%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP001^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:09:58 AM UTC 2026
% Result : Theorem 0.25s 0.34s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 12 unt; 0 typ; 3 def)
% Number of atoms : 138 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 66 ( 29 ~; 28 |; 3 &; 0 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 21 con; 0-4 aty)
% Number of variables : 8 ( 0 sgn 6 !; 2 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
u: $tType ).
thf(type_def_6,type,
d: $tType ).
thf(type_def_7,type,
du: $tType ).
thf(type_def_8,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
tyop_2Emin_2Ebool: d ).
thf(func_def_1,type,
tyop_2Emin_2Efun: d > d > d ).
thf(func_def_2,type,
s: d > u > du ).
thf(func_def_3,type,
app_2E2: du > du > u ).
thf(func_def_4,type,
combin_i_2E0: u ).
thf(func_def_5,type,
combin_k_2E0: u ).
thf(func_def_6,type,
combin_s_2E0: u ).
thf(func_def_7,type,
c_2Ebool_2E_21_2E0: u ).
thf(func_def_8,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(func_def_9,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(func_def_10,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(func_def_11,type,
c_2Emin_2E_3D_2E0: u ).
thf(func_def_12,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(func_def_13,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(func_def_14,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(func_def_15,type,
c_2Ebool_2E_3F_2E0: u ).
thf(func_def_16,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(func_def_17,type,
c_2Ebool_2EF_2E0: u ).
thf(func_def_18,type,
c_2Ebool_2ET_2E0: u ).
thf(func_def_19,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(func_def_20,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(func_def_21,type,
c_2Ebool_2E_7E_2E0: u ).
thf(func_def_22,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(func_def_23,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(func_def_24,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(func_def_25,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_26,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_27,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(func_def_28,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(func_def_29,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_30,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(func_def_31,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(func_def_32,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(func_def_33,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
thf(func_def_34,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(func_def_35,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(func_def_36,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_41,type,
sK0: u > u > d > d > u ).
thf(func_def_42,type,
sK1: u > d > u ).
thf(func_def_43,type,
sK2: u > d > u ).
thf(func_def_44,type,
sK3: $o ).
thf(f25,axiom,
( mono_2Ec_2Ebool_2ET
<=> ! [X0: $o] : ( X0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ET__DEF) ).
thf(f26,conjecture,
mono_2Ec_2Ebool_2ET,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(f27,negated_conjecture,
~ mono_2Ec_2Ebool_2ET,
inference(negated_conjecture,[status(cth)],[f26]) ).
thf(f44,plain,
( mono_2Ec_2Ebool_2ET
<=> ! [X0: $o] : ( X0 = X0 ) ),
inference(rectify,[],[f25]) ).
thf(f45,plain,
( ( mono_2Ec_2Ebool_2ET = $true )
<=> ! [X0: $o] : ( X0 = X0 ) ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
~ mono_2Ec_2Ebool_2ET,
inference(rectify,[],[f27]) ).
thf(f47,plain,
mono_2Ec_2Ebool_2ET != $true,
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
mono_2Ec_2Ebool_2ET != $true,
inference(flattening,[],[f47]) ).
thf(f66,plain,
( ( ( mono_2Ec_2Ebool_2ET = $true )
| ? [X0: $o] : ( X0 != X0 ) )
& ( ! [X0: $o] : ( X0 = X0 )
| ( mono_2Ec_2Ebool_2ET != $true ) ) ),
inference(nnf_transformation,[],[f45]) ).
thf(f67,plain,
( ( ( mono_2Ec_2Ebool_2ET = $true )
| ? [X0: $o] : ( X0 != X0 ) )
& ( ! [X1: $o] : ( X1 = X1 )
| ( mono_2Ec_2Ebool_2ET != $true ) ) ),
inference(rectify,[],[f66]) ).
thf(f68,plain,
( ( ( mono_2Ec_2Ebool_2ET = $true )
| ( sK3 != sK3 ) )
& ( ! [X1: $o] : ( X1 = X1 )
| ( mono_2Ec_2Ebool_2ET != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f67]) ).
thf(f104,plain,
( ( mono_2Ec_2Ebool_2ET = $true )
| ( sK3 != sK3 ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f105,plain,
mono_2Ec_2Ebool_2ET != $true,
inference(cnf_transformation,[],[f48]) ).
thf(f116,plain,
( ( mono_2Ec_2Ebool_2ET = $true )
| ( $true = sK3 )
| ( $true = sK3 ) ),
inference(xor_proxy_clausification,[],[f104]) ).
thf(f117,plain,
( ( mono_2Ec_2Ebool_2ET = $true )
| ( sK3 = $false )
| ( sK3 = $false ) ),
inference(xor_proxy_clausification,[],[f104]) ).
thf(f118,plain,
( ( mono_2Ec_2Ebool_2ET = $true )
| ( sK3 = $false ) ),
inference(duplicate_literal_removal,[],[f117]) ).
thf(f119,plain,
( ( mono_2Ec_2Ebool_2ET = $true )
| ( $true = sK3 ) ),
inference(duplicate_literal_removal,[],[f116]) ).
thf(f133,definition,
( spl4_1
<=> ( sK3 = $false ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f135,plain,
( ( sK3 = $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f133]) ).
thf(f137,definition,
( spl4_2
<=> ( mono_2Ec_2Ebool_2ET = $true ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f139,plain,
( ( mono_2Ec_2Ebool_2ET = $true )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f140,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f118,f137,f133]) ).
thf(f142,definition,
( spl4_3
<=> ( $true = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f144,plain,
( ( $true = sK3 )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f142]) ).
thf(f145,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f119,f137,f142]) ).
thf(f146,plain,
( ( $true != $true )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f105,f139]) ).
thf(f147,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f146]) ).
thf(f148,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f147]) ).
thf(f149,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_3 ),
inference(constrained_superposition,[],[f144,f135]) ).
thf(f153,plain,
( $false
| ~ spl4_1
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f149]) ).
thf(f154,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f153]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f140]) ).
cnf(s2,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f145]) ).
cnf(s3,plain,
~ spl4_2,
inference(sat_conversion,[],[f148]) ).
cnf(s5,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(sat_conversion,[],[f154]) ).
cnf(s6,plain,
spl4_3,
inference(rat,[],[s2,s3]) ).
cnf(s7,plain,
~ spl4_1,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s3,s7]) ).
thf(f155,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP001^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.26 % Computer : n008.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 19:17:54 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.25/0.30 Running first-order model finding
% 0.25/0.30 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.25/0.34 % (3603519)Will run a generic schedule for satisfiability detection.
% 0.25/0.34 % (3603526)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3094157471:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.34 % (3603530)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3550500426:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.25/0.34 % (3603525)% WARNING: option uhcvi not known.
% 0.25/0.34 % (3603530) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3603519-3603530"...
% 0.25/0.34 % (3603526) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3603519-3603526"...
% 0.25/0.34 % (3603530)...printing done.
% 0.25/0.34 % (3603524)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1865576830_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.34 % (3603530)Refutation found. Thanks to Tanya!
% 0.25/0.34 % SZS status Theorem for theBenchmark
% 0.25/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.34 % (3603530)------------------------------
% 0.25/0.34 % (3603530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.34 % (3603530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.34 % (3603530)CaDiCaL version: 2.1.3
% 0.25/0.34 % (3603530)Termination reason: Refutation
% 0.25/0.34 % (3603530)Time elapsed: 0.007 s
% 0.25/0.34 % (3603530)Peak memory usage: 13 MB
% 0.25/0.34 % (3603530)Instructions burned: 13 (million)
% 0.25/0.34 % (3603519)Success in time 0.035 s
% 0.25/0.34 % Vampire exiting
%------------------------------------------------------------------------------