%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM651^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:18:24 AM UTC 2026
% Result : Theorem 0.25s 0.30s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 64 ( 17 unt; 0 typ; 5 def)
% Number of atoms : 155 ( 89 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 354 ( 101 ~; 54 |; 12 &; 162 @)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 46 !; 12 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: nat ).
thf(func_def_1,type,
y: nat ).
thf(func_def_2,type,
pl: nat > nat > nat ).
thf(func_def_6,type,
sK0: nat ).
thf(func_def_7,type,
sK1: nat ).
thf(func_def_8,type,
sK2: nat ).
thf(func_def_9,type,
sK3: nat ).
thf(func_def_10,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X1: nat,X0: nat] :
( X1
!= ( pl @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz7) ).
thf(f2,axiom,
! [X1: nat,X0: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).
thf(f4,axiom,
! [X2: nat,X0: nat,X1: nat] :
( ( pl @ ( pl @ X0 @ X1 ) @ X2 )
= ( pl @ X0 @ ( pl @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz5) ).
thf(f5,conjecture,
~ ( ( ( x = y )
=> ~ ~ ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) ) )
=> ~ ~ ( ( ~ ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) )
=> ~ ~ ! [X0: nat] :
( y
!= ( pl @ x @ X0 ) ) )
=> ~ ( ~ ! [X0: nat] :
( y
!= ( pl @ x @ X0 ) )
=> ( x != y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz9b) ).
thf(f6,negated_conjecture,
~ ~ ( ( ( x = y )
=> ~ ~ ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) ) )
=> ~ ~ ( ( ~ ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) )
=> ~ ~ ! [X0: nat] :
( y
!= ( pl @ x @ X0 ) ) )
=> ~ ( ~ ! [X0: nat] :
( y
!= ( pl @ x @ X0 ) )
=> ( x != y ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f9,plain,
! [X0: nat,X1: nat] :
( ( pl @ X1 @ X0 )
!= X0 ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
~ ~ ( ( ( x = y )
=> ~ ~ ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) ) )
=> ~ ~ ( ( ~ ! [X1: nat] :
( x
!= ( pl @ y @ X1 ) )
=> ~ ~ ! [X2: nat] :
( y
!= ( pl @ x @ X2 ) ) )
=> ~ ( ~ ! [X3: nat] :
( y
!= ( pl @ x @ X3 ) )
=> ( x != y ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f12,plain,
( ( ( x = y )
=> ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) ) )
=> ( ( ~ ! [X1: nat] :
( x
!= ( pl @ y @ X1 ) )
=> ! [X2: nat] :
( y
!= ( pl @ x @ X2 ) ) )
=> ~ ( ~ ! [X3: nat] :
( y
!= ( pl @ x @ X3 ) )
=> ( x != y ) ) ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( pl @ ( pl @ X1 @ X2 ) @ X0 )
= ( pl @ X1 @ ( pl @ X2 @ X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
! [X1: nat,X0: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f16,plain,
( ( ( x = y )
& ? [X3: nat] :
( y
= ( pl @ x @ X3 ) ) )
| ( ? [X1: nat] :
( x
= ( pl @ y @ X1 ) )
& ? [X2: nat] :
( y
= ( pl @ x @ X2 ) ) )
| ( ? [X0: nat] :
( x
= ( pl @ y @ X0 ) )
& ( x = y ) ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f17,plain,
( ( ? [X0: nat] :
( x
= ( pl @ y @ X0 ) )
& ( x = y ) )
| ( ( x = y )
& ? [X3: nat] :
( y
= ( pl @ x @ X3 ) ) )
| ( ? [X1: nat] :
( x
= ( pl @ y @ X1 ) )
& ? [X2: nat] :
( y
= ( pl @ x @ X2 ) ) ) ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
( ( ? [X0: nat] :
( x
= ( pl @ y @ X0 ) )
& ( x = y ) )
| ( ( x = y )
& ? [X1: nat] :
( y
= ( pl @ x @ X1 ) ) )
| ( ? [X2: nat] :
( x
= ( pl @ y @ X2 ) )
& ? [X3: nat] :
( y
= ( pl @ x @ X3 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f19,plain,
( ( ( x
= ( pl @ y @ sK0 ) )
& ( x = y ) )
| ( ( x = y )
& ( y
= ( pl @ x @ sK1 ) ) )
| ( ( x
= ( pl @ y @ sK2 ) )
& ( y
= ( pl @ x @ sK3 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f18]) ).
thf(f20,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(rectify,[],[f14]) ).
thf(f21,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( pl @ ( pl @ X2 @ X0 ) @ X1 )
= ( pl @ X2 @ ( pl @ X0 @ X1 ) ) ),
inference(rectify,[],[f13]) ).
thf(f22,plain,
! [X0: nat,X1: nat] :
( ( pl @ X1 @ X0 )
!= X0 ),
inference(cnf_transformation,[],[f9]) ).
thf(f26,plain,
( ( x = y )
| ( y
= ( pl @ x @ sK3 ) )
| ( x = y ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f27,plain,
( ( x = y )
| ( x = y )
| ( x
= ( pl @ y @ sK2 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f29,plain,
( ( y
= ( pl @ x @ sK1 ) )
| ( x
= ( pl @ y @ sK2 ) )
| ( x
= ( pl @ y @ sK0 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f32,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f33,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( pl @ ( pl @ X2 @ X0 ) @ X1 )
= ( pl @ X2 @ ( pl @ X0 @ X1 ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f37,plain,
( ( x
= ( pl @ y @ sK2 ) )
| ( x = y ) ),
inference(duplicate_literal_removal,[],[f27]) ).
thf(f38,plain,
( ( x = y )
| ( y
= ( pl @ x @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f26]) ).
thf(f40,definition,
( spl4_1
<=> ( y
= ( pl @ x @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f42,plain,
( ( y
= ( pl @ x @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f44,definition,
( spl4_2
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f46,plain,
( ( x = y )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f48,definition,
( spl4_3
<=> ( y
= ( pl @ x @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f50,plain,
( ( y
= ( pl @ x @ sK1 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f53,definition,
( spl4_4
<=> ( x
= ( pl @ y @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f55,plain,
( ( x
= ( pl @ y @ sK2 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f56,plain,
( spl4_4
| spl4_2 ),
inference(avatar_split_clause,[],[f37,f44,f53]) ).
thf(f58,definition,
( spl4_5
<=> ( x
= ( pl @ y @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f60,plain,
( ( x
= ( pl @ y @ sK0 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f62,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f38,f40,f44]) ).
thf(f64,plain,
( spl4_5
| spl4_4
| spl4_3 ),
inference(avatar_split_clause,[],[f29,f48,f53,f58]) ).
thf(f72,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
!= X0 ),
inference(constrained_superposition,[],[f22,f32]) ).
thf(f74,plain,
( ( x != y )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f72,f50]) ).
thf(f80,plain,
( $false
| ~ spl4_2
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f74,f46]) ).
thf(f81,plain,
( ~ spl4_2
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f80]) ).
thf(f82,plain,
( ( y
= ( pl @ y @ sK0 ) )
| ~ spl4_2
| ~ spl4_5 ),
inference(forward_demodulation,[],[f60,f46]) ).
thf(f84,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f82,f72]) ).
thf(f85,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f84]) ).
thf(f87,plain,
( ( y
= ( pl @ y @ sK2 ) )
| ~ spl4_2
| ~ spl4_4 ),
inference(forward_demodulation,[],[f55,f46]) ).
thf(f91,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f87,f72]) ).
thf(f92,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f91]) ).
thf(f99,plain,
( ! [X0: nat] :
( ( pl @ y @ X0 )
= ( pl @ x @ ( pl @ sK3 @ X0 ) ) )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f33,f42]) ).
thf(f115,plain,
( ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f72,f99]) ).
thf(f121,plain,
( ( x != x )
| ~ spl4_1
| ~ spl4_4 ),
inference(constrained_superposition,[],[f115,f55]) ).
thf(f122,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f123,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f122]) ).
cnf(s2,plain,
( spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f62]) ).
cnf(s6,plain,
( spl4_3
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f64]) ).
cnf(s10,plain,
( ~ spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f81]) ).
cnf(s11,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f85]) ).
cnf(s13,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f92]) ).
cnf(s14,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f123]) ).
cnf(s15,plain,
~ spl4_2,
inference(rat,[],[s6,s10,s11,s13]) ).
cnf(s16,plain,
spl4_1,
inference(rat,[],[s4,s15]) ).
cnf(s17,plain,
spl4_4,
inference(rat,[],[s2,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s14,s17,s16]) ).
thf(f124,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM651^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n026.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 12:34:27 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.25/0.30 % (528918)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.30 % (528933)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=410478422:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.30 % (528933) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-528918-528933"...
% 0.25/0.30 % (528933)...printing done.
% 0.25/0.30 % (528939)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.30 % (528939)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
% 0.25/0.30 % (528933)Refutation found. Thanks to Tanya!
% 0.25/0.30 % SZS status Theorem for theBenchmark
% 0.25/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.30 % (528933)------------------------------
% 0.25/0.30 % (528933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.30 % (528933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.30 % (528933)CaDiCaL version: 2.1.3
% 0.25/0.30 % (528933)Termination reason: Refutation
% 0.25/0.30 % (528933)Time elapsed: 0.003 s
% 0.25/0.30 % (528933)Peak memory usage: 13 MB
% 0.25/0.30 % (528933)Instructions burned: 8 (million)
% 0.25/0.30 % (528918)Success in time 0.035 s
% 0.25/0.30 % Vampire exiting
%------------------------------------------------------------------------------