%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP001^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:07:34 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 92 ( 34 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 31 ( 12 ~; 13 |; 3 &; 0 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 43 usr; 18 con; 0-4 aty)
% Number of variables : 8 ( 0 ^; 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: d > u > u ).
thf(func_def_42,type,
sK1: u > d > u > d > u ).
thf(func_def_43,type,
sK2: $o ).
thf(func_def_44,type,
sK3: u > d > u ).
thf(f25,axiom,
( mono_2Ec_2Ebool_2ET
<=> ! [X0: $o] : ( X0 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ET__DEF) ).
thf(f26,conjecture,
mono_2Ec_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(f27,negated_conjecture,
~ mono_2Ec_2Ebool_2ET,
inference(negated_conjecture,[status(cth)],[f26]) ).
thf(f28,plain,
( mono_2Ec_2Ebool_2ET
<=> ! [X0: $o] : ( X0 = X0 ) ),
inference(rectify,[],[f25]) ).
thf(f29,plain,
( ( mono_2Ec_2Ebool_2ET = $true )
<=> ! [X0: $o] : ( X0 = X0 ) ),
inference(fool_elimination,[],[f28]) ).
thf(f44,plain,
~ mono_2Ec_2Ebool_2ET,
inference(rectify,[],[f27]) ).
thf(f45,plain,
mono_2Ec_2Ebool_2ET != $true,
inference(fool_elimination,[],[f44]) ).
thf(f53,plain,
mono_2Ec_2Ebool_2ET != $true,
inference(flattening,[],[f45]) ).
thf(f72,plain,
( ( ( mono_2Ec_2Ebool_2ET = $true )
| ? [X0: $o] : ( X0 != X0 ) )
& ( ! [X0: $o] : ( X0 = X0 )
| ( mono_2Ec_2Ebool_2ET != $true ) ) ),
inference(nnf_transformation,[],[f29]) ).
thf(f73,plain,
( ( ( mono_2Ec_2Ebool_2ET = $true )
| ? [X0: $o] : ( X0 != X0 ) )
& ( ! [X1: $o] : ( X1 = X1 )
| ( mono_2Ec_2Ebool_2ET != $true ) ) ),
inference(rectify,[],[f72]) ).
thf(f74,plain,
( ( ( mono_2Ec_2Ebool_2ET = $true )
| ( sK2 != sK2 ) )
& ( ! [X1: $o] : ( X1 = X1 )
| ( mono_2Ec_2Ebool_2ET != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f73]) ).
thf(f96,plain,
mono_2Ec_2Ebool_2ET != $true,
inference(cnf_transformation,[],[f53]) ).
thf(f108,plain,
( ( sK2 != sK2 )
| ( mono_2Ec_2Ebool_2ET = $true ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f132,plain,
( ( sK2 = $true )
| ( mono_2Ec_2Ebool_2ET = $true )
| ( sK2 = $true ) ),
inference(xor_proxy_clausification,[],[f108]) ).
thf(f133,plain,
( ( mono_2Ec_2Ebool_2ET = $true )
| ( $false = sK2 )
| ( $false = sK2 ) ),
inference(xor_proxy_clausification,[],[f108]) ).
thf(f134,plain,
( ( mono_2Ec_2Ebool_2ET = $true )
| ( $false = sK2 ) ),
inference(duplicate_literal_removal,[],[f133]) ).
thf(f135,plain,
( ( mono_2Ec_2Ebool_2ET = $true )
| ( sK2 = $true ) ),
inference(duplicate_literal_removal,[],[f132]) ).
thf(f149,plain,
$false = sK2,
inference(forward_subsumption_resolution,[],[f134,f96]) ).
thf(f150,plain,
sK2 = $true,
inference(forward_subsumption_resolution,[],[f135,f96]) ).
thf(f151,plain,
$false = $true,
inference(forward_demodulation,[],[f150,f149]) ).
thf(f152,plain,
$false,
inference(trivial_inequality_removal,[],[f151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP001^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n019.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 19:17:18 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.28 % (1225876)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1225885)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2496243642:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.28 % (1225885) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1225876-1225885"...
% 0.22/0.28 % (1225887)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (1225885)...printing done.
% 0.22/0.28 % (1225887)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.28 % (1225885)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (1225885)------------------------------
% 0.22/0.29 % (1225885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (1225885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (1225885)CaDiCaL version: 2.1.3
% 0.22/0.29 % (1225885)Termination reason: Refutation
% 0.22/0.29 % (1225885)Time elapsed: 0.003 s
% 0.22/0.29 % (1225885)Peak memory usage: 12 MB
% 0.22/0.29 % (1225885)Instructions burned: 12 (million)
% 0.22/0.29 % (1225876)Success in time 0.039 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------