%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP010^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:07:42 AM UTC 2026
% Result : Theorem 0.28s 0.40s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 17 unt; 0 typ; 4 def)
% Number of atoms : 95 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 112 ( 33 ~; 10 |; 0 &; 64 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 8 con; 0-4 aty)
% Number of variables : 20 ( 0 sgn 16 !; 4 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
tyop_2Emin_2Ebool: $tType ).
thf(type_def_6,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
sK13: $tType ).
thf(type_def_9,type,
sK14: $tType ).
thf(func_def_0,type,
c_2Ebool_2E_21:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_2,type,
c_2Emin_2E_3D:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_3,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_4,type,
c_2Ebool_2E_3F:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
c_2Ebool_2EF: $o ).
thf(func_def_6,type,
c_2Ebool_2ET: $o ).
thf(func_def_7,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_8,type,
c_2Ecardinal_2Ecardleq:
!>[X0: $tType,X1: $tType] : ( ( X0 > $o ) > ( X1 > $o ) > $o ) ).
thf(func_def_9,type,
c_2Ebool_2E_7E: $o > $o ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(func_def_14,type,
vOR: $o > $o > $o ).
thf(func_def_15,type,
sP0: $o > $o ).
thf(func_def_16,type,
sP1: $o > $o > $o ).
thf(func_def_17,type,
sP2: $o > $o > $o ).
thf(func_def_18,type,
sP3: $o > $o > $o ).
thf(func_def_19,type,
sP4: $o > $o > $o ).
thf(func_def_20,type,
sP5: $o > $o > $o > $o ).
thf(func_def_21,type,
sP6: $o > $o > $o > $o ).
thf(func_def_22,type,
sP7: $o > $o > $o > $o ).
thf(func_def_23,type,
sP8: $o > $o > $o > $o ).
thf(func_def_24,type,
sP9: $o > $o > $o > $o ).
thf(func_def_25,type,
sP10: $o > $o > $o > $o ).
thf(func_def_26,type,
sK11:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_27,type,
sK12:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_28,type,
sK15: sK14 > $o ).
thf(func_def_29,type,
sK16: sK13 > $o ).
thf(func_def_30,type,
sF17: $o ).
thf(func_def_31,type,
sF18: $o ).
thf(f23,conjecture,
! [X1: $tType,X0: $tType,X2: X0 > $o,X3: X1 > $o] :
( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 )
<=> ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ECARD__NOT__LE) ).
thf(f24,negated_conjecture,
~ ! [X1: $tType,X0: $tType,X2: X0 > $o,X3: X1 > $o] :
( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 )
<=> ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f39,plain,
~ ! [X0: $tType,X1: $tType,X2: X1 > $o,X3: X0 > $o] :
( ~ ( c_2Ecardinal_2Ecardleq @ X1 @ X0 @ X2 @ X3 )
<=> ~ ( c_2Ecardinal_2Ecardleq @ X1 @ X0 @ X2 @ X3 ) ),
inference(rectify,[],[f24]) ).
thf(f40,plain,
~ ! [X1: $tType,X0: $tType,X3: X0 > $o,X2: X1 > $o] :
( ( ~ ( c_2Ecardinal_2Ecardleq @ X1 @ X0 @ X2 @ X3 ) )
= ( ~ ( c_2Ecardinal_2Ecardleq @ X1 @ X0 @ X2 @ X3 ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f81,plain,
? [X0: $tType,X1: $tType,X2: X1 > $o,X3: X0 > $o] :
( ( ~ ( c_2Ecardinal_2Ecardleq @ X1 @ X0 @ X2 @ X3 ) )
!= ( ~ ( c_2Ecardinal_2Ecardleq @ X1 @ X0 @ X2 @ X3 ) ) ),
inference(ennf_transformation,[],[f40]) ).
thf(f148,plain,
( ( ~ ( c_2Ecardinal_2Ecardleq @ sK14 @ sK13 @ sK15 @ sK16 ) )
!= ( ~ ( c_2Ecardinal_2Ecardleq @ sK14 @ sK13 @ sK15 @ sK16 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15),skolemize(X3,sK16)],[f81]) ).
thf(f246,plain,
( ( ~ ( c_2Ecardinal_2Ecardleq @ sK14 @ sK13 @ sK15 @ sK16 ) )
!= ( ~ ( c_2Ecardinal_2Ecardleq @ sK14 @ sK13 @ sK15 @ sK16 ) ) ),
inference(cnf_transformation,[],[f148]) ).
thf(f322,definition,
( sF17
= ( c_2Ecardinal_2Ecardleq @ sK14 @ sK13 @ sK15 @ sK16 ) ),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
thf(f323,plain,
( ( c_2Ecardinal_2Ecardleq @ sK14 @ sK13 @ sK15 @ sK16 )
= sF17 ),
inference(reorient_equations,[],[f322]) ).
thf(f324,definition,
( sF18 = ( ~ sF17 ) ),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
thf(f325,plain,
sF18 != sF18,
inference(definition_folding,[],[f246,f324,f323,f324,f323]) ).
thf(f375,plain,
( ( sF18 = $true )
| ( sF18 = $true ) ),
inference(xor_proxy_clausification,[],[f325]) ).
thf(f376,plain,
( ( $false = sF18 )
| ( $false = sF18 ) ),
inference(xor_proxy_clausification,[],[f325]) ).
thf(f377,plain,
$false = sF18,
inference(duplicate_literal_removal,[],[f376]) ).
thf(f378,plain,
sF18 = $true,
inference(duplicate_literal_removal,[],[f375]) ).
thf(f467,definition,
( spl19_10
<=> ( $false = sF18 ) ),
introduced(definition,[new_symbols(definition,[spl19_10])],[avatar_definition]) ).
thf(f469,plain,
( ( $false = sF18 )
| ~ spl19_10 ),
inference(avatar_component_clause,[],[f467]) ).
thf(f472,definition,
( spl19_11
<=> ( sF18 = $true ) ),
introduced(definition,[new_symbols(definition,[spl19_11])],[avatar_definition]) ).
thf(f474,plain,
( ( sF18 = $true )
| ~ spl19_11 ),
inference(avatar_component_clause,[],[f472]) ).
thf(f486,plain,
spl19_10,
inference(avatar_split_clause,[],[f377,f467]) ).
thf(f487,plain,
spl19_11,
inference(avatar_split_clause,[],[f378,f472]) ).
thf(f518,plain,
( ( $false = $true )
| ~ spl19_10
| ~ spl19_11 ),
inference(forward_demodulation,[],[f474,f469]) ).
thf(f519,plain,
( $false
| ~ spl19_10
| ~ spl19_11 ),
inference(trivial_inequality_removal,[],[f518]) ).
thf(f520,plain,
( ~ spl19_10
| ~ spl19_11 ),
inference(avatar_contradiction_clause,[],[f519]) ).
cnf(s14,plain,
spl19_10,
inference(sat_conversion,[],[f486]) ).
cnf(s15,plain,
spl19_11,
inference(sat_conversion,[],[f487]) ).
cnf(s33,plain,
( ~ spl19_10
| ~ spl19_11 ),
inference(sat_conversion,[],[f520]) ).
cnf(s34,plain,
~ spl19_10,
inference(rat,[],[s33,s15]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s14,s34]) ).
thf(f521,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ITP010^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 % Computer : n013.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Tue Sep 29 19:24:36 UTC 2026
% 0.11/0.28 % CPUTime :
% 0.11/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.33 Running higher-order theorem proving
% 0.28/0.35 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
% 0.28/0.40 % (2538396)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.28/0.40 % (2538407)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.28/0.40 % (2538407)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
% 0.28/0.40 % (2538407)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3189298378:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.28/0.40 % (2538407) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2538396-2538407"...
% 0.28/0.40 % (2538407)...printing done.
% 0.28/0.40 % (2538407)Refutation found. Thanks to Tanya!
% 0.28/0.40 % SZS status Theorem for theBenchmark
% 0.28/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.28/0.40 % (2538407)------------------------------
% 0.28/0.40 % (2538407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.40 % (2538407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.40 % (2538407)CaDiCaL version: 2.1.3
% 0.28/0.40 % (2538407)Termination reason: Refutation
% 0.28/0.40 % (2538407)Time elapsed: 0.007 s
% 0.28/0.40 % (2538407)Peak memory usage: 13 MB
% 0.28/0.40 % (2538407)Instructions burned: 11 (million)
% 0.28/0.40 % (2538396)Success in time 0.04 s
% 0.28/0.40 % Vampire exiting
%------------------------------------------------------------------------------