%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX228_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 : Tue Sep 29 01:46:47 PM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 85 ( 32 unt; 0 typ; 9 def)
% Number of atoms : 304 ( 23 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 176 ( 81 ~; 82 |; 0 &)
% ( 12 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 142 ( 128 fml; 14 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 19 usr; 13 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 83 ( 0 sgn 79 !; 4 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_1,type,
barbar: ( $o * $o ) > $o ).
tff(pred_def_5,type,
sP0: $o > $o ).
tff(pred_def_6,type,
sP1: $o > $o ).
tff(f2,axiom,
! [X0: $i,X1: $i] : ( tail(cons(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
tff(f3,axiom,
! [X0: $i,X1: $i] : ( nil != cons(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
tff(f6,axiom,
! [X0: $o,X1: $o] :
( barbar((X0),(X1))
<=> ( (X0)
| (X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
tff(f11,axiom,
eqNat(z,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
tff(f13,axiom,
! [X0: $i,X1: $i,X2: $i] :
( elem(X0,cons(X1,X2))
<=> barbar(eqNat(X0,X1),elem(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
tff(f14,axiom,
! [X0: $i] : ( union(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
tff(f15,axiom,
! [X0: $i,X1: $i,X2: $i] :
( elem(X1,X0)
=> ( union(cons(X1,X2),X0) = union(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
tff(f17,conjecture,
? [X0: $i,X1: $i] : ( union(X0,X1) != union(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_018) ).
tff(f18,negated_conjecture,
~ ? [X0: $i,X1: $i] : ( union(X0,X1) != union(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
tff(f19,plain,
! [X0: $o,X1: $o] :
( barbar((X0),(X1))
<=> ( (X0)
| (X1) ) ),
inference(rectify,[],[f6]) ).
tff(f21,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( union(cons(X1,X2),X0) = union(X2,X0) )
| ~ elem(X1,X0) ),
inference(ennf_transformation,[],[f15]) ).
tff(f23,plain,
! [X0: $i,X1: $i] : ( union(X0,X1) = union(X1,X0) ),
inference(ennf_transformation,[],[f18]) ).
tff(f25,plain,
! [X0: $i,X1: $i] : ( tail(cons(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f2]) ).
tff(f26,plain,
! [X0: $i,X1: $i] : ( cons(X0,X1) != nil ),
inference(cnf_transformation,[],[f3]) ).
tff(f29,plain,
sP1($true),
inference(cnf_transformation,[],[f19]) ).
tff(f31,plain,
sP0($true),
inference(cnf_transformation,[],[f19]) ).
tff(f32,plain,
~ sP0($false),
inference(cnf_transformation,[],[f19]) ).
tff(f33,plain,
! [X1: $o] :
( sP0((X1))
| ~ sP1($true)
| barbar($true,$false) ),
inference(cnf_transformation,[],[f19]) ).
tff(f43,plain,
! [X0: $o] :
( ~ sP0($true)
| ~ sP1((X0))
| barbar($true,$true) ),
inference(cnf_transformation,[],[f19]) ).
tff(f49,plain,
eqNat(z,z),
inference(cnf_transformation,[],[f11]) ).
tff(f55,plain,
! [X2: $i,X0: $i,X1: $i] :
( elem(X0,X2)
| ~ eqNat(X0,X1)
| ~ barbar($true,$false)
| elem(X0,cons(X1,X2)) ),
inference(cnf_transformation,[],[f13]) ).
tff(f57,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ elem(X0,X2)
| ~ eqNat(X0,X1)
| ~ barbar($true,$true)
| elem(X0,cons(X1,X2)) ),
inference(cnf_transformation,[],[f13]) ).
tff(f59,plain,
! [X0: $i] : ( union(nil,X0) = X0 ),
inference(cnf_transformation,[],[f14]) ).
tff(f60,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ elem(X1,X0)
| ( union(cons(X1,X2),X0) = union(X2,X0) ) ),
inference(cnf_transformation,[],[f21]) ).
tff(f62,plain,
! [X0: $i,X1: $i] : ( union(X0,X1) = union(X1,X0) ),
inference(cnf_transformation,[],[f23]) ).
tff(f69,plain,
~ eqNat(z,z),
inference(consistent_polarity_flipping,[],[f49]) ).
tff(f71,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ elem(X0,X2)
| eqNat(X0,X1)
| ~ barbar($true,$true)
| elem(X0,cons(X1,X2)) ),
inference(consistent_polarity_flipping,[],[f57]) ).
tff(f73,plain,
! [X2: $i,X0: $i,X1: $i] :
( elem(X0,X2)
| eqNat(X0,X1)
| ~ barbar($true,$false)
| elem(X0,cons(X1,X2)) ),
inference(consistent_polarity_flipping,[],[f55]) ).
tff(f79,definition,
( spl2_1
<=> barbar($true,$false) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f95,definition,
( spl2_5
<=> barbar($true,$true) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
tff(f111,definition,
( spl2_9
<=> ! [X2: $i,X0: $i,X1: $i] :
( elem(X0,X2)
| elem(X0,cons(X1,X2))
| eqNat(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
tff(f112,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( elem(X0,cons(X1,X2))
| elem(X0,X2)
| eqNat(X0,X1) )
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f111]) ).
tff(f113,plain,
( ~ spl2_1
| spl2_9 ),
inference(avatar_split_clause,[],[f73,f111,f79]) ).
tff(f119,definition,
( spl2_11
<=> ! [X2: $i,X0: $i,X1: $i] :
( ~ elem(X0,X2)
| elem(X0,cons(X1,X2))
| eqNat(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
tff(f120,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ~ elem(X0,X2)
| elem(X0,cons(X1,X2))
| eqNat(X0,X1) )
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f119]) ).
tff(f121,plain,
( ~ spl2_5
| spl2_11 ),
inference(avatar_split_clause,[],[f71,f119,f95]) ).
tff(f127,definition,
( spl2_13
<=> sP1($true) ),
introduced(definition,[new_symbols(definition,[spl2_13])],[avatar_definition]) ).
tff(f128,plain,
( sP1($true)
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f127]) ).
tff(f131,definition,
( spl2_14
<=> ! [X1: $o] : sP0((X1)) ),
introduced(definition,[new_symbols(definition,[spl2_14])],[avatar_definition]) ).
tff(f132,plain,
( ! [X1: $o] : sP0((X1))
| ~ spl2_14 ),
inference(avatar_component_clause,[],[f131]) ).
tff(f133,plain,
( spl2_1
| ~ spl2_13
| spl2_14 ),
inference(avatar_split_clause,[],[f33,f131,f127,f79]) ).
tff(f145,definition,
( spl2_17
<=> sP0($false) ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
tff(f147,plain,
( ~ sP0($false)
| spl2_17 ),
inference(avatar_component_clause,[],[f145]) ).
tff(f153,definition,
( spl2_18
<=> ! [X0: $o] : ~ sP1((X0)) ),
introduced(definition,[new_symbols(definition,[spl2_18])],[avatar_definition]) ).
tff(f154,plain,
( ! [X0: $o] : ~ sP1((X0))
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f153]) ).
tff(f156,definition,
( spl2_19
<=> sP0($true) ),
introduced(definition,[new_symbols(definition,[spl2_19])],[avatar_definition]) ).
tff(f164,plain,
( spl2_5
| spl2_18
| ~ spl2_19 ),
inference(avatar_split_clause,[],[f43,f156,f153,f95]) ).
tff(f166,plain,
spl2_13,
inference(avatar_split_clause,[],[f29,f127]) ).
tff(f168,plain,
spl2_19,
inference(avatar_split_clause,[],[f31,f156]) ).
tff(f169,plain,
~ spl2_17,
inference(avatar_split_clause,[],[f32,f145]) ).
tff(f170,plain,
( $false
| ~ spl2_14
| spl2_17 ),
inference(forward_subsumption_resolution,[],[f147,f132]) ).
tff(f171,plain,
( ~ spl2_14
| spl2_17 ),
inference(avatar_contradiction_clause,[],[f170]) ).
tff(f172,plain,
( $false
| ~ spl2_13
| ~ spl2_18 ),
inference(backward_subsumption_resolution,[],[f128,f154]) ).
tff(f173,plain,
( ~ spl2_13
| ~ spl2_18 ),
inference(avatar_contradiction_clause,[],[f172]) ).
tff(f221,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( elem(X0,cons(X1,X2))
| eqNat(X0,X1) )
| ~ spl2_9
| ~ spl2_11 ),
inference(forward_subsumption_resolution,[],[f120,f112]) ).
tff(f234,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( eqNat(X0,X2)
| ( union(cons(X0,X1),cons(X2,X3)) = union(X1,cons(X2,X3)) ) )
| ~ spl2_9
| ~ spl2_11 ),
inference(resolution,[],[f60,f221]) ).
tff(f335,plain,
( ! [X0: $i,X1: $i] : ( union(cons(z,X0),cons(z,X1)) = union(X0,cons(z,X1)) )
| ~ spl2_9
| ~ spl2_11 ),
inference(resolution,[],[f234,f69]) ).
tff(f521,plain,
( ! [X0: $i,X1: $i] : ( union(cons(z,X0),cons(z,X1)) = union(X1,cons(z,X0)) )
| ~ spl2_9
| ~ spl2_11 ),
inference(superposition,[],[f335,f62]) ).
tff(f537,plain,
( ! [X0: $i,X1: $i] : ( union(X0,cons(z,X1)) = union(X1,cons(z,X0)) )
| ~ spl2_9
| ~ spl2_11 ),
inference(superposition,[],[f521,f335]) ).
tff(f890,plain,
( ! [X0: $i] : ( cons(z,X0) = union(X0,cons(z,nil)) )
| ~ spl2_9
| ~ spl2_11 ),
inference(superposition,[],[f537,f59]) ).
tff(f988,plain,
( ! [X0: $i] : ( union(X0,cons(z,nil)) = cons(z,cons(z,X0)) )
| ~ spl2_9
| ~ spl2_11 ),
inference(superposition,[],[f335,f890]) ).
tff(f997,plain,
( ! [X0: $i] : ( cons(z,X0) = cons(z,cons(z,X0)) )
| ~ spl2_9
| ~ spl2_11 ),
inference(forward_demodulation,[],[f988,f890]) ).
tff(f1179,plain,
( ! [X0: $i] : ( cons(z,X0) = tail(cons(z,X0)) )
| ~ spl2_9
| ~ spl2_11 ),
inference(superposition,[],[f25,f997]) ).
tff(f1203,plain,
( ! [X0: $i] : ( cons(z,X0) = X0 )
| ~ spl2_9
| ~ spl2_11 ),
inference(forward_demodulation,[],[f1179,f25]) ).
tff(f1214,plain,
( ! [X0: $i] : ( nil != X0 )
| ~ spl2_9
| ~ spl2_11 ),
inference(superposition,[],[f26,f1203]) ).
tff(f1297,plain,
( $false
| ~ spl2_9
| ~ spl2_11 ),
inference(equality_resolution,[],[f1214]) ).
tff(f1298,plain,
( ~ spl2_9
| ~ spl2_11 ),
inference(avatar_contradiction_clause,[],[f1297]) ).
cnf(s5,plain,
( ~ spl2_1
| spl2_9 ),
inference(sat_conversion,[],[f113]) ).
cnf(s7,plain,
( ~ spl2_5
| spl2_11 ),
inference(sat_conversion,[],[f121]) ).
cnf(s9,plain,
( spl2_1
| ~ spl2_13
| spl2_14 ),
inference(sat_conversion,[],[f133]) ).
cnf(s19,plain,
( spl2_5
| spl2_18
| ~ spl2_19 ),
inference(sat_conversion,[],[f164]) ).
cnf(s21,plain,
spl2_13,
inference(sat_conversion,[],[f166]) ).
cnf(s23,plain,
spl2_19,
inference(sat_conversion,[],[f168]) ).
cnf(s24,plain,
~ spl2_17,
inference(sat_conversion,[],[f169]) ).
cnf(s25,plain,
( ~ spl2_14
| spl2_17 ),
inference(sat_conversion,[],[f171]) ).
cnf(s26,plain,
( ~ spl2_13
| ~ spl2_18 ),
inference(sat_conversion,[],[f173]) ).
cnf(s49,plain,
( ~ spl2_9
| ~ spl2_11 ),
inference(sat_conversion,[],[f1298]) ).
cnf(s50,plain,
~ spl2_14,
inference(rat,[],[s25,s24]) ).
cnf(s51,plain,
~ spl2_18,
inference(rat,[],[s26,s21]) ).
cnf(s53,plain,
spl2_5,
inference(rat,[],[s19,s23,s51]) ).
cnf(s55,plain,
spl2_1,
inference(rat,[],[s9,s50,s21]) ).
cnf(s56,plain,
spl2_11,
inference(rat,[],[s7,s53]) ).
cnf(s57,plain,
~ spl2_9,
inference(rat,[],[s49,s56]) ).
cnf(s58,plain,
$false,
inference(rat,[],[s5,s57,s55]) ).
tff(f1299,plain,
$false,
inference(avatar_sat_refutation,[],[s58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX228_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n009.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 15:13:30 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.31 % (3138248)Will run a generic schedule for satisfiability detection.
% 0.22/0.31 % (3138259)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1376286789:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.31 % (3138254)% WARNING: option uhcvi not known.
% 0.22/0.31 % (3138257)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1517289795:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.31 % (3138253)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3066077388_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.31 % (3138254)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3960465707:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.31 % (3138256)dis+10_1_sil=32000:sp=arity:random_seed=378081825:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.31 % (3138255)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=291203997:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.31 % (3138258)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3586567892:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.31 % Detected minimum model sizes of [1,1]
% 0.22/0.31 % Detected maximum model sizes of [max,2]
% 0.22/0.31 % TRYING [1,1]
% 0.22/0.31 % TRYING [1,2]
% 0.22/0.31 % TRYING [2,2]
% 0.22/0.31 % TRYING [3,2]
% 0.22/0.31 % TRYING [4,2]
% 0.22/0.31 % TRYING [5,2]
% 0.22/0.31 % TRYING [6,2]
% 0.22/0.31 % (3138254) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3138248-3138254"...
% 0.22/0.31 % (3138254)...printing done.
% 0.22/0.31 % (3138254)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (3138254)------------------------------
% 0.22/0.31 % (3138254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3138254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3138254)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3138254)Termination reason: Refutation
% 0.22/0.31 % (3138254)Time elapsed: 0.037 s
% 0.22/0.31 % (3138254)Peak memory usage: 13 MB
% 0.22/0.31 % (3138254)Instructions burned: 64 (million)
% 0.22/0.31 % (3138248)Success in time 0.075 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------