%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV067^5 : 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 : 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 08:37:35 AM UTC 2026
% Result : Theorem 0.26s 0.31s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 17 unt; 0 typ; 6 def)
% Number of atoms : 539 ( 148 equ; 0 cnn)
% Maximal formula atoms : 19 ( 9 avg)
% Number of connectives : 573 ( 94 ~; 97 |; 72 &; 276 @)
% ( 6 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 128 ( 0 sgn 122 !; 6 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cS: a > $o ).
thf(func_def_1,type,
cT: a > $o ).
thf(func_def_2,type,
cR: a > a > $o ).
thf(func_def_6,type,
sK0: a ).
thf(func_def_7,type,
sK1: a ).
thf(f1,conjecture,
( ( ! [X1: a,X0: a] :
( ( ( cR @ X1 @ X0 )
& ( cR @ X0 @ X1 ) )
=> ( X0 = X1 ) )
& ! [X1: a,X0: a] :
( ( cR @ X1 @ X0 )
| ( cR @ X0 @ X1 ) )
& ! [X1: a,X2: a,X0: a] :
( ( ( cR @ X1 @ X2 )
& ( cR @ X0 @ X1 ) )
=> ( cR @ X0 @ X2 ) )
& ! [X3: a,X4: a] :
( ( ( cT @ X4 )
& ( cR @ X3 @ X4 ) )
=> ( cT @ X3 ) )
& ! [X3: a,X4: a] :
( ( ( cS @ X4 )
& ( cR @ X3 @ X4 ) )
=> ( cS @ X3 ) )
& ! [X0: a] : ( cR @ X0 @ X0 ) )
=> ( ! [X0: a] :
( ( cS @ X0 )
=> ( cT @ X0 ) )
| ! [X0: a] :
( ( cT @ X0 )
=> ( cS @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM553_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: a,X0: a] :
( ( ( cR @ X1 @ X0 )
& ( cR @ X0 @ X1 ) )
=> ( X0 = X1 ) )
& ! [X1: a,X0: a] :
( ( cR @ X1 @ X0 )
| ( cR @ X0 @ X1 ) )
& ! [X1: a,X2: a,X0: a] :
( ( ( cR @ X1 @ X2 )
& ( cR @ X0 @ X1 ) )
=> ( cR @ X0 @ X2 ) )
& ! [X3: a,X4: a] :
( ( ( cT @ X4 )
& ( cR @ X3 @ X4 ) )
=> ( cT @ X3 ) )
& ! [X3: a,X4: a] :
( ( ( cS @ X4 )
& ( cR @ X3 @ X4 ) )
=> ( cS @ X3 ) )
& ! [X0: a] : ( cR @ X0 @ X0 ) )
=> ( ! [X0: a] :
( ( cS @ X0 )
=> ( cT @ X0 ) )
| ! [X0: a] :
( ( cT @ X0 )
=> ( cS @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: a,X1: a] :
( ( ( cR @ X0 @ X1 )
& ( cR @ X1 @ X0 ) )
=> ( X0 = X1 ) )
& ! [X2: a,X3: a] :
( ( cR @ X2 @ X3 )
| ( cR @ X3 @ X2 ) )
& ! [X4: a,X5: a,X6: a] :
( ( ( cR @ X4 @ X5 )
& ( cR @ X6 @ X4 ) )
=> ( cR @ X6 @ X5 ) )
& ! [X7: a,X8: a] :
( ( ( cT @ X8 )
& ( cR @ X7 @ X8 ) )
=> ( cT @ X7 ) )
& ! [X9: a,X10: a] :
( ( ( cS @ X10 )
& ( cR @ X9 @ X10 ) )
=> ( cS @ X9 ) )
& ! [X11: a] : ( cR @ X11 @ X11 ) )
=> ( ! [X12: a] :
( ( cS @ X12 )
=> ( cT @ X12 ) )
| ! [X13: a] :
( ( cT @ X13 )
=> ( cS @ X13 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X9: a,X10: a] :
( ( ( $true
= ( cR @ X9 @ X10 ) )
& ( ( cS @ X10 )
= $true ) )
=> ( ( cS @ X9 )
= $true ) )
& ! [X8: a,X7: a] :
( ( ( $true
= ( cR @ X7 @ X8 ) )
& ( ( cT @ X8 )
= $true ) )
=> ( $true
= ( cT @ X7 ) ) )
& ! [X3: a,X2: a] :
( ( ( cR @ X3 @ X2 )
= $true )
| ( $true
= ( cR @ X2 @ X3 ) ) )
& ! [X0: a,X1: a] :
( ( ( ( cR @ X1 @ X0 )
= $true )
& ( ( cR @ X0 @ X1 )
= $true ) )
=> ( X0 = X1 ) )
& ! [X6: a,X4: a,X5: a] :
( ( ( ( cR @ X4 @ X5 )
= $true )
& ( ( cR @ X6 @ X4 )
= $true ) )
=> ( $true
= ( cR @ X6 @ X5 ) ) )
& ! [X11: a] :
( $true
= ( cR @ X11 @ X11 ) ) )
=> ( ! [X12: a] :
( ( $true
= ( cS @ X12 ) )
=> ( $true
= ( cT @ X12 ) ) )
| ! [X13: a] :
( ( $true
= ( cT @ X13 ) )
=> ( $true
= ( cS @ X13 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X12: a] :
( ( $true
= ( cS @ X12 ) )
& ( $true
!= ( cT @ X12 ) ) )
& ? [X13: a] :
( ( $true
= ( cT @ X13 ) )
& ( $true
!= ( cS @ X13 ) ) )
& ! [X9: a,X10: a] :
( ( ( cS @ X9 )
= $true )
| ( $true
!= ( cR @ X9 @ X10 ) )
| ( ( cS @ X10 )
!= $true ) )
& ! [X8: a,X7: a] :
( ( $true
= ( cT @ X7 ) )
| ( $true
!= ( cR @ X7 @ X8 ) )
| ( ( cT @ X8 )
!= $true ) )
& ! [X3: a,X2: a] :
( ( ( cR @ X3 @ X2 )
= $true )
| ( $true
= ( cR @ X2 @ X3 ) ) )
& ! [X0: a,X1: a] :
( ( X0 = X1 )
| ( ( cR @ X1 @ X0 )
!= $true )
| ( ( cR @ X0 @ X1 )
!= $true ) )
& ! [X6: a,X4: a,X5: a] :
( ( $true
= ( cR @ X6 @ X5 ) )
| ( ( cR @ X4 @ X5 )
!= $true )
| ( ( cR @ X6 @ X4 )
!= $true ) )
& ! [X11: a] :
( $true
= ( cR @ X11 @ X11 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X11: a] :
( $true
= ( cR @ X11 @ X11 ) )
& ? [X12: a] :
( ( $true
= ( cS @ X12 ) )
& ( $true
!= ( cT @ X12 ) ) )
& ! [X3: a,X2: a] :
( ( ( cR @ X3 @ X2 )
= $true )
| ( $true
= ( cR @ X2 @ X3 ) ) )
& ! [X7: a,X8: a] :
( ( ( cT @ X8 )
!= $true )
| ( $true
= ( cT @ X7 ) )
| ( $true
!= ( cR @ X7 @ X8 ) ) )
& ! [X0: a,X1: a] :
( ( ( cR @ X1 @ X0 )
!= $true )
| ( X0 = X1 )
| ( ( cR @ X0 @ X1 )
!= $true ) )
& ! [X5: a,X4: a,X6: a] :
( ( $true
= ( cR @ X6 @ X5 ) )
| ( ( cR @ X6 @ X4 )
!= $true )
| ( ( cR @ X4 @ X5 )
!= $true ) )
& ! [X10: a,X9: a] :
( ( $true
!= ( cR @ X9 @ X10 ) )
| ( ( cS @ X9 )
= $true )
| ( ( cS @ X10 )
!= $true ) )
& ? [X13: a] :
( ( $true
= ( cT @ X13 ) )
& ( $true
!= ( cS @ X13 ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X0: a] :
( ( cR @ X0 @ X0 )
= $true )
& ? [X1: a] :
( ( ( cS @ X1 )
= $true )
& ( $true
!= ( cT @ X1 ) ) )
& ! [X2: a,X3: a] :
( ( $true
= ( cR @ X2 @ X3 ) )
| ( ( cR @ X3 @ X2 )
= $true ) )
& ! [X4: a,X5: a] :
( ( ( cT @ X5 )
!= $true )
| ( ( cT @ X4 )
= $true )
| ( ( cR @ X4 @ X5 )
!= $true ) )
& ! [X6: a,X7: a] :
( ( $true
!= ( cR @ X7 @ X6 ) )
| ( X6 = X7 )
| ( $true
!= ( cR @ X6 @ X7 ) ) )
& ! [X8: a,X9: a,X10: a] :
( ( $true
= ( cR @ X10 @ X8 ) )
| ( $true
!= ( cR @ X10 @ X9 ) )
| ( $true
!= ( cR @ X9 @ X8 ) ) )
& ! [X11: a,X12: a] :
( ( $true
!= ( cR @ X12 @ X11 ) )
| ( $true
= ( cS @ X12 ) )
| ( $true
!= ( cS @ X11 ) ) )
& ? [X13: a] :
( ( $true
= ( cT @ X13 ) )
& ( $true
!= ( cS @ X13 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X0: a] :
( ( cR @ X0 @ X0 )
= $true )
& ( ( cS @ sK0 )
= $true )
& ( ( cT @ sK0 )
!= $true )
& ! [X2: a,X3: a] :
( ( $true
= ( cR @ X2 @ X3 ) )
| ( ( cR @ X3 @ X2 )
= $true ) )
& ! [X4: a,X5: a] :
( ( ( cT @ X5 )
!= $true )
| ( ( cT @ X4 )
= $true )
| ( ( cR @ X4 @ X5 )
!= $true ) )
& ! [X6: a,X7: a] :
( ( $true
!= ( cR @ X7 @ X6 ) )
| ( X6 = X7 )
| ( $true
!= ( cR @ X6 @ X7 ) ) )
& ! [X8: a,X9: a,X10: a] :
( ( $true
= ( cR @ X10 @ X8 ) )
| ( $true
!= ( cR @ X10 @ X9 ) )
| ( $true
!= ( cR @ X9 @ X8 ) ) )
& ! [X11: a,X12: a] :
( ( $true
!= ( cR @ X12 @ X11 ) )
| ( $true
= ( cS @ X12 ) )
| ( $true
!= ( cS @ X11 ) ) )
& ( $true
= ( cT @ sK1 ) )
& ( $true
!= ( cS @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0),skolemize(X13,sK1)],[f7]) ).
thf(f9,plain,
( $true
!= ( cS @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( $true
= ( cT @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X11: a,X12: a] :
( ( $true
!= ( cR @ X12 @ X11 ) )
| ( $true
!= ( cS @ X11 ) )
| ( $true
= ( cS @ X12 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X4: a,X5: a] :
( ( ( cR @ X4 @ X5 )
!= $true )
| ( ( cT @ X5 )
!= $true )
| ( ( cT @ X4 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
! [X2: a,X3: a] :
( ( $true
= ( cR @ X2 @ X3 ) )
| ( ( cR @ X3 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
( ( cT @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
( ( cS @ sK0 )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f21,definition,
( spl2_1
<=> ( $true
= ( cS @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f23,plain,
( ( $true
!= ( cS @ sK1 ) )
| spl2_1 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f24,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f9,f21]) ).
thf(f26,definition,
( spl2_2
<=> ( $true
= ( cT @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f28,plain,
( ( $true
= ( cT @ sK1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f29,plain,
spl2_2,
inference(avatar_split_clause,[],[f10,f26]) ).
thf(f31,definition,
( spl2_3
<=> ( ( cT @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f33,plain,
( ( ( cT @ sK0 )
!= $true )
| spl2_3 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f34,plain,
~ spl2_3,
inference(avatar_split_clause,[],[f16,f31]) ).
thf(f36,definition,
( spl2_4
<=> ( ( cS @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f38,plain,
( ( ( cS @ sK0 )
= $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f39,plain,
spl2_4,
inference(avatar_split_clause,[],[f17,f36]) ).
thf(f46,plain,
! [X0: a,X1: a] :
( ( ( cT @ X0 )
= $true )
| ( ( cR @ X1 @ X0 )
= $true )
| ( $true
!= ( cT @ X1 ) )
| ( $true != $true ) ),
inference(superposition,[],[f14,f15]) ).
thf(f47,plain,
! [X0: a,X1: a] :
( ( ( cR @ X1 @ X0 )
= $true )
| ( ( cT @ X0 )
= $true )
| ( $true
!= ( cT @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f55,definition,
( spl2_5
<=> ! [X0: a] :
( ( ( cS @ X0 )
!= $true )
| ( ( cT @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
thf(f56,plain,
( ! [X0: a] :
( ( ( cT @ X0 )
= $true )
| ( ( cS @ X0 )
!= $true ) )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f58,definition,
( spl2_6
<=> ! [X1: a] :
( ( ( cS @ X1 )
= $true )
| ( $true
!= ( cT @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
thf(f59,plain,
( ! [X1: a] :
( ( ( cS @ X1 )
= $true )
| ( $true
!= ( cT @ X1 ) ) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f67,plain,
( ( $true
!= ( cT @ sK1 ) )
| ( $true != $true )
| spl2_1
| ~ spl2_6 ),
inference(superposition,[],[f23,f59]) ).
thf(f68,plain,
( ( $true
!= ( cT @ sK1 ) )
| spl2_1
| ~ spl2_6 ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f69,plain,
( $false
| spl2_1
| ~ spl2_2
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f68,f28]) ).
thf(f70,plain,
( spl2_1
| ~ spl2_2
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f69]) ).
thf(f71,plain,
! [X0: a,X1: a] :
( ( ( cS @ X1 )
!= $true )
| ( $true
= ( cT @ X1 ) )
| ( ( cS @ X0 )
= $true )
| ( $true != $true )
| ( ( cT @ X0 )
!= $true ) ),
inference(superposition,[],[f11,f47]) ).
thf(f75,plain,
! [X0: a,X1: a] :
( ( ( cS @ X0 )
= $true )
| ( ( cS @ X1 )
!= $true )
| ( $true
= ( cT @ X1 ) )
| ( ( cT @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f76,plain,
( spl2_6
| spl2_5 ),
inference(avatar_split_clause,[],[f75,f55,f58]) ).
thf(f77,plain,
( ( $true != $true )
| ( ( cS @ sK0 )
!= $true )
| spl2_3
| ~ spl2_5 ),
inference(superposition,[],[f33,f56]) ).
thf(f78,plain,
( ( ( cS @ sK0 )
!= $true )
| spl2_3
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f79,plain,
( $false
| spl2_3
| ~ spl2_4
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f78,f38]) ).
thf(f80,plain,
( spl2_3
| ~ spl2_4
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f79]) ).
cnf(s1,plain,
~ spl2_1,
inference(sat_conversion,[],[f24]) ).
cnf(s2,plain,
spl2_2,
inference(sat_conversion,[],[f29]) ).
cnf(s3,plain,
~ spl2_3,
inference(sat_conversion,[],[f34]) ).
cnf(s4,plain,
spl2_4,
inference(sat_conversion,[],[f39]) ).
cnf(s6,plain,
( spl2_1
| ~ spl2_2
| ~ spl2_6 ),
inference(sat_conversion,[],[f70]) ).
cnf(s7,plain,
( spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f76]) ).
cnf(s8,plain,
( spl2_3
| ~ spl2_4
| ~ spl2_5 ),
inference(sat_conversion,[],[f80]) ).
cnf(s9,plain,
~ spl2_5,
inference(rat,[],[s8,s4,s3]) ).
cnf(s10,plain,
spl2_6,
inference(rat,[],[s7,s9]) ).
cnf(s11,plain,
spl2_1,
inference(rat,[],[s6,s10,s2]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s11]) ).
thf(f81,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV067^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 % Computer : n007.cluster.edu
% 0.12/0.23 % Model : x86_64 x86_64
% 0.12/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.23 % Memory : 8046.5625MB
% 0.12/0.23 % OS : Linux 6.8.0-71-generic
% 0.12/0.23 % CPULimit : 300
% 0.12/0.23 % WCLimit : 300
% 0.12/0.23 % DateTime : Tue Sep 29 15:04:26 UTC 2026
% 0.12/0.23 % CPUTime :
% 0.12/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.26 Running higher-order theorem proving
% 0.12/0.27 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
% 0.26/0.31 % (3478640)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.31 % (3478648)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=1761198943: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)
% 0.26/0.31 % (3478648) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3478640-3478648"...
% 0.26/0.31 % (3478648)...printing done.
% 0.26/0.31 % (3478648)Refutation found. Thanks to Tanya!
% 0.26/0.31 % SZS status Theorem for theBenchmark
% 0.26/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.31 % (3478648)------------------------------
% 0.26/0.31 % (3478648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.31 % (3478648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.31 % (3478648)CaDiCaL version: 2.1.3
% 0.26/0.31 % (3478648)Termination reason: Refutation
% 0.26/0.31 % (3478648)Time elapsed: 0.003 s
% 0.26/0.31 % (3478648)Peak memory usage: 13 MB
% 0.26/0.31 % (3478648)Instructions burned: 7 (million)
% 0.26/0.31 % (3478640)Success in time 0.026 s
% 0.26/0.31 % Vampire exiting
%------------------------------------------------------------------------------