%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV067^5 : 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 : n017.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 08:38:57 AM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 480 ( 140 equ; 0 cnn)
% Maximal formula atoms : 19 ( 12 avg)
% Number of connectives : 524 ( 77 ~; 77 |; 72 &; 268 @)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 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 : 11 ( 8 usr; 6 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,
( ( ! [X3: a,X4: a] :
( ( ( cT @ X4 )
& ( cR @ X3 @ X4 ) )
=> ( cT @ X3 ) )
& ! [X3: a,X4: a] :
( ( ( cS @ X4 )
& ( cR @ X3 @ X4 ) )
=> ( cS @ X3 ) )
& ! [X0: a,X1: a] :
( ( cR @ X1 @ X0 )
| ( cR @ X0 @ X1 ) )
& ! [X0: a,X1: a] :
( ( ( cR @ X1 @ X0 )
& ( cR @ X0 @ X1 ) )
=> ( X0 = X1 ) )
& ! [X0: a] : ( cR @ X0 @ X0 )
& ! [X0: a,X1: a,X2: a] :
( ( ( cR @ X1 @ X2 )
& ( cR @ X0 @ X1 ) )
=> ( cR @ X0 @ X2 ) ) )
=> ( ! [X0: a] :
( ( cT @ X0 )
=> ( cS @ X0 ) )
| ! [X0: a] :
( ( cS @ X0 )
=> ( cT @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM553_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: a,X4: a] :
( ( ( cT @ X4 )
& ( cR @ X3 @ X4 ) )
=> ( cT @ X3 ) )
& ! [X3: a,X4: a] :
( ( ( cS @ X4 )
& ( cR @ X3 @ X4 ) )
=> ( cS @ X3 ) )
& ! [X0: a,X1: a] :
( ( cR @ X1 @ X0 )
| ( cR @ X0 @ X1 ) )
& ! [X0: a,X1: a] :
( ( ( cR @ X1 @ X0 )
& ( cR @ X0 @ X1 ) )
=> ( X0 = X1 ) )
& ! [X0: a] : ( cR @ X0 @ X0 )
& ! [X0: a,X1: a,X2: a] :
( ( ( cR @ X1 @ X2 )
& ( cR @ X0 @ X1 ) )
=> ( cR @ X0 @ X2 ) ) )
=> ( ! [X0: a] :
( ( cT @ X0 )
=> ( cS @ X0 ) )
| ! [X0: a] :
( ( cS @ X0 )
=> ( cT @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: a,X1: a] :
( ( ( cT @ X1 )
& ( cR @ X0 @ X1 ) )
=> ( cT @ X0 ) )
& ! [X2: a,X3: a] :
( ( ( cS @ X3 )
& ( cR @ X2 @ X3 ) )
=> ( cS @ X2 ) )
& ! [X4: a,X5: a] :
( ( cR @ X5 @ X4 )
| ( cR @ X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( cR @ X7 @ X6 )
& ( cR @ X6 @ X7 ) )
=> ( X6 = X7 ) )
& ! [X8: a] : ( cR @ X8 @ X8 )
& ! [X9: a,X10: a,X11: a] :
( ( ( cR @ X10 @ X11 )
& ( cR @ X9 @ X10 ) )
=> ( cR @ X9 @ X11 ) ) )
=> ( ! [X12: a] :
( ( cT @ X12 )
=> ( cS @ X12 ) )
| ! [X13: a] :
( ( cS @ X13 )
=> ( cT @ X13 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: a,X1: a] :
( ( ( ( cT @ X1 )
= $true )
& ( ( cR @ X0 @ X1 )
= $true ) )
=> ( ( cT @ X0 )
= $true ) )
& ! [X2: a,X3: a] :
( ( ( ( cS @ X3 )
= $true )
& ( ( cR @ X2 @ X3 )
= $true ) )
=> ( ( cS @ X2 )
= $true ) )
& ! [X4: a,X5: a] :
( ( ( cR @ X5 @ X4 )
= $true )
| ( ( cR @ X4 @ X5 )
= $true ) )
& ! [X6: a,X7: a] :
( ( ( ( cR @ X7 @ X6 )
= $true )
& ( ( cR @ X6 @ X7 )
= $true ) )
=> ( X6 = X7 ) )
& ! [X8: a] :
( ( cR @ X8 @ X8 )
= $true )
& ! [X9: a,X10: a,X11: a] :
( ( ( ( cR @ X10 @ X11 )
= $true )
& ( ( cR @ X9 @ X10 )
= $true ) )
=> ( ( cR @ X9 @ X11 )
= $true ) ) )
=> ( ! [X12: a] :
( ( ( cT @ X12 )
= $true )
=> ( ( cS @ X12 )
= $true ) )
| ! [X13: a] :
( ( ( cS @ X13 )
= $true )
=> ( ( cT @ X13 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X12: a] :
( ( ( cS @ X12 )
!= $true )
& ( ( cT @ X12 )
= $true ) )
& ? [X13: a] :
( ( ( cT @ X13 )
!= $true )
& ( ( cS @ X13 )
= $true ) )
& ! [X0: a,X1: a] :
( ( ( cT @ X0 )
= $true )
| ( ( cT @ X1 )
!= $true )
| ( ( cR @ X0 @ X1 )
!= $true ) )
& ! [X2: a,X3: a] :
( ( ( cS @ X2 )
= $true )
| ( ( cS @ X3 )
!= $true )
| ( ( cR @ X2 @ X3 )
!= $true ) )
& ! [X4: a,X5: a] :
( ( ( cR @ X5 @ X4 )
= $true )
| ( ( cR @ X4 @ X5 )
= $true ) )
& ! [X6: a,X7: a] :
( ( X6 = X7 )
| ( ( cR @ X7 @ X6 )
!= $true )
| ( ( cR @ X6 @ X7 )
!= $true ) )
& ! [X8: a] :
( ( cR @ X8 @ X8 )
= $true )
& ! [X9: a,X10: a,X11: a] :
( ( ( cR @ X9 @ X11 )
= $true )
| ( ( cR @ X10 @ X11 )
!= $true )
| ( ( cR @ X9 @ X10 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ? [X12: a] :
( ( ( cS @ X12 )
!= $true )
& ( ( cT @ X12 )
= $true ) )
& ? [X13: a] :
( ( ( cT @ X13 )
!= $true )
& ( ( cS @ X13 )
= $true ) )
& ! [X0: a,X1: a] :
( ( ( cT @ X0 )
= $true )
| ( ( cT @ X1 )
!= $true )
| ( ( cR @ X0 @ X1 )
!= $true ) )
& ! [X2: a,X3: a] :
( ( ( cS @ X2 )
= $true )
| ( ( cS @ X3 )
!= $true )
| ( ( cR @ X2 @ X3 )
!= $true ) )
& ! [X4: a,X5: a] :
( ( ( cR @ X5 @ X4 )
= $true )
| ( ( cR @ X4 @ X5 )
= $true ) )
& ! [X6: a,X7: a] :
( ( X6 = X7 )
| ( ( cR @ X7 @ X6 )
!= $true )
| ( ( cR @ X6 @ X7 )
!= $true ) )
& ! [X8: a] :
( ( cR @ X8 @ X8 )
= $true )
& ! [X9: a,X10: a,X11: a] :
( ( ( cR @ X9 @ X11 )
= $true )
| ( ( cR @ X10 @ X11 )
!= $true )
| ( ( cR @ X9 @ X10 )
!= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ? [X0: a] :
( ( ( cS @ X0 )
!= $true )
& ( ( cT @ X0 )
= $true ) )
& ? [X1: a] :
( ( ( cT @ X1 )
!= $true )
& ( $true
= ( cS @ X1 ) ) )
& ! [X2: a,X3: a] :
( ( $true
= ( cT @ X2 ) )
| ( ( cT @ X3 )
!= $true )
| ( ( cR @ X2 @ X3 )
!= $true ) )
& ! [X4: a,X5: a] :
( ( ( cS @ X4 )
= $true )
| ( $true
!= ( cS @ X5 ) )
| ( ( cR @ X4 @ X5 )
!= $true ) )
& ! [X6: a,X7: a] :
( ( ( cR @ X7 @ X6 )
= $true )
| ( ( cR @ X6 @ X7 )
= $true ) )
& ! [X8: a,X9: a] :
( ( X8 = X9 )
| ( $true
!= ( cR @ X9 @ X8 ) )
| ( $true
!= ( cR @ X8 @ X9 ) ) )
& ! [X10: a] :
( $true
= ( cR @ X10 @ X10 ) )
& ! [X11: a,X12: a,X13: a] :
( ( $true
= ( cR @ X11 @ X13 ) )
| ( $true
!= ( cR @ X12 @ X13 ) )
| ( $true
!= ( cR @ X11 @ X12 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( $true
!= ( cS @ sK0 ) )
& ( $true
= ( cT @ sK0 ) )
& ( $true
!= ( cT @ sK1 ) )
& ( $true
= ( cS @ sK1 ) )
& ! [X2: a,X3: a] :
( ( $true
= ( cT @ X2 ) )
| ( ( cT @ X3 )
!= $true )
| ( ( cR @ X2 @ X3 )
!= $true ) )
& ! [X4: a,X5: a] :
( ( ( cS @ X4 )
= $true )
| ( $true
!= ( cS @ X5 ) )
| ( ( cR @ X4 @ X5 )
!= $true ) )
& ! [X6: a,X7: a] :
( ( ( cR @ X7 @ X6 )
= $true )
| ( ( cR @ X6 @ X7 )
= $true ) )
& ! [X8: a,X9: a] :
( ( X8 = X9 )
| ( $true
!= ( cR @ X9 @ X8 ) )
| ( $true
!= ( cR @ X8 @ X9 ) ) )
& ! [X10: a] :
( $true
= ( cR @ X10 @ X10 ) )
& ! [X11: a,X12: a,X13: a] :
( ( $true
= ( cR @ X11 @ X13 ) )
| ( $true
!= ( cR @ X12 @ X13 ) )
| ( $true
!= ( cR @ X11 @ X12 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f7]) ).
thf(f12,plain,
! [X6: a,X7: a] :
( ( ( cR @ X7 @ X6 )
= $true )
| ( ( cR @ X6 @ X7 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
! [X4: a,X5: a] :
( ( ( cR @ X4 @ X5 )
!= $true )
| ( $true
!= ( cS @ X5 ) )
| ( ( cS @ X4 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X2: a,X3: a] :
( ( ( cR @ X2 @ X3 )
!= $true )
| ( ( cT @ X3 )
!= $true )
| ( $true
= ( cT @ X2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( $true
= ( cS @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
( $true
!= ( cT @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
( $true
= ( cT @ sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f18,plain,
( $true
!= ( cS @ sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f27,plain,
! [X0: a,X1: a] :
( ( $true != $true )
| ( $true
!= ( cS @ X1 ) )
| ( ( cS @ X0 )
= $true )
| ( ( cR @ X1 @ X0 )
= $true ) ),
inference(constrained_superposition,[],[f13,f12]) ).
thf(f28,plain,
! [X0: a,X1: a] :
( ( ( cR @ X1 @ X0 )
= $true )
| ( ( cS @ X0 )
= $true )
| ( $true
!= ( cS @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f27]) ).
thf(f35,plain,
! [X0: a,X1: a] :
( ( $true != $true )
| ( ( cT @ X1 )
!= $true )
| ( ( cT @ X0 )
= $true )
| ( $true
= ( cS @ X1 ) )
| ( ( cS @ X0 )
!= $true ) ),
inference(constrained_superposition,[],[f14,f28]) ).
thf(f37,plain,
! [X0: a,X1: a] :
( ( ( cT @ X1 )
!= $true )
| ( ( cT @ X0 )
= $true )
| ( $true
= ( cS @ X1 ) )
| ( ( cS @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f39,definition,
( spl2_1
<=> ! [X0: a] :
( ( ( cT @ X0 )
= $true )
| ( ( cS @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f40,plain,
( ! [X0: a] :
( ( ( cT @ X0 )
= $true )
| ( ( cS @ X0 )
!= $true ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f42,definition,
( spl2_2
<=> ! [X1: a] :
( ( ( cT @ X1 )
!= $true )
| ( $true
= ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f43,plain,
( ! [X1: a] :
( ( ( cT @ X1 )
!= $true )
| ( $true
= ( cS @ X1 ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f44,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f37,f42,f39]) ).
thf(f53,plain,
( ( $true != $true )
| ( $true
= ( cS @ sK0 ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f43,f17]) ).
thf(f54,plain,
( ( $true
= ( cS @ sK0 ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f55,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f54,f18]) ).
thf(f56,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f55]) ).
thf(f57,plain,
( ( $true != $true )
| ( $true
!= ( cS @ sK1 ) )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f16,f40]) ).
thf(f58,plain,
( ( $true
!= ( cS @ sK1 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f59,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f58,f15]) ).
thf(f60,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f59]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
~ spl2_2,
inference(sat_conversion,[],[f56]) ).
cnf(s3,plain,
~ spl2_1,
inference(sat_conversion,[],[f60]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f61,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV067^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:01:52 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.18/0.27 % (440216)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (440242)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3116011097:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.27 % (440242)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27 % (440242) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-440216-440242"...
% 0.18/0.27 % (440239)% WARNING: option uhcvi not known.
% 0.18/0.27 % (440242)...printing done.
% 0.18/0.27 % (440242)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (440242)------------------------------
% 0.18/0.27 % (440242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (440242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (440242)CaDiCaL version: 2.1.3
% 0.18/0.27 % (440242)Termination reason: Refutation
% 0.18/0.27 % (440242)Time elapsed: 0.003 s
% 0.18/0.27 % (440242)Peak memory usage: 12 MB
% 0.18/0.27 % (440242)Instructions burned: 6 (million)
% 0.18/0.27 % (440216)Success in time 0.038 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------