%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM420-1.000 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 12:24:14 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 67 ( 22 unt; 6 def)
% Number of atoms : 131 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 132 ( 68 ~; 58 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] : plus(X0,X1) = plus(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f9,axiom,
! [X0] : plus(n0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f22,axiom,
! [X0,X1] : times(X0,X1) = times(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
fof(f29,axiom,
! [X0] : times(n1,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
fof(f41,axiom,
! [X0] : less(n0,plus(X0,n1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_30) ).
fof(f75,negated_conjecture,
( ~ less(n0,p__0)
| p__0 = plus(s_7(p__0),n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_18) ).
fof(f85,negated_conjecture,
! [X2,X0,X1] :
( ~ less(n0,X0)
| ~ less(n0,p__0)
| ~ less(X0,p__0)
| plus(X0,times(X1,p__0)) != plus(n0,times(X2,p__0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_24) ).
fof(f86,negated_conjecture,
! [X0] : plus(n1,plus(X0,n1)) != n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_25) ).
fof(f87,plain,
! [X0] : n1 != plus(n1,plus(X0,n1)),
inference(reorient_equations,[],[f86]) ).
fof(f101,negated_conjecture,
( ~ less(plus(n0,n1),p__0)
| less(n0,p__0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_34) ).
fof(f103,negated_conjecture,
plus(n0,n1) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_36) ).
fof(f104,plain,
n1 = plus(n0,n1),
inference(reorient_equations,[],[f103]) ).
fof(f116,negated_conjecture,
! [X0] :
( X0 != p__0
| less(n1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_44) ).
fof(f117,plain,
! [X0] :
( p__0 != X0
| less(n1,X0) ),
inference(reorient_equations,[],[f116]) ).
fof(f124,negated_conjecture,
! [X0] :
( X0 = n1
| times(s_1(X0),s_4(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_48) ).
fof(f125,plain,
! [X0] :
( n1 = X0
| times(s_1(X0),s_4(X0)) = X0 ),
inference(reorient_equations,[],[f124]) ).
fof(f134,negated_conjecture,
! [X0] :
( X0 = n1
| s_1(X0) = p__0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_53) ).
fof(f135,plain,
! [X0] :
( p__0 = s_1(X0)
| n1 = X0 ),
inference(reorient_equations,[],[f134]) ).
fof(f143,plain,
( ~ less(n1,p__0)
| less(n0,p__0) ),
inference(forward_demodulation,[],[f101,f104]) ).
fof(f148,definition,
( spl0_2
<=> less(n0,p__0) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f157,definition,
( spl0_4
<=> ! [X2,X0,X1] :
( ~ less(n0,X0)
| plus(X0,times(X1,p__0)) != plus(n0,times(X2,p__0))
| ~ less(X0,p__0) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f158,plain,
( ! [X2,X0,X1] :
( ~ less(n0,X0)
| plus(X0,times(X1,p__0)) != plus(n0,times(X2,p__0))
| ~ less(X0,p__0) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f159,plain,
( ~ spl0_2
| spl0_4 ),
inference(avatar_split_clause,[],[f85,f157,f148]) ).
fof(f169,definition,
( spl0_7
<=> p__0 = plus(s_7(p__0),n1) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f171,plain,
( p__0 = plus(s_7(p__0),n1)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
( spl0_7
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f75,f148,f169]) ).
fof(f182,definition,
( spl0_10
<=> less(n1,p__0) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f183,plain,
( less(n1,p__0)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f184,plain,
( ~ less(n1,p__0)
| spl0_10 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f185,plain,
( spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f143,f182,f148]) ).
fof(f186,plain,
less(n1,p__0),
inference(equality_resolution,[],[f117]) ).
fof(f187,plain,
( $false
| spl0_10 ),
inference(forward_subsumption_resolution,[],[f186,f184]) ).
fof(f188,plain,
spl0_10,
inference(avatar_contradiction_clause,[],[f187]) ).
fof(f189,plain,
( ! [X2,X0,X1] :
( ~ less(n0,X0)
| times(X2,p__0) != plus(X0,times(X1,p__0))
| ~ less(X0,p__0) )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f158,f9]) ).
fof(f191,plain,
( p__0 = plus(n1,s_7(p__0))
| ~ spl0_7 ),
inference(forward_demodulation,[],[f171,f7]) ).
fof(f209,plain,
! [X0] :
( times(p__0,s_4(X0)) = X0
| n1 = X0
| n1 = X0 ),
inference(superposition,[],[f125,f135]) ).
fof(f216,plain,
! [X0] :
( times(p__0,s_4(X0)) = X0
| n1 = X0 ),
inference(duplicate_literal_removal,[],[f209]) ).
fof(f275,definition,
( spl0_14
<=> ! [X0,X1] : times(X0,p__0) != plus(n1,times(X1,p__0)) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f276,plain,
( ! [X0,X1] : times(X0,p__0) != plus(n1,times(X1,p__0))
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f299,definition,
( spl0_19
<=> less(n0,n1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f301,plain,
( less(n0,n1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f377,plain,
( ! [X0] : times(X0,p__0) != plus(n1,p__0)
| ~ spl0_14 ),
inference(superposition,[],[f276,f29]) ).
fof(f390,plain,
less(n0,n1),
inference(superposition,[],[f41,f9]) ).
fof(f391,plain,
spl0_19,
inference(avatar_split_clause,[],[f390,f299]) ).
fof(f393,plain,
( ! [X0,X1] :
( times(X0,p__0) != plus(n1,times(X1,p__0))
| ~ less(n1,p__0) )
| ~ spl0_4
| ~ spl0_19 ),
inference(resolution,[],[f301,f189]) ).
fof(f430,plain,
! [X0] : n1 != plus(n1,plus(n1,X0)),
inference(superposition,[],[f87,f7]) ).
fof(f446,plain,
( n1 != plus(n1,p__0)
| ~ spl0_7 ),
inference(superposition,[],[f430,f191]) ).
fof(f471,plain,
( ! [X0] : plus(n1,p__0) != times(p__0,X0)
| ~ spl0_14 ),
inference(superposition,[],[f377,f22]) ).
fof(f541,plain,
( ! [X0] :
( plus(n1,p__0) != X0
| n1 = X0 )
| ~ spl0_14 ),
inference(superposition,[],[f471,f216]) ).
fof(f586,plain,
( n1 = plus(n1,p__0)
| ~ spl0_14 ),
inference(equality_resolution,[],[f541]) ).
fof(f587,plain,
( $false
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f586,f446]) ).
fof(f588,plain,
( ~ spl0_7
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f587]) ).
fof(f589,plain,
( ! [X0,X1] : times(X0,p__0) != plus(n1,times(X1,p__0))
| ~ spl0_4
| ~ spl0_10
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f393,f183]) ).
fof(f590,plain,
( spl0_14
| ~ spl0_4
| ~ spl0_10
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f589,f299,f182,f157,f275]) ).
cnf(s3,plain,
( ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f159]) ).
cnf(s6,plain,
( ~ spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f172]) ).
cnf(s9,plain,
( spl0_2
| ~ spl0_10 ),
inference(sat_conversion,[],[f185]) ).
cnf(s10,plain,
spl0_10,
inference(sat_conversion,[],[f188]) ).
cnf(s18,plain,
spl0_19,
inference(sat_conversion,[],[f391]) ).
cnf(s20,plain,
( ~ spl0_7
| ~ spl0_14 ),
inference(sat_conversion,[],[f588]) ).
cnf(s21,plain,
( ~ spl0_4
| ~ spl0_10
| spl0_14
| ~ spl0_19 ),
inference(sat_conversion,[],[f590]) ).
cnf(s22,plain,
spl0_2,
inference(rat,[],[s9,s10]) ).
cnf(s25,plain,
spl0_7,
inference(rat,[],[s6,s22]) ).
cnf(s26,plain,
~ spl0_14,
inference(rat,[],[s20,s25]) ).
cnf(s27,plain,
~ spl0_4,
inference(rat,[],[s21,s18,s10,s26]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s3,s27,s22]) ).
fof(f591,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM420-1.000 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 19:48:55 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 0.18/0.47 % (3275010)Will run a generic schedule for satisfiability detection.
% 0.18/0.47 % (3275020)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=401062437:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.47 % (3275016)% WARNING: option uhcvi not known.
% 0.18/0.47 % (3275016)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4162214530:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.47 % (3275015)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2581989875_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.47 % (3275017)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3670078970:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.47 % (3275018)dis+10_1_sil=32000:sp=arity:random_seed=4143490581:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.47 % (3275019)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=425951323:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.47 % (3275021)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=48664947:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.47 % (3275020) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3275010-3275020"...
% 0.18/0.47 % (3275020)...printing done.
% 0.18/0.47 % (3275020)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47 % (3275020)------------------------------
% 0.18/0.47 % (3275020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.47 % (3275020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.47 % (3275020)CaDiCaL version: 2.1.3
% 0.18/0.47 % (3275020)Termination reason: Refutation
% 0.18/0.47 % (3275020)Time elapsed: 0.009 s
% 0.18/0.47 % (3275020)Peak memory usage: 12 MB
% 0.18/0.47 % (3275020)Instructions burned: 22 (million)
% 0.18/0.47 % (3275010)Success in time 0.043 s
% 0.18/0.47 % Vampire exiting
%------------------------------------------------------------------------------