%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU919^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:31:56 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 66 ( 32 unt; 0 typ; 12 def)
% Number of atoms : 223 ( 52 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 186 ( 36 ~; 26 |; 4 &; 106 @)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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 : 22 ( 19 usr; 15 con; 0-4 aty)
% Number of variables : 18 ( 0 sgn 2 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
g: $i > $i ).
thf(func_def_3,type,
cP: $i > $o ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
sF2: $o ).
thf(func_def_14,type,
sF5: $o ).
thf(f1,conjecture,
( ( ( ^ [X0: $i] : ( g @ ( f @ X0 ) ) )
= ( ^ [X0: $i] : ( f @ ( g @ X0 ) ) ) )
=> ( ( cP @ ( f @ ( g @ a ) ) )
=> ( cP @ ( g @ ( f @ a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM127_pme) ).
thf(f2,negated_conjecture,
~ ( ( ( ^ [X0: $i] : ( g @ ( f @ X0 ) ) )
= ( ^ [X0: $i] : ( f @ ( g @ X0 ) ) ) )
=> ( ( cP @ ( f @ ( g @ a ) ) )
=> ( cP @ ( g @ ( f @ a ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ^ [X0: $i] : ( g @ ( f @ X0 ) ) )
= ( ^ [X1: $i] : ( f @ ( g @ X1 ) ) ) )
=> ( ( cP @ ( f @ ( g @ a ) ) )
=> ( cP @ ( g @ ( f @ a ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) )
= ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) ) )
=> ( ( ( cP @ ( f @ ( g @ a ) ) )
= $true )
=> ( ( cP @ ( g @ ( f @ a ) ) )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( cP @ ( g @ ( f @ a ) ) )
!= $true )
& ( ( cP @ ( f @ ( g @ a ) ) )
= $true )
& ( ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) )
= ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( cP @ ( f @ ( g @ a ) ) )
= $true )
& ( ( cP @ ( g @ ( f @ a ) ) )
!= $true )
& ( ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) )
= ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) )
= ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( ( cP @ ( g @ ( f @ a ) ) )
!= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
( ( cP @ ( f @ ( g @ a ) ) )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f12,definition,
( sF0
= ( g @ a ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f13,plain,
( ( g @ a )
= sF0 ),
inference(reorient_equations,[],[f12]) ).
thf(f14,definition,
( sF1
= ( f @ sF0 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f15,plain,
( ( f @ sF0 )
= sF1 ),
inference(reorient_equations,[],[f14]) ).
thf(f16,definition,
( sF2
= ( cP @ sF1 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f17,plain,
( ( cP @ sF1 )
= sF2 ),
inference(reorient_equations,[],[f16]) ).
thf(f18,plain,
$true = sF2,
inference(definition_folding,[],[f9,f17,f15,f13]) ).
thf(f19,definition,
( sF3
= ( f @ a ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f20,plain,
( ( f @ a )
= sF3 ),
inference(reorient_equations,[],[f19]) ).
thf(f21,definition,
( sF4
= ( g @ sF3 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f22,definition,
( sF5
= ( cP @ sF4 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f23,plain,
( ( cP @ sF4 )
= sF5 ),
inference(reorient_equations,[],[f22]) ).
thf(f24,plain,
$true != sF5,
inference(definition_folding,[],[f8,f23,f21,f20]) ).
thf(f26,plain,
( ( $true = sF5 )
| ( ( cP @ sF4 )
= $false ) ),
inference(iff_proxy_clausification,[],[f23]) ).
thf(f27,plain,
( ( sF2 = $false )
| ( ( cP @ sF1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f17]) ).
thf(f30,definition,
( spl6_1
<=> ( ( cP @ sF4 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f32,plain,
( ( ( cP @ sF4 )
= $false )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f34,definition,
( spl6_2
<=> ( $true = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f37,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f26,f34,f30]) ).
thf(f47,plain,
~ spl6_2,
inference(avatar_split_clause,[],[f24,f34]) ).
thf(f49,definition,
( spl6_5
<=> ( ( cP @ sF1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f51,plain,
( ( ( cP @ sF1 )
= $false )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f53,definition,
( spl6_6
<=> ( $true = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f55,plain,
( ( $true = sF2 )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f58,definition,
( spl6_7
<=> ( sF2 = $false ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f60,plain,
( ( sF2 = $false )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f62,definition,
( spl6_8
<=> ( ( cP @ sF1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f64,plain,
( ( ( cP @ sF1 )
= $true )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f65,plain,
( spl6_7
| spl6_8 ),
inference(avatar_split_clause,[],[f27,f62,f58]) ).
thf(f66,plain,
spl6_6,
inference(avatar_split_clause,[],[f18,f53]) ).
thf(f67,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) )
@ X1 )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[],[f7]) ).
thf(f68,plain,
! [X1: $i] :
( ( f @ ( g @ X1 ) )
= ( g @ ( f @ X1 ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
( ( $true = $false )
| ~ spl6_6
| ~ spl6_7 ),
inference(forward_demodulation,[],[f60,f55]) ).
thf(f70,plain,
( $false
| ~ spl6_6
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f71,plain,
( ~ spl6_6
| ~ spl6_7 ),
inference(avatar_contradiction_clause,[],[f70]) ).
thf(f94,plain,
( ( f @ ( g @ a ) )
= ( g @ sF3 ) ),
inference(constrained_superposition,[],[f68,f20]) ).
thf(f95,plain,
( ( f @ sF0 )
= ( g @ sF3 ) ),
inference(forward_demodulation,[],[f94,f13]) ).
thf(f96,plain,
( sF1
= ( g @ sF3 ) ),
inference(forward_demodulation,[],[f95,f15]) ).
thf(f97,plain,
sF1 = sF4,
inference(forward_demodulation,[],[f96,f21]) ).
thf(f98,plain,
( ( ( cP @ sF1 )
= $false )
| ~ spl6_1 ),
inference(forward_demodulation,[],[f32,f97]) ).
thf(f99,plain,
( spl6_5
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f98,f30,f49]) ).
thf(f104,plain,
( ( $true = $false )
| ~ spl6_5
| ~ spl6_8 ),
inference(forward_demodulation,[],[f64,f51]) ).
thf(f105,plain,
( $false
| ~ spl6_5
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f106,plain,
( ~ spl6_5
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f105]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f37]) ).
cnf(s3,plain,
~ spl6_2,
inference(sat_conversion,[],[f47]) ).
cnf(s5,plain,
( spl6_7
| spl6_8 ),
inference(sat_conversion,[],[f65]) ).
cnf(s6,plain,
spl6_6,
inference(sat_conversion,[],[f66]) ).
cnf(s7,plain,
( ~ spl6_6
| ~ spl6_7 ),
inference(sat_conversion,[],[f71]) ).
cnf(s9,plain,
( ~ spl6_1
| spl6_5 ),
inference(sat_conversion,[],[f99]) ).
cnf(s11,plain,
( ~ spl6_5
| ~ spl6_8 ),
inference(sat_conversion,[],[f106]) ).
cnf(s12,plain,
~ spl6_7,
inference(rat,[],[s7,s6]) ).
cnf(s13,plain,
spl6_8,
inference(rat,[],[s5,s12]) ).
cnf(s14,plain,
~ spl6_5,
inference(rat,[],[s11,s13]) ).
cnf(s15,plain,
~ spl6_1,
inference(rat,[],[s9,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s3,s15]) ).
thf(f107,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU919^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n005.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 14:46:01 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.21/0.28 % (1761971)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (1761992)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (1761992)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
% 0.21/0.28 % (1761992)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=1791574018:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (1761992) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1761971-1761992"...
% 0.21/0.28 % (1761992)...printing done.
% 0.21/0.28 % (1761992)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (1761992)------------------------------
% 0.21/0.28 % (1761992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1761992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1761992)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1761992)Termination reason: Refutation
% 0.21/0.28 % (1761992)Time elapsed: 0.003 s
% 0.21/0.28 % (1761992)Peak memory usage: 13 MB
% 0.21/0.28 % (1761992)Instructions burned: 7 (million)
% 0.21/0.28 % (1761971)Success in time 0.036 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------