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Vampire---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : SWX102_1 : TPTP v9.3.1. Released v9.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% 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 01:45:53 PM UTC 2026

% Result   : Theorem 0.19s 1.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   13 (   6 unt;   0 typ;   0 def)
%            Number of atoms       :   46 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :   52 (  19   ~;  18   |;  13   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  131 (  30 atm;  40 fun;  45 num;  16 var)
%            Number of types       :    4 (   2 usr;   1 ari;   0 dat;   0 cdt)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  11 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   16 (  14   !;   2   ?;  16   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    general: $tType ).

tff(type_def_6,type,
    symbol: $tType ).

tff(func_def_0,type,
    f__integer__: $int > general ).

tff(func_def_1,type,
    f__symbolic__: symbol > general ).

tff(func_def_2,type,
    c__infimum__: general ).

tff(func_def_3,type,
    c__supremum__: general ).

tff(func_def_4,type,
    a_i: $int ).

tff(func_def_5,type,
    b_i: $int ).

tff(func_def_12,type,
    sK0: general > symbol ).

tff(func_def_13,type,
    sK1: general > $int ).

tff(func_def_14,type,
    '$inst2': $int ).

tff(func_def_26,type,
    '$inst3': $int ).

tff(pred_def_1,type,
    p__is_integer__: general > $o ).

tff(pred_def_2,type,
    p__is_symbolic__: general > $o ).

tff(pred_def_3,type,
    p__less_equal__: ( general * general ) > $o ).

tff(pred_def_4,type,
    p__less__: ( general * general ) > $o ).

tff(pred_def_5,type,
    p__greater_equal__: ( general * general ) > $o ).

tff(pred_def_6,type,
    p__greater__: ( general * general ) > $o ).

tff(pred_def_8,type,
    composite: general > $o ).

tff(pred_def_9,type,
    sqrtb: general > $o ).

tff(pred_def_10,type,
    composite_p: general > $o ).

tff(pred_def_11,type,
    prime: general > $o ).

tff(pred_def_12,type,
    sqrt: ( general * general ) > $o ).

tff(f21,axiom,
    ! [X0: $int,X1: $int] :
      ( ( $lesseq($product(X0,X0),X1)
        & $greatereq(X0,0)
        & $less(X1,$product($sum(X0,1),$sum(X0,1))) )
    <=> sqrt(f__integer__(X0),f__integer__(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_5_unnamed_formula) ).

tff(f23,conjecture,
    ? [X0: $int] : sqrt(f__integer__(X0),f__integer__(0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_7_base_case) ).

tff(f24,negated_conjecture,
    ~ ? [X0: $int] : sqrt(f__integer__(X0),f__integer__(0)),
    inference(negated_conjecture,[status(cth)],[f23]) ).

tff(f31,plain,
    ! [X1: $int,X0: $int] :
      ( ( ~ $less(X1,$product(X0,X0))
        & $less(X1,$product($sum(X0,1),$sum(X0,1)))
        & ~ $less(X0,0) )
    <=> sqrt(f__integer__(X0),f__integer__(X1)) ),
    inference(theory_normalization,[],[f21]) ).

tff(f63,plain,
    ! [X0: $int] : ~ sqrt(f__integer__(X0),f__integer__(0)),
    inference(ennf_transformation,[],[f24]) ).

tff(f82,plain,
    ! [X1: $int,X0: $int] :
      ( ( ( ~ $less(X1,$product(X0,X0))
          & $less(X1,$product($sum(X0,1),$sum(X0,1)))
          & ~ $less(X0,0) )
        | ~ sqrt(f__integer__(X0),f__integer__(X1)) )
      & ( sqrt(f__integer__(X0),f__integer__(X1))
        | $less(X1,$product(X0,X0))
        | ~ $less(X1,$product($sum(X0,1),$sum(X0,1)))
        | $less(X0,0) ) ),
    inference(nnf_transformation,[],[f31]) ).

tff(f83,plain,
    ! [X1: $int,X0: $int] :
      ( ( ( ~ $less(X1,$product(X0,X0))
          & $less(X1,$product($sum(X0,1),$sum(X0,1)))
          & ~ $less(X0,0) )
        | ~ sqrt(f__integer__(X0),f__integer__(X1)) )
      & ( sqrt(f__integer__(X0),f__integer__(X1))
        | $less(X1,$product(X0,X0))
        | ~ $less(X1,$product($sum(X0,1),$sum(X0,1)))
        | $less(X0,0) ) ),
    inference(flattening,[],[f82]) ).

tff(f84,plain,
    ! [X0: $int,X1: $int] :
      ( ( ( ~ $less(X0,$product(X1,X1))
          & $less(X0,$product($sum(X1,1),$sum(X1,1)))
          & ~ $less(X1,0) )
        | ~ sqrt(f__integer__(X1),f__integer__(X0)) )
      & ( sqrt(f__integer__(X1),f__integer__(X0))
        | $less(X0,$product(X1,X1))
        | ~ $less(X0,$product($sum(X1,1),$sum(X1,1)))
        | $less(X1,0) ) ),
    inference(rectify,[],[f83]) ).

tff(f94,plain,
    ! [X0: $int] : ~ sqrt(f__integer__(X0),f__integer__(0)),
    inference(cnf_transformation,[],[f63]) ).

tff(f105,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,$product($sum(X1,1),$sum(X1,1)))
      | $less(X0,$product(X1,X1))
      | sqrt(f__integer__(X1),f__integer__(X0))
      | $less(X1,0) ),
    inference(cnf_transformation,[],[f84]) ).

tff(f1142,plain,
    ( ~ $less(0,$product($sum(0,1),$sum(0,1)))
    | $less(0,$product(0,0))
    | sqrt(f__integer__(0),f__integer__(0))
    | $less(0,0) ),
    inference(instantiation,[],[f105]) ).

tff(f1143,plain,
    sqrt(f__integer__(0),f__integer__(0)),
    inference(interpreted_simplification,[],[f1142]) ).

tff(f1151,plain,
    $false,
    inference(forward_subsumption_resolution,[],[f1143,f94]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SWX102_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.18  % Computer : n009.cluster.edu
% 0.11/0.18  % Model    : x86_64 x86_64
% 0.11/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18  % Memory   : 8046.5625MB
% 0.11/0.18  % OS       : Linux 6.8.0-71-generic
% 0.11/0.18  % CPULimit : 300
% 0.11/0.18  % WCLimit  : 300
% 0.11/0.18  % DateTime : Mon Sep 28 15:01:15 UTC 2026
% 0.11/0.18  % CPUTime  : 
% 0.11/0.18  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21  Running first-order theorem proving
% 0.11/0.21  Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.91/1.30  % (3124799)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.91/1.30  % (3124835)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2217533971:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.91/1.30  % (3124833)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3617085076:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.91/1.30  % (3124831)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1096572155:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.91/1.30  % (3124834)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1157584766:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.91/1.30  % (3124834)Instruction limit reached! 
% 3.91/1.30  % (3124834)------------------------------
% 3.91/1.30  % (3124834)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.30  % (3124834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.30  % (3124834)CaDiCaL version: 2.1.3
% 3.91/1.30  % (3124834)Termination reason: Instruction limit
% 3.91/1.30  % (3124834)Termination phase: Saturation
% 3.91/1.30  % (3124834)Time elapsed: 0.006 s
% 3.91/1.30  % (3124834)Peak memory usage: 88 MB
% 3.91/1.30  % (3124834)Instructions burned: 4 (million)
% 3.91/1.30  % (3124833)Instruction limit reached! 
% 3.91/1.30  % (3124833)------------------------------
% 3.91/1.30  % (3124833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.30  % (3124833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.30  % (3124833)CaDiCaL version: 2.1.3
% 3.91/1.30  % (3124833)Termination reason: Instruction limit
% 3.91/1.30  % (3124833)Termination phase: Saturation
% 3.91/1.30  % (3124833)Time elapsed: 0.008 s
% 3.91/1.30  % (3124833)Peak memory usage: 88 MB
% 3.91/1.30  % (3124833)Instructions burned: 7 (million)
% 3.91/1.30  % (3124835)Instruction limit reached! 
% 3.91/1.30  % (3124835)------------------------------
% 3.91/1.30  % (3124835)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.30  % (3124835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.30  % (3124835)CaDiCaL version: 2.1.3
% 3.91/1.30  % (3124835)Termination reason: Instruction limit
% 3.91/1.30  % (3124835)Termination phase: Saturation
% 3.91/1.30  % (3124835)Time elapsed: 0.056 s
% 3.91/1.30  % (3124835)Peak memory usage: 115 MB
% 3.91/1.30  % (3124835)Instructions burned: 46 (million)
% 3.91/1.30  % (3124836)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3770266958:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.91/1.30  % (3124832)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2743292984:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.91/1.30  % (3124830)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=833239919:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.91/1.30  % (3124830)Instruction limit reached! 
% 3.91/1.30  % (3124830)------------------------------
% 3.91/1.30  % (3124830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.30  % (3124830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.30  % (3124830)CaDiCaL version: 2.1.3
% 3.91/1.30  % (3124830)Termination reason: Instruction limit
% 3.91/1.30  % (3124830)Termination phase: Saturation
% 3.91/1.30  % (3124830)Time elapsed: 0.036 s
% 3.91/1.30  % (3124830)Peak memory usage: 112 MB
% 3.91/1.30  % (3124830)Instructions burned: 12 (million)
% 3.91/1.30  % (3124836)Instruction limit reached! 
% 3.91/1.30  % (3124836)------------------------------
% 3.91/1.30  % (3124836)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.30  % (3124836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.30  % (3124836)CaDiCaL version: 2.1.3
% 3.91/1.30  % (3124836)Termination reason: Instruction limit
% 3.91/1.30  % (3124836)Termination phase: Saturation
% 3.91/1.30  % (3124836)Time elapsed: 0.060 s
% 3.91/1.30  % (3124836)Peak memory usage: 115 MB
% 3.91/1.30  % (3124836)Instructions burned: 33 (million)
% 3.91/1.30  % (3124854)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=2582881273:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 3.91/1.30  % (3124832)First to succeed.
% 3.91/1.30  % (3124832)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3124799"
% 0.19/1.50  % (3124854)Instruction limit reached! 
% 0.19/1.50  % (3124854)------------------------------
% 0.19/1.50  % (3124854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50  % (3124854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50  % (3124854)CaDiCaL version: 2.1.3
% 0.19/1.50  % (3124854)Termination reason: Instruction limit
% 0.19/1.50  % (3124854)Termination phase: Saturation
% 0.19/1.50  % (3124854)Time elapsed: 0.016 s
% 0.19/1.50  % (3124854)Peak memory usage: 89 MB
% 0.19/1.50  % (3124854)Instructions burned: 31 (million)
% 0.19/1.50  % (3124859)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=375875289:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 0.19/1.50  % (3124859)Instruction limit reached! 
% 0.19/1.50  % (3124859)------------------------------
% 0.19/1.50  % (3124859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50  % (3124859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50  % (3124859)CaDiCaL version: 2.1.3
% 0.19/1.50  % (3124859)Termination reason: Instruction limit
% 0.19/1.50  % (3124859)Termination phase: Saturation
% 0.19/1.50  % (3124859)Time elapsed: 0.015 s
% 0.19/1.50  % (3124859)Peak memory usage: 90 MB
% 0.19/1.50  % (3124859)Instructions burned: 16 (million)
% 0.19/1.50  % (3124853)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=4171919898:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 0.19/1.50  % (3124853)Instruction limit reached! 
% 0.19/1.50  % (3124853)------------------------------
% 0.19/1.50  % (3124853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50  % (3124853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50  % (3124853)CaDiCaL version: 2.1.3
% 0.19/1.50  % (3124853)Termination reason: Instruction limit
% 0.19/1.50  % (3124853)Termination phase: Saturation
% 0.19/1.50  % (3124853)Time elapsed: 0.014 s
% 0.19/1.50  % (3124853)Peak memory usage: 88 MB
% 0.19/1.50  % (3124853)Instructions burned: 14 (million)
% 0.19/1.50  % (3124860)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=919207079:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 0.19/1.50  % (3124860)Also succeeded, but the first one will report.
% 0.19/1.50  % (3124863)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=2207497648:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 0.19/1.50  % (3124863)Refutation not found, incomplete strategy
% 0.19/1.50  % (3124863)------------------------------
% 0.19/1.50  % (3124863)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50  % (3124863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50  % (3124863)CaDiCaL version: 2.1.3
% 0.19/1.50  % (3124863)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.50  % (3124863)Time elapsed: 0.004 s
% 0.19/1.50  % (3124863)Peak memory usage: 89 MB
% 0.19/1.50  % (3124863)Instructions burned: 2 (million)
% 0.19/1.50  % (3124869)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=2894560253:i=85:gtgl=4:rtra=on:gtg=exists_sym_2996 on theBenchmark for (2996ds/85Mi)
% 0.19/1.50  % (3124831)Instruction limit reached! 
% 0.19/1.50  % (3124831)------------------------------
% 0.19/1.50  % (3124831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50  % (3124831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50  % (3124831)CaDiCaL version: 2.1.3
% 0.19/1.50  % (3124831)Termination reason: Instruction limit
% 0.19/1.50  % (3124831)Termination phase: Saturation
% 0.19/1.50  % (3124831)Time elapsed: 0.349 s
% 0.19/1.50  % (3124831)Peak memory usage: 117 MB
% 0.19/1.50  % (3124831)Instructions burned: 307 (million)
% 0.19/1.50  % (3124869)Instruction limit reached! 
% 0.19/1.50  % (3124869)------------------------------
% 0.19/1.50  % (3124869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50  % (3124869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50  % (3124869)CaDiCaL version: 2.1.3
% 0.19/1.50  % (3124869)Termination reason: Instruction limit
% 0.19/1.50  % (3124869)Termination phase: Saturation
% 0.19/1.50  % (3124869)Time elapsed: 0.036 s
% 0.19/1.50  % (3124869)Peak memory usage: 88 MB
% 0.19/1.50  % (3124869)Instructions burned: 88 (million)
% 0.19/1.50  % (3124871)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=2829274201:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2996 on theBenchmark for (2996ds/2Mi)
% 0.19/1.50  % (3124874)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=440321185:i=181:rtra=on:ss=axioms:ev=cautious_2995 on theBenchmark for (2995ds/181Mi)
% 0.19/1.50  % (3124871)Instruction limit reached! 
% 0.19/1.50  % (3124871)------------------------------
% 0.19/1.50  % (3124871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50  % (3124871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50  % (3124871)CaDiCaL version: 2.1.3
% 0.19/1.50  % (3124871)Termination reason: Instruction limit
% 0.19/1.50  % (3124871)Termination phase: Saturation
% 0.19/1.50  % (3124871)Time elapsed: 0.003 s
% 0.19/1.50  % (3124871)Peak memory usage: 88 MB
% 0.19/1.50  % (3124871)Instructions burned: 2 (million)
% 0.19/1.50  % (3124886)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=1603844084:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2994 on theBenchmark for (2994ds/66Mi)
% 0.19/1.50  % (3124832)Refutation found. Thanks to Tanya!
% 0.19/1.50  % SZS status Theorem for theBenchmark
% 0.19/1.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.50  % (3124832)------------------------------
% 0.19/1.50  % (3124832)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50  % (3124832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50  % (3124832)CaDiCaL version: 2.1.3
% 0.19/1.50  % (3124832)Termination reason: Refutation
% 0.19/1.50  % (3124832)Time elapsed: 0.140 s
% 0.19/1.50  % (3124832)Peak memory usage: 118 MB
% 0.19/1.50  % (3124832)Instructions burned: 101 (million)
% 0.19/1.50  % (3124832)------------------------------
% 0.19/1.50  % (3124832)------------------------------
% 0.19/1.50  % (3124799)Success in time 0.704 s
% 0.19/1.50  % Vampire exiting
%------------------------------------------------------------------------------