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Vampire---5.0.1.UNS-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : RNG001-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n005.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 12:35:03 PM UTC 2026

% Result   : Unsatisfiable 8.42s 2.24s
% Output   : Refutation 8.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   33 (   8 unt;   0 def)
%            Number of atoms       :   96 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  151 (  88   ~;  63   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :  105 ( 105   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] : sum(additive_identity,X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).

fof(f2,axiom,
    ! [X0] : sum(additive_inverse(X0),X0,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).

fof(f3,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( sum(X0,X4,X5)
      | ~ sum(X1,X3,X4)
      | ~ sum(X2,X3,X5)
      | ~ sum(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).

fof(f4,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( sum(X2,X3,X5)
      | ~ sum(X1,X3,X4)
      | ~ sum(X0,X4,X5)
      | ~ sum(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).

fof(f5,axiom,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).

fof(f6,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( sum(X2,X4,X6)
      | ~ product(X0,X3,X4)
      | ~ sum(X1,X3,X5)
      | ~ product(X0,X5,X6)
      | ~ product(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).

fof(f7,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( product(X0,X5,X6)
      | ~ product(X0,X3,X4)
      | ~ sum(X1,X3,X5)
      | ~ sum(X2,X4,X6)
      | ~ product(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).

fof(f8,negated_conjecture,
    ~ product(a,additive_identity,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).

fof(f9,plain,
    ! [X2,X3,X0,X1] :
      ( ~ product(a,X0,X1)
      | ~ sum(X2,X0,additive_identity)
      | ~ sum(X3,X1,additive_identity)
      | ~ product(a,X2,X3) ),
    inference(resolution,[],[f7,f8]) ).

fof(f10,plain,
    ! [X2,X0,X1] :
      ( ~ product(a,X0,X2)
      | ~ sum(X2,multiply(a,X1),additive_identity)
      | ~ sum(X0,X1,additive_identity) ),
    inference(resolution,[],[f9,f5]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ~ sum(multiply(a,X0),multiply(a,X1),additive_identity)
      | ~ sum(X0,X1,additive_identity) ),
    inference(resolution,[],[f10,f5]) ).

fof(f15,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ sum(X4,X2,multiply(a,X0))
      | ~ sum(X2,multiply(a,X1),X3)
      | ~ sum(X4,X3,additive_identity)
      | ~ sum(X0,X1,additive_identity) ),
    inference(resolution,[],[f12,f4]) ).

fof(f20,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ sum(X7,X6,multiply(a,X4))
      | ~ sum(X3,X2,additive_identity)
      | ~ sum(X4,X1,additive_identity)
      | ~ sum(X5,X6,X0)
      | ~ sum(X0,multiply(a,X1),X2)
      | ~ sum(X3,X5,X7) ),
    inference(resolution,[],[f15,f3]) ).

fof(f59,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ sum(X0,X4,additive_identity)
      | ~ sum(X2,X3,additive_identity)
      | ~ sum(X4,multiply(a,X2),X5)
      | ~ sum(X5,multiply(a,X3),X1)
      | ~ sum(X0,X1,additive_identity) ),
    inference(resolution,[],[f20,f1]) ).

fof(f64,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ sum(additive_inverse(X2),X4,additive_identity)
      | ~ sum(X2,multiply(a,X0),X3)
      | ~ sum(X3,multiply(a,X1),X4)
      | ~ sum(X0,X1,additive_identity) ),
    inference(resolution,[],[f59,f2]) ).

fof(f76,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sum(X1,X3,additive_identity)
      | ~ sum(X2,multiply(a,X3),X0)
      | ~ sum(X0,multiply(a,X1),X2) ),
    inference(resolution,[],[f64,f2]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ~ sum(X0,multiply(a,additive_identity),X1)
      | ~ sum(X1,multiply(a,additive_identity),X0) ),
    inference(resolution,[],[f76,f1]) ).

fof(f85,plain,
    ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity),
    inference(resolution,[],[f80,f1]) ).

fof(f91,plain,
    ! [X2,X0,X1] :
      ( ~ sum(X2,X0,multiply(a,additive_identity))
      | ~ sum(X2,X1,additive_identity)
      | ~ sum(X0,multiply(a,additive_identity),X1) ),
    inference(resolution,[],[f85,f4]) ).

fof(f109,plain,
    ! [X0] :
      ( ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),X0)
      | ~ sum(additive_identity,X0,additive_identity) ),
    inference(resolution,[],[f91,f1]) ).

fof(f113,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ product(X1,X2,multiply(a,additive_identity))
      | ~ sum(additive_identity,X0,additive_identity)
      | ~ sum(X3,X2,X4)
      | ~ product(X1,X4,X0)
      | ~ product(X1,X3,multiply(a,additive_identity)) ),
    inference(resolution,[],[f109,f6]) ).

fof(f904,plain,
    ! [X2,X0,X1] :
      ( ~ product(a,X1,multiply(a,additive_identity))
      | ~ sum(X1,additive_identity,X2)
      | ~ product(a,X2,X0)
      | ~ sum(additive_identity,X0,additive_identity) ),
    inference(resolution,[],[f113,f5]) ).

fof(f906,plain,
    ! [X0,X1] :
      ( ~ product(a,X0,X1)
      | ~ sum(additive_identity,additive_identity,X0)
      | ~ sum(additive_identity,X1,additive_identity) ),
    inference(resolution,[],[f904,f5]) ).

fof(f908,plain,
    ! [X0] :
      ( ~ sum(additive_identity,multiply(a,X0),additive_identity)
      | ~ sum(additive_identity,additive_identity,X0) ),
    inference(resolution,[],[f906,f5]) ).

fof(f911,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sum(additive_identity,additive_identity,X0)
      | ~ sum(X1,multiply(a,X0),X2)
      | ~ sum(X3,X2,additive_identity)
      | ~ sum(X3,X1,additive_identity) ),
    inference(resolution,[],[f908,f4]) ).

fof(f913,plain,
    ! [X2,X0,X1] :
      ( ~ sum(X2,X1,additive_identity)
      | ~ sum(X0,multiply(a,additive_identity),X1)
      | ~ sum(X2,X0,additive_identity) ),
    inference(resolution,[],[f911,f1]) ).

fof(f918,plain,
    ! [X0,X1] :
      ( ~ sum(additive_inverse(X1),X0,additive_identity)
      | ~ sum(X0,multiply(a,additive_identity),X1) ),
    inference(resolution,[],[f913,f2]) ).

fof(f929,plain,
    ! [X0] : ~ sum(X0,multiply(a,additive_identity),X0),
    inference(resolution,[],[f918,f2]) ).

fof(f933,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ product(X0,X1,multiply(a,additive_identity))
      | ~ sum(X2,X1,X3)
      | ~ product(X0,X3,X4)
      | ~ product(X0,X2,X4) ),
    inference(resolution,[],[f929,f6]) ).

fof(f1306,plain,
    ! [X2,X0,X1] :
      ( ~ product(a,X1,X2)
      | ~ sum(X0,additive_identity,X1)
      | ~ product(a,X0,X2) ),
    inference(resolution,[],[f933,f5]) ).

fof(f1308,plain,
    ! [X0,X1] :
      ( ~ product(a,X0,multiply(a,X1))
      | ~ sum(X0,additive_identity,X1) ),
    inference(resolution,[],[f1306,f5]) ).

fof(f1310,plain,
    ! [X0] : ~ sum(X0,additive_identity,X0),
    inference(resolution,[],[f1308,f5]) ).

fof(f1312,plain,
    $false,
    inference(resolution,[],[f1310,f1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : RNG001-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40  % Computer : n005.cluster.edu
% 0.14/0.40  % Model    : x86_64 x86_64
% 0.14/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40  % Memory   : 8046.5625MB
% 0.14/0.40  % OS       : Linux 6.8.0-71-generic
% 0.14/0.40  % CPULimit : 300
% 0.14/0.40  % WCLimit  : 300
% 0.14/0.40  % DateTime : Sun Sep 27 22:57:32 UTC 2026
% 0.14/0.40  % CPUTime  : 
% 0.14/0.40  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.44  Running first-order theorem proving
% 0.14/0.44  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
% 6.06/1.99  % (275148)Input is clausal, will run a generic CNF schedule.
% 6.06/1.99  % (275258)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1187493103:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.06/1.99  % (275258)Instruction limit reached! 
% 6.06/1.99  % (275258)------------------------------
% 6.06/1.99  % (275258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.06/1.99  % (275258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.99  % (275258)CaDiCaL version: 2.1.3
% 6.06/1.99  % (275258)Termination reason: Instruction limit
% 6.06/1.99  % (275258)Termination phase: Saturation
% 6.06/1.99  % (275258)Time elapsed: 0.028 s
% 6.06/1.99  % (275258)Peak memory usage: 87 MB
% 6.06/1.99  % (275258)Instructions burned: 116 (million)
% 6.06/1.99  % (275256)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1070606182:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.06/1.99  % (275254)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2654460895:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.06/1.99  % (275257)lrs+10_1_sil=8000:sp=occurrence:random_seed=2504500599:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.06/1.99  % (275259)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=255079099:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.06/1.99  % (275255)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3107972700:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.06/1.99  % (275260)dis-21_1_sil=8000:lcm=predicate:random_seed=3459338110:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 6.06/1.99  % (275260)Instruction limit reached! 
% 6.06/1.99  % (275260)------------------------------
% 6.06/1.99  % (275260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.06/1.99  % (275260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.99  % (275260)CaDiCaL version: 2.1.3
% 6.06/1.99  % (275260)Termination reason: Instruction limit
% 6.06/1.99  % (275260)Termination phase: Saturation
% 6.06/1.99  % (275260)Time elapsed: 0.061 s
% 6.06/1.99  % (275260)Peak memory usage: 88 MB
% 6.06/1.99  % (275260)Instructions burned: 117 (million)
% 6.06/1.99  % (275257)Instruction limit reached! 
% 6.06/1.99  % (275257)------------------------------
% 6.06/1.99  % (275257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.06/1.99  % (275257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.99  % (275257)CaDiCaL version: 2.1.3
% 6.06/1.99  % (275257)Termination reason: Instruction limit
% 6.06/1.99  % (275257)Termination phase: Saturation
% 6.06/1.99  % (275257)Time elapsed: 0.071 s
% 6.06/1.99  % (275257)Peak memory usage: 87 MB
% 6.06/1.99  % (275257)Instructions burned: 108 (million)
% 6.06/1.99  % (275262)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=575565752:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 6.06/1.99  % (275262)Refutation not found, incomplete strategy
% 6.06/1.99  % (275262)------------------------------
% 6.06/1.99  % (275262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.06/1.99  % (275262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.99  % (275262)CaDiCaL version: 2.1.3
% 6.06/1.99  % (275262)Termination reason: Refutation not found, incomplete strategy
% 6.06/1.99  % (275262)Time elapsed: 0.0000 s
% 6.06/1.99  % (275262)Peak memory usage: 87 MB
% 6.06/1.99  % (275259)Instruction limit reached! 
% 6.06/1.99  % (275259)------------------------------
% 6.06/1.99  % (275259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.06/1.99  % (275259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.99  % (275259)CaDiCaL version: 2.1.3
% 6.06/1.99  % (275259)Termination reason: Instruction limit
% 6.06/1.99  % (275259)Termination phase: Saturation
% 6.06/1.99  % (275259)Time elapsed: 0.117 s
% 6.06/1.99  % (275259)Peak memory usage: 88 MB
% 6.06/1.99  % (275259)Instructions burned: 181 (million)
% 6.06/1.99  % (275273)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1421550979:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 8.42/2.24  % (275274)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=956628885:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 8.42/2.24  % (275287)lrs+10_64_to=lpo:sil=8000:random_seed=3403293688:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 8.42/2.24  % (275262)------------------------------
% 8.42/2.24  % (275262)------------------------------
% 8.42/2.24  % (275273)Instruction limit reached! 
% 8.42/2.24  % (275273)------------------------------
% 8.42/2.24  % (275273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.42/2.24  % (275273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/2.24  % (275273)CaDiCaL version: 2.1.3
% 8.42/2.24  % (275273)Termination reason: Instruction limit
% 8.42/2.24  % (275273)Termination phase: Saturation
% 8.42/2.24  % (275273)Time elapsed: 0.170 s
% 8.42/2.24  % (275273)Peak memory usage: 88 MB
% 8.42/2.24  % (275273)Instructions burned: 189 (million)
% 8.42/2.24  % (275287)Instruction limit reached! 
% 8.42/2.24  % (275287)------------------------------
% 8.42/2.24  % (275287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.42/2.24  % (275287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/2.24  % (275287)CaDiCaL version: 2.1.3
% 8.42/2.24  % (275287)Termination reason: Instruction limit
% 8.42/2.24  % (275287)Termination phase: Saturation
% 8.42/2.24  % (275287)Time elapsed: 0.116 s
% 8.42/2.24  % (275287)Peak memory usage: 87 MB
% 8.42/2.24  % (275287)Instructions burned: 127 (million)
% 8.42/2.24  % (275274)Instruction limit reached! 
% 8.42/2.24  % (275274)------------------------------
% 8.42/2.24  % (275274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.42/2.24  % (275274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/2.24  % (275274)CaDiCaL version: 2.1.3
% 8.42/2.24  % (275274)Termination reason: Instruction limit
% 8.42/2.24  % (275274)Termination phase: Saturation
% 8.42/2.24  % (275274)Time elapsed: 0.194 s
% 8.42/2.24  % (275274)Peak memory usage: 89 MB
% 8.42/2.24  % (275274)Instructions burned: 220 (million)
% 8.42/2.24  % (275311)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3462164667:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 8.42/2.24  % (275311)First to succeed.
% 8.42/2.24  % (275311)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-275148"
% 8.42/2.24  % (275314)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1218435709:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 8.42/2.24  % (275316)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2668044066:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 8.42/2.24  % (275318)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=2526847256:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 8.42/2.24  % (275318)Also succeeded, but the first one will report.
% 8.42/2.24  % (275314)Instruction limit reached! 
% 8.42/2.24  % (275314)------------------------------
% 8.42/2.24  % (275314)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.42/2.24  % (275314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/2.24  % (275314)CaDiCaL version: 2.1.3
% 8.42/2.24  % (275314)Termination reason: Instruction limit
% 8.42/2.24  % (275314)Termination phase: Saturation
% 8.42/2.24  % (275314)Time elapsed: 0.161 s
% 8.42/2.24  % (275314)Peak memory usage: 89 MB
% 8.42/2.24  % (275314)Instructions burned: 157 (million)
% 8.42/2.24  % (275311)Refutation found. Thanks to Tanya!
% 8.42/2.24  % SZS status Unsatisfiable for theBenchmark
% 8.42/2.24  % SZS output start Proof for theBenchmark
% See solution above
% 8.42/2.24  % (275311)------------------------------
% 8.42/2.24  % (275311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.42/2.24  % (275311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/2.24  % (275311)CaDiCaL version: 2.1.3
% 8.42/2.24  % (275311)Termination reason: Refutation
% 8.42/2.24  % (275311)Time elapsed: 0.090 s
% 8.42/2.24  % (275311)Peak memory usage: 89 MB
% 8.42/2.24  % (275311)Instructions burned: 169 (million)
% 8.42/2.24  % (275311)------------------------------
% 8.42/2.24  % (275311)------------------------------
% 8.42/2.24  % (275148)Success in time 1.109 s
% 8.42/2.24  % Vampire exiting
%------------------------------------------------------------------------------