%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV412^5 : 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 : n009.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 08:39:28 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 9 unt; 0 typ; 5 def)
% Number of atoms : 399 ( 91 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 266 ( 60 ~; 79 |; 16 &; 78 @)
% ( 5 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 17 !; 6 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cG: $o ).
thf(func_def_1,type,
cB: $i > $o ).
thf(func_def_2,type,
cA: $i > $o ).
thf(f1,conjecture,
( ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG )
| ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) )
=> ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cDUAL_EG2_pme) ).
thf(f2,negated_conjecture,
~ ( ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG )
| ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) )
=> ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG )
| ( ! [X1: $i] :
( ( cA @ X1 )
=> ( cB @ X1 ) )
=> cG ) )
=> ( ! [X2: $i] :
( ( cA @ X2 )
=> ( cB @ X2 ) )
=> cG ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ! [X0: $i] :
( ( ( cA @ X0 )
= $true )
=> ( ( cB @ X0 )
= $true ) )
=> ( cG = $true ) )
| ( ! [X1: $i] :
( ( ( cA @ X1 )
= $true )
=> ( ( cB @ X1 )
= $true ) )
=> ( cG = $true ) ) )
=> ( ! [X2: $i] :
( ( ( cA @ X2 )
= $true )
=> ( ( cB @ X2 )
= $true ) )
=> ( cG = $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( cG != $true )
& ! [X2: $i] :
( ( ( cB @ X2 )
= $true )
| ( ( cA @ X2 )
!= $true ) )
& ( ( cG = $true )
| ? [X0: $i] :
( ( ( cB @ X0 )
!= $true )
& ( ( cA @ X0 )
= $true ) )
| ( cG = $true )
| ? [X1: $i] :
( ( ( cB @ X1 )
!= $true )
& ( ( cA @ X1 )
= $true ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( cG != $true )
& ! [X2: $i] :
( ( ( cB @ X2 )
= $true )
| ( ( cA @ X2 )
!= $true ) )
& ( ( cG = $true )
| ? [X0: $i] :
( ( ( cB @ X0 )
!= $true )
& ( ( cA @ X0 )
= $true ) )
| ( cG = $true )
| ? [X1: $i] :
( ( ( cB @ X1 )
!= $true )
& ( ( cA @ X1 )
= $true ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( cG != $true )
& ! [X0: $i] :
( ( ( cB @ X0 )
= $true )
| ( ( cA @ X0 )
!= $true ) )
& ( ( cG = $true )
| ? [X1: $i] :
( ( ( cB @ X1 )
!= $true )
& ( ( cA @ X1 )
= $true ) )
| ( cG = $true )
| ? [X2: $i] :
( ( ( cB @ X2 )
!= $true )
& ( ( cA @ X2 )
= $true ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( cG != $true )
& ! [X0: $i] :
( ( ( cB @ X0 )
= $true )
| ( ( cA @ X0 )
!= $true ) )
& ( ( cG = $true )
| ( ( $true
!= ( cB @ sK0 ) )
& ( $true
= ( cA @ sK0 ) ) )
| ( cG = $true )
| ( ( $true
!= ( cB @ sK1 ) )
& ( $true
= ( cA @ sK1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0),skolemize(X2,sK1)],[f7]) ).
thf(f9,plain,
( ( cG = $true )
| ( $true
= ( cA @ sK0 ) )
| ( cG = $true )
| ( $true
= ( cA @ sK1 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( cG = $true )
| ( $true
= ( cA @ sK0 ) )
| ( cG = $true )
| ( $true
!= ( cB @ sK1 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( cG = $true )
| ( $true
!= ( cB @ sK0 ) )
| ( cG = $true )
| ( $true
= ( cA @ sK1 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( ( cG = $true )
| ( $true
!= ( cB @ sK0 ) )
| ( cG = $true )
| ( $true
!= ( cB @ sK1 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
! [X0: $i] :
( ( ( cA @ X0 )
!= $true )
| ( ( cB @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
cG != $true,
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
( ( cG = $true )
| ( $true
= ( cA @ sK0 ) )
| ( $true
= ( cA @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f9]) ).
thf(f18,plain,
( ( cG = $true )
| ( $true
= ( cA @ sK0 ) )
| ( $true
!= ( cB @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f10]) ).
thf(f19,plain,
( ( cG = $true )
| ( $true
!= ( cB @ sK0 ) )
| ( $true
= ( cA @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f11]) ).
thf(f20,plain,
( ( cG = $true )
| ( $true
!= ( cB @ sK0 ) )
| ( $true
!= ( cB @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f12]) ).
thf(f22,definition,
( spl2_1
<=> ( $true
= ( cA @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f24,plain,
( ( $true
= ( cA @ sK1 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f22]) ).
thf(f26,definition,
( spl2_2
<=> ( $true
= ( cA @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f28,plain,
( ( $true
= ( cA @ sK0 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f30,definition,
( spl2_3
<=> ( cG = $true ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f33,plain,
( spl2_1
| spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f17,f30,f26,f22]) ).
thf(f35,definition,
( spl2_4
<=> ( $true
= ( cB @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f37,plain,
( ( $true
!= ( cB @ sK1 ) )
| spl2_4 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f38,plain,
( ~ spl2_4
| spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f18,f30,f26,f35]) ).
thf(f40,definition,
( spl2_5
<=> ( $true
= ( cB @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
thf(f42,plain,
( ( $true
!= ( cB @ sK0 ) )
| spl2_5 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,plain,
( spl2_1
| ~ spl2_5
| spl2_3 ),
inference(avatar_split_clause,[],[f19,f30,f40,f22]) ).
thf(f44,plain,
( ~ spl2_4
| ~ spl2_5
| spl2_3 ),
inference(avatar_split_clause,[],[f20,f30,f40,f35]) ).
thf(f45,plain,
~ spl2_3,
inference(avatar_split_clause,[],[f14,f30]) ).
thf(f46,plain,
( ( $true != $true )
| ( $true
= ( cB @ sK0 ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f13,f28]) ).
thf(f47,plain,
( ( $true
= ( cB @ sK0 ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f48,plain,
( $false
| ~ spl2_2
| spl2_5 ),
inference(forward_subsumption_resolution,[],[f47,f42]) ).
thf(f49,plain,
( ~ spl2_2
| spl2_5 ),
inference(avatar_contradiction_clause,[],[f48]) ).
thf(f50,plain,
( ( $true != $true )
| ( $true
= ( cB @ sK1 ) )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f13,f24]) ).
thf(f51,plain,
( ( $true
= ( cB @ sK1 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f50]) ).
thf(f52,plain,
( $false
| ~ spl2_1
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f51,f37]) ).
thf(f53,plain,
( ~ spl2_1
| spl2_4 ),
inference(avatar_contradiction_clause,[],[f52]) ).
cnf(s1,plain,
( spl2_1
| spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f33]) ).
cnf(s2,plain,
( spl2_2
| spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s3,plain,
( spl2_1
| spl2_3
| ~ spl2_5 ),
inference(sat_conversion,[],[f43]) ).
cnf(s4,plain,
( spl2_3
| ~ spl2_4
| ~ spl2_5 ),
inference(sat_conversion,[],[f44]) ).
cnf(s5,plain,
~ spl2_3,
inference(sat_conversion,[],[f45]) ).
cnf(s6,plain,
( ~ spl2_2
| spl2_5 ),
inference(sat_conversion,[],[f49]) ).
cnf(s7,plain,
( ~ spl2_1
| spl2_4 ),
inference(sat_conversion,[],[f53]) ).
cnf(s8,plain,
( ~ spl2_4
| ~ spl2_5 ),
inference(rat,[],[s4,s5]) ).
cnf(s9,plain,
( spl2_1
| ~ spl2_5 ),
inference(rat,[],[s3,s5]) ).
cnf(s10,plain,
( spl2_2
| ~ spl2_4 ),
inference(rat,[],[s2,s5]) ).
cnf(s11,plain,
( spl2_1
| spl2_2 ),
inference(rat,[],[s1,s5]) ).
cnf(s12,plain,
spl2_1,
inference(rat,[],[s6,s11,s9]) ).
cnf(s13,plain,
spl2_4,
inference(rat,[],[s7,s12]) ).
cnf(s14,plain,
~ spl2_5,
inference(rat,[],[s8,s13]) ).
cnf(s15,plain,
spl2_2,
inference(rat,[],[s10,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s6,s14,s15]) ).
thf(f54,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV412^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.17 % Computer : n009.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 15:45:15 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 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
% 0.10/0.25 % (4166224)Will run a generic schedule for satisfiability detection.
% 0.10/0.25 % (4166230)% WARNING: option uhcvi not known.
% 0.10/0.25 % (4166230)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1461855920:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.25 % (4166232)dis+10_1_sil=32000:sp=arity:random_seed=3625369216:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.25 % (4166231)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2734864957:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.25 % (4166233)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2896007565:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.25 % (4166234)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=190460192:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.25 % (4166235)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=860962400:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.25 % (4166230)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.25 % (4166233)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.25 % (4166230)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.10/0.25 % (4166234) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4166224-4166234"...
% 0.10/0.25 % (4166230) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4166224-4166230"...
% 0.10/0.25 % (4166235) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4166224-4166235"...
% 0.10/0.25 % (4166233) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4166224-4166233"...
% 0.10/0.25 % (4166232) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4166224-4166232"...
% 0.10/0.25 % (4166231) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4166224-4166231"...
% 0.10/0.25 % (4166234)...printing done.
% 0.10/0.25 % (4166235)...printing done.
% 0.10/0.25 % (4166233)...printing done.
% 0.10/0.25 % (4166232)...printing done.
% 0.10/0.25 % (4166230)...printing done.
% 0.10/0.25 % (4166229)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2623073788_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.25 % Exception at run slice level
% 0.10/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.10/0.25 % (4166233)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (4166233)------------------------------
% 0.10/0.26 % (4166233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (4166233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (4166233)CaDiCaL version: 2.1.3
% 0.10/0.26 % (4166233)Termination reason: Refutation
% 0.10/0.26 % (4166233)Time elapsed: 0.003 s
% 0.10/0.26 % (4166233)Peak memory usage: 12 MB
% 0.10/0.26 % (4166233)Instructions burned: 2 (million)
% 0.10/0.26 % (4166224)Success in time 0.041 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------