
% 0.12/0.27 % (198607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.27 % (198607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.27 % (198607)CaDiCaL version: 2.1.3
% 0.12/0.27 % (198607)Termination reason: Refutation
% 0.12/0.27 % (198607)Time elapsed: 0.002 s
% 0.12/0.27 % (198607)Peak memory usage: 13 MB
% 0.12/0.27 % (198607)Instructions burned: 5 (million)
% 0.12/0.27 % (198599)Success in time 0.046 s
% 0.12/0.27 % Vampire exiting
%------------------------------------------------------------------------------