%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM651^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 08:19:12 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 13 unt; 0 typ; 3 def)
% Number of atoms : 124 ( 86 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 300 ( 82 ~; 41 |; 12 &; 142 @)
% ( 3 <=>; 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 : 14 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 34 !; 12 ?; 46 :)
% 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,
! [X0: nat,X1: nat] :
( X1
!= ( pl @ X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz7) ).
thf(f2,axiom,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
thf(f4,axiom,
! [X0: nat,X1: nat,X2: nat] :
( ( pl @ ( pl @ X0 @ X1 ) @ X2 )
= ( pl @ X0 @ ( pl @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/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/sandbox/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(f10,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(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(flattening,[],[f10]) ).
thf(f13,plain,
( ( ( x = y )
& ? [X3: nat] :
( y
= ( pl @ x @ X3 ) ) )
| ( ? [X2: nat] :
( y
= ( pl @ x @ X2 ) )
& ? [X1: nat] :
( x
= ( pl @ y @ X1 ) ) )
| ( ? [X0: nat] :
( x
= ( pl @ y @ X0 ) )
& ( x = y ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f14,plain,
( ( ( x = y )
& ? [X3: nat] :
( y
= ( pl @ x @ X3 ) ) )
| ( ? [X2: nat] :
( y
= ( pl @ x @ X2 ) )
& ? [X1: nat] :
( x
= ( pl @ y @ X1 ) ) )
| ( ? [X0: nat] :
( x
= ( pl @ y @ X0 ) )
& ( x = y ) ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ( ( x = y )
& ? [X0: nat] :
( y
= ( pl @ x @ X0 ) ) )
| ( ? [X1: nat] :
( y
= ( pl @ x @ X1 ) )
& ? [X2: nat] :
( x
= ( pl @ y @ X2 ) ) )
| ( ? [X3: nat] :
( x
= ( pl @ y @ X3 ) )
& ( x = y ) ) ),
inference(rectify,[],[f14]) ).
thf(f16,plain,
( ( ( x = y )
& ( y
= ( pl @ x @ sK0 ) ) )
| ( ( y
= ( pl @ x @ sK1 ) )
& ( x
= ( pl @ y @ sK2 ) ) )
| ( ( x
= ( pl @ y @ sK3 ) )
& ( x = y ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f15]) ).
thf(f17,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
!= X1 ),
inference(cnf_transformation,[],[f1]) ).
thf(f18,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f2]) ).
thf(f20,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( pl @ ( pl @ X0 @ X1 ) @ X2 )
= ( pl @ X0 @ ( pl @ X1 @ X2 ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f22,plain,
( ( y
= ( pl @ x @ sK0 ) )
| ( x
= ( pl @ y @ sK2 ) )
| ( x
= ( pl @ y @ sK3 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f25,plain,
( ( x = y )
| ( x
= ( pl @ y @ sK2 ) )
| ( x = y ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,plain,
( ( x = y )
| ( y
= ( pl @ x @ sK1 ) )
| ( x = y ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f32,plain,
( ( x = y )
| ( x
= ( pl @ y @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f25]) ).
thf(f33,plain,
( ( x = y )
| ( y
= ( pl @ x @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f27]) ).
thf(f37,definition,
( spl4_1
<=> ( x
= ( pl @ y @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f39,plain,
( ( x
= ( pl @ y @ sK2 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f41,definition,
( spl4_2
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f43,plain,
( ( x = y )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f44,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f32,f41,f37]) ).
thf(f47,definition,
( spl4_3
<=> ( y
= ( pl @ x @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f49,plain,
( ( y
= ( pl @ x @ sK1 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f47]) ).
thf(f50,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f33,f41,f47]) ).
thf(f106,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
!= X0 ),
inference(constrained_superposition,[],[f17,f18]) ).
thf(f122,plain,
( ( x
= ( pl @ x @ sK0 ) )
| ( x
= ( pl @ y @ sK2 ) )
| ( x
= ( pl @ y @ sK3 ) )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f22,f43]) ).
thf(f123,plain,
( ( x
= ( pl @ y @ sK2 ) )
| ( x
= ( pl @ y @ sK3 ) )
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f122,f106]) ).
thf(f124,plain,
( ( x
= ( pl @ x @ sK2 ) )
| ( x
= ( pl @ y @ sK3 ) )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f123,f43]) ).
thf(f125,plain,
( ( x
= ( pl @ y @ sK3 ) )
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f124,f106]) ).
thf(f126,plain,
( ( x
= ( pl @ x @ sK3 ) )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f125,f43]) ).
thf(f127,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f126,f106]) ).
thf(f128,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f127]) ).
thf(f137,plain,
( ! [X0: nat] :
( ( pl @ y @ X0 )
= ( pl @ x @ ( pl @ sK1 @ X0 ) ) )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f20,f49]) ).
thf(f466,plain,
( ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f106,f137]) ).
thf(f506,plain,
( ( x != x )
| ~ spl4_1
| ~ spl4_3 ),
inference(constrained_superposition,[],[f466,f39]) ).
thf(f507,plain,
( $false
| ~ spl4_1
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f506]) ).
thf(f508,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f507]) ).
cnf(s19,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s25,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f50]) ).
cnf(s54,plain,
~ spl4_2,
inference(sat_conversion,[],[f128]) ).
cnf(s249,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(sat_conversion,[],[f508]) ).
cnf(s252,plain,
spl4_3,
inference(rat,[],[s25,s54]) ).
cnf(s253,plain,
~ spl4_1,
inference(rat,[],[s249,s252]) ).
cnf(s254,plain,
$false,
inference(rat,[],[s19,s54,s253]) ).
thf(f509,plain,
$false,
inference(avatar_sat_refutation,[],[s254]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 12:34:28 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.26 % (529108)Will run a generic schedule for satisfiability detection.
% 0.20/0.26 % (529115)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1321941928:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.20/0.26 % (529114)% WARNING: option uhcvi not known.
% 0.20/0.26 % (529116)dis+10_1_sil=32000:sp=arity:random_seed=3540110291:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.20/0.26 % (529113)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2144783754_3000 on theBenchmark for (3000ds/0Mi)
% 0.20/0.26 % (529114)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=980216634:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.20/0.26 % (529117)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=854516496:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.20/0.26 % (529119)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2305989143:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.20/0.26 % (529114)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.26 % Exception at run slice level
% 0.20/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.26 % (529118)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3983805644:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.20/0.26 % (529117)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.26 % (529114)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.26 % (529115) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-529108-529115"...
% 0.20/0.26 % (529115)...printing done.
% 0.20/0.26 % (529116) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-529108-529116"...
% 0.20/0.26 % (529115)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.26 % (529115)------------------------------
% 0.20/0.26 % (529115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (529115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (529115)CaDiCaL version: 2.1.3
% 0.20/0.26 % (529115)Termination reason: Refutation
% 0.20/0.26 % (529115)Time elapsed: 0.011 s
% 0.20/0.26 % (529115)Peak memory usage: 13 MB
% 0.20/0.26 % (529115)Instructions burned: 36 (million)
% 0.20/0.26 % (529108)Success in time 0.026 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------